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What is the relationship between self-efficacy of community college mathematics faculty and effective instructional practice?

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What is the relationship between self-efficacy of community college mathematics faculty and effective instructional practice?

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WHAT IS THE RELATIONSHIP BETWEEN SELF-EFFICACY OF
COMMUNITY COLLEGE MATHEMATICS FACULTY AND EFFECTIVE
INSTRUCTIONAL PRACTICE?

by
Oghwa Ladner

A Dissertation Presented to the
FACULTY OF THE ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirement for the Degree
DOCTOR OF EDUCATION

May 2008

Copyright 2008 Oghwa Ladner

Dedication
Christ Jesus, the original efficacy theorist and practitioner, for he has instilled the
efficacy that I can do all things through Him who strengthens me.

Bong Jae Yim and Chun Ja Pak for their parenting skills of love, resourcefulness,
and creativity.

Joong Hwan Yim, Dong Hwan Yim, and Moon Hwan Yim, for their presence in my
life as my younger brothers.

Sun Ja Pak, an aunt, who was the first generation college student who planted the
seeds for my curiosity and the desire for higher education.

Yoon Hee Pak and In Young Jung, who constantly supported the family members
to raise the collective efficacy by sharing their resources.

Barry J. Ladner, the one who introduced me to have faith, hope, and
Compassion through Christ, loved me for who I am, and lived the life to
appreciate the beauty of learning and teaching as he completed the Ph. D.
journey.

Jeremiah, Nehemiah, and Gabrielle Ladner, their spouses, and their children to
live a purpose driven life to transform the human society from being good to great.

ii

Acknowledgements
The completion of this manuscript is possible due to many people’s
contributions in my learning journey as a doctoral student at the University of
Southern California. First of all, I want to thank Dr. Dennis Hocevar. His guidance
as the Chair for my dissertation has been invaluable. Without his intervention, I
may not have finished this dissertation. He believed in me and that this study
would generate a meaningful contribution to the scholarly community. His
continuous support has raised my efficacy and revitalized my efficacy force
knowing that conducting a mixed method research is a comprehensible and
meaningful experience. During the quantitative data analysis, his input has made
the SPSS data interpretation to be meaningful and manageable. He made all the
difference in my third year of dissertation research learning journey as I persisted
through as a researcher and practitioner.
In addition, I thank my committee members, Dr. Stowe and Dr. Gothold.
Dr. Kathy Stowe provided critical support for finding the Chair and steadfastly
supported me by serving on the committee. Also, Dr. Stuart Gothold served as a
committee member and helped me to experience transformational leadership
through the Ed. D. journey at the University of Southern California.
I appreciate the community college mathematics faculty who participated in
my study by completing the surveys and the institutional researchers, deans, and
department chairs. I am especially thankful to the faculty who gave me permission
to interview and observe them for their humility, honesty, and courage to be
evaluated by an outsider.
During the struggling and difficult days of integrating theory and practice,
the inscription on my book by Dr. Albert Bandura, “May the efficacy force be with
iii

you” reminded me to exercise the four building blocks of the efficacy force
continually.
My adult children, Nehemiah James Ladner, Gabrielle Sungkyung Ladner,
and Jeremiah James Ladner, inspired me for the desire to seek effective
instructional practice. I thank them for their understanding and patience by
tolerating this learning driven mother, overcoming the loss of their father, allowing
to downsize and minimize the family time in order for me to continually work on my
dissertation, and praying and believing in me that I could bring this learning
process to a successful closure.
Lastly, I deeply appreciate my guiding friend, Ralph Robson, for lending his
shoulders to me during the most difficult and critical time of the Ed. D. journey with
his words of encouragement and acts of kindness when making a choice to leave
a previous Chair to write this dissertation independently. His counsel of wisdom
and understanding generated objectivity to keep my eyes on the goal of
completing the course. His empathy created a capacity in me to analyze and be
critical of my choices, reflect, and regroup in order to get back on the course of
fighting to complete the journey. His critical feedback with prayers of compassion
for my writing has been invaluable.
This dissertation is possible because I have been blessed with many
special people in my life. Making active choices, applying mental effort, and
persistently learning, I have grown to appreciate the rigor and the beauty of
infusing theory and practice that has been the hallmark of my educational
experiences at USC.

iv

Table of Contents
Dedication ii
Acknowledgements iii
List of Tables vi
List of Figures vii
Abstract viii
Chapter One: Introduction 1
Introduction of the researcher
Statement of the Problem 2
Significance of the Study 3
Conceptual Framework through Gap Analysis 15

Chapter Two: Literature Review 40
Knowledge Economy 41
Teacher Self-efficacy 54
Community College Mathematics Faculty 82
Effective Instructional Practice 101

Chapter Three: Methodology 141
A Description of the Research Design 142
Methods and Procedures for the Prospective Study 148
Data Analysis Procedures 149
The Population and Sampling Procedures 154

Chapter Four: Results 162
Data Analysis of Surveys 168
Reliability Analysis 182
Correlations 184
Interviews and Observations 197

Chapter Five: Findings and Conclusion 221
Recommendations for Further Research 228
Limitations 229
Implications and Interpretations 231
Discussion, Conclusion, and Recommendations 242

References 271

Appendices 299

v

List of Tables
Table 1: Student Headcount by Ethnicity 47
Table 2: Student Headcount by Age Group 47
Table 3: Student Headcount by Gender 47
Table 4: Five Phases of Direct Instruction 112
Table 5: The Taxonomy of Knowledge and Cognitive Dimensions 115
Table 6: Nine Research-based Instructional Strategies 122
Table 7: Six Types of Tasks to Generate and Test Hypotheses 130
Table 8: Eight Components of the SIOP Model 134
Table 9: Frequency Distribution of Eleven Constructs 169
Table 10: Reliability Analysis Scale 183

Table 11: Pearson Coefficient Correlation and strength of Scale Values 185

Table 12: Correlations of Self-efficacy Constructs 185
Table 13: Correlations of Ability and Effectiveness of AMATYC’s 187
Three Strands and Marzano’s Instructional Strategies

Table 14: Correlations of Constructs between Self-efficacy 190
and Others

Table 15: Mean and Standard Deviation Scores between 194
Self-efficacy and Marzano’s Instructional Strategies

Table 16: Correlations of Constructs between Self-efficacy 196
and Marzano’s Instructional Strategies

Table 17: Interview Responses from Six Community College 200
Mathematics Faculty

Table 18: Key for Instructional Approaches Scale 208
Table 19: Key for Self-efficacy Scale 208
Table 20: Observations of Six Mathematics Faculty 209

vi

List of Figures
Figure 1: Significance of This Study 14
Figure 2: Hemorrhaging Educational Pipeline of California 49
Figure 3: Shortage of College-Educated Workers 52
Figure 4: Effective Community College Mathematics Instruction 110
Figure 5: Five Types of Student Engagement 119
Figure 6: Classroom Management That Works 137
(Marzano et al., 2003)

Figure 7: Assessment Items (Marzano et al., 2003) 139
Figure 8: Classroom Management Histogram 172
Figure 9: Instructional Strategy Histogram 173
Figure 10: Student Engagement Histogram 174
Figure 11: Intellectual Development Ability Histogram 176
Figure 12: Intellectual Development Effectiveness Histogram 177
Figure 13: Pedagogy Ability Histogram 178
Figure 14: Pedagogy Effectiveness Histogram 178
Figure 15: Content Ability Histogram 179
Figure 16: Content Effectiveness Histogram 180
Figure 17: Marzano Ability Histogram 181
Figure 18: Marzano Effectiveness Histogram 181
Figure 19: Integrating Self-efficacy and Effective Instructional 250
Strategies through the Components of Gap Analysis:
Knowledge/Skills, Motivation, and Organizational
Barriers

vii

Abstract
This study, What Is the Relationship between Community College
Mathematics Faculty and Effective Instructional Practice, stems from the
research that teachers’ self-efficacy has proved to be significantly related to
teachers’ success that impacts student learning. Researchers note that the
most important factor affecting a student‘s learning is the teacher. The
teacher’s beliefs about self-efficacy shape their instructional practice.
Data collection for this research consists of a mixed method of
quantitative data that include three surveys and the qualitative data of
interviews and observations. Out of 277 delivered surveys, 50 mathematics
faculty responded. Using SPSS software, the results of the quantitative
data reveal that teachers perceive themselves to be highly efficacious. The
qualitative data from interviews support the quantitative data; however, a
discrepancy is found from the observation data of the six teachers. The
instructor’s actual instructional practice tends to be less efficacious or less
effective than their self-reporting perception of efficaciousness in
instructional effectiveness.
When analyzing the efficacy and effectiveness levels of the six
community college mathematics teachers, the range of efficaciousness
varies from “moderately efficacious to slightly efficacious” and the
effectiveness also ranges from “very effective and moderately effective” to
“slightly effective and not effective.” Two teachers who are “slightly
effective and not effective” do not possess a K-12 teaching background.
viii

ix
These two instructors’ ineffective teaching cannot be attributed solely to a
lack of K-12 teaching experience. However, the lack of training in
pedagogical knowledge and skills is an indicator that points out the
importance of faculty’s need for professional development.
As a result of this research, a definition of effective instruction is as
follows. Effective instruction is the outcome of the input of pedagogy that
engages student learning. The objective of this pedagogy is the mastery of
content knowledge to increase student intellectual development by
cognitively engaging the student with various types of knowledge
dimension, direct instruction, and research-based strategies with the gravity
force of classroom management in a caring learning environment. Effective
teaching requires highly efficacious teachers who are motivated. Effective
instruction and teacher efficacy are highly correlated by reciprocity of input
and output.

1
Chapter One
Introduction
“Kids find themselves sitting on the threatening boundaries of the
classroom. Marginal. Designated as “slow learners” or “remedial” or,
eventually, vocational (Rose, 1989, p. 8).”

This dissertation stems from my personal experience as a South
Korean who immigrated to America at age 24. I began my higher education
as a full time student at a community college in California while raising three
young children. I was motivated to acquire a vocational Early Childhood
certificate at a community college in order to operate a home day care
center. Eventually, after receiving the certificate, I enrolled in basic skills
classes as a second language learner after taking the placement tests. I
took all the basic skills Mathematics and English classes as I pursued an
associate’s degree. Since then, today, twenty-five years later, I realize that
I was a remedial and developmental student, who learned slowly with a
simple desire for a better future. As an adult English language learner who
felt the threatening boundaries of the classroom, often was marginalized
due to lack of communication skills in English, and was designated to stay
in remedial classes, I overcame the odds of not being matriculated into a
four year university. As years went by and as a result of my learning
experiences in higher education, I became a public school teacher in
California in 1996. Reflecting on my educational journey, I realize the
community college provided the foundational skills while establishing the

2
bedrock of my American dream for serving my community as a public
school educator in teaching mathematics. Through my example and others
like me, education provided tools to regulate my learning and teach my
children, students, and teachers. As the result of this process, I function as
a reflective practitioner who inquires and shares knowledge and skills to
refine and to improve mathematics pedagogy in K-16.
I. Why Research the Relationship between Self-efficacy and
Instructional Practice?
Statement of the Problem
The research question, What Is the Relationship between Self-
efficacy of Community College Mathematics Faculty and Effective
Instructional Practice?, stems from the importance of instructional practice
and student learning. This dissertation explores the factors that are
associated with self-efficacy of community college instructors. According to
researchers, the self-efficacy of teachers (Hoy, Tarter, & Woolfolk Hoy,
2006; Pajares & Urdan, 2006; Pintrich & Maher, 2004; Shaw, 2004;
Goddard, Hoy, & Woolfolk Hoy, 2004; Bandura, 2002; Pajares, 2002;
Tschannen-Moran & Hoy, 2001; Moore & Esselman, 1994; Schunk, 1989;
Ashton& Webb, 1986) is an important variable in student achievement and
teachers are significantly important in student learning (Schwartzer &
Schmitz, 2000; Marzano, 2006; Marzano, Pickering, Pollock, 2001).
Teachers’ self-efficacy has been proved to be significantly related to
teachers’ success (Armor et al, 1976) which directly impacts student

3
learning (Hoy, Tarter, & Woolfolk Hoy, 2006). Researchers (Marzano,
Marzano, & Pickering, 2003; Wright, Horn, & Sanders, 1997) note that the
most important factors affecting student learning is the teacher. Also,
researchers find that teachers’ beliefs shape their instructional practices
(Bustillos, 2006; Nathan & Koedinger, 2000; Parrott, 2001; Schoenfeld,
1998; Shulman, 1986). In addition, the relationship between teachers’
mathematical beliefs and student performance (Chen, 2005), teachers’
belief systems and their psychological type preferences and practices
(Cetinkaya, 2006), and teachers’ beliefs shape the patterns of practice in
mathematics (Cesario, 2006). Realizing the beliefs of teachers is a force
that shapes their instructional practice, I am curious as to how their beliefs
relate to community college mathematics instructional practice and their
self-perceptions of efficaciousness in delivering mathematics instruction.
Significance of the Study
The significance of the study is multifold. First, this study about the
self-efficacy of community mathematics faculty and their effective
instructional practice is critically important because community college
mathematics faculty function as mediators to promote student learning; at
the same time, they are gatekeepers of students’ success through teaching.
The mathematics faculty’s role is crucially important because they pave
pathways creating hope in finding right careers for adult students of color,
English learners, low income, special education students, as well as English
only students. As the faculty members instill and impart basic and

4
advanced skills in mathematical knowledge, the faculty’s role becomes
even more crucial for students who lack basic skills. The education of
remedial students is one of the most important educational problems in
America (Ehrlich, 2000) because solutions that remedy students’ deficient
basic skills in mathematics could alleviate our most serious social and
economic problems. One of the social and economic problems is the result
of the changing knowledge economy of this nation.
Although the transformation of the U. S. economy from an
agricultural to a manufacturing to a service economy over the past 200
years has led to higher standards of living, America faces two worries.
These worries are the result of job losses due to off-shoring of substituting
foreign for domestic labor and the lack of a skilled labor force to fill the new
jobs that will be created (Dellow & Romano, 2006). Dellow and Romano
(2006) assert,
It seems clear workers will require higher level math and
science skills, more creative thinking, and a greater ability to
interact with workers in other countries if they are to compete
in a global economy. Greater knowledge of other countries,
their cultures, and their languages will be an asset, if not a
requirement. Responding to these competency needs will be
challenging for community college educators (p. 20).

Educating students for the global economy happens in a time when
53% of students are placed in basic skills mathematics while requiring
much remediation (NCPPHE, 2006). The knowledge shortage in basic
skills in mathematics is going to affect negatively the labor force. The U. S.
Department of Labor’s Bureau of Labor Statistics estimates that America’s

5
economy will be short 10 million workers by 2011 (Career Advancement
Management Facts and Trends, 2004; Zeiss, 2006). The serious lack of
skilled workers that began in 2005 will grow to 14 million by 2015. If the
need for unskilled workers is included, the shortage will be 21 million by
2015 (Kaihla, 2003; Zeiss, 2006). In addition, Hargreaves (2003) notes,
“We live in a knowledge economy, a knowledge society. Knowledge
economies are stimulated and driven by creativity and ingenuity.
Knowledge-society schools have to create these qualities; otherwise, their
people and their nations will be left behind (Hargreaves, 2003, p.1).
Hargreaves states that a knowledge society is really a learning society.
Hargreaves (2003) also points out,
Knowledge societies process information and knowledge in
ways that maximize learning, stimulate ingenuity and
invention, and develop the capacity to initiate and cope with
change. In the knowledge economy, wealth and prosperity
depend on people’s capacity to out-invent and outwit their
competitors, to tune in to the desires and demands of the
consumer market, and to change jobs or develop new skills as
economic fluctuations and downturns require. In the
knowledge economy, these capacities are the property not
just of individuals, but also of organizations. They depend on
collective as well as individual intelligence. Knowledge-
society organizations develop these capacities by providing
their members with extensive opportunities for up-skilling and
retraining; by breaking down barriers to learning and
communication and getting people to work in overlapping,
flexible teams; by looking at problems and mistakes as
opportunities for learning more than as occasions for blame;
by involving everyone in the ‘big picture’ of where the
organization is going, and by developing the ‘social capital’ of
networks and relationships that provide people with extra
support and further learning (p. 3).

6
In this knowledge society, teachers create the capacity in students by
equipping them with knowledge and skills. As teachers strive to maximize
student learning, teachers develop lessons that engage all learners.
Knowing the changing demographics of the adult student population,
community college mathematics teachers develop new skills in engaging
adult learners. By depending on the collective faculty intelligence, the
teacher breaks down barriers of the learning gap by gaining pedagogical
skills that benefit all learners. In this process, the mathematics teacher
becomes an inquirer to learn and apply teaching knowledge in teaching to
influence student learning.
Secondly, this study is important because it could improve the
knowledge of the labor force of this nation’s knowledge economy. This can
be achieved by raising community college mathematics teachers’ efficacy
through helping them to master effective instructional strategies in
pedagogical knowledge and skills. Studying the self-efficacy of community
college faculty and instructional practice could directly influence faculty’s
performance in narrowing the gap of student achievement and student
learning difficulties. The learning difficulties are as follows: (1) lack of
graduation and transfer rates from community colleges (Lumina, August
2007; Nora, 2007; Swanson, 2004; COCCC, 2002; CCCCC, 2008; Ward-
Roof, 2004); (2) lack of basic skills in mathematics and under-prepared
students from low K-12 performance (CSS/RP, 2005); (3) lack of students’
mathematical performance that affects the national knowledge economy

7
and global knowledge society that requires changes in mission, curriculum
content, pedagogy and modes of inquiry (O'Hara, 2007); and (4) lack of
students majoring in Science, Technology, Engineering, and Mathematics
(National Academies, 2007). In other words, many of the student learning
problems are the result of the lack of mathematical knowledge among
community college students.
Thirdly, this study is important because mastering instructional
strategies by the mathematics faculty could impact student achievement
positively through effective instruction. In turn, the mastery experience will
raise the faculty’s efficacy. Raising the efficacy of the faculty is more likely
to contribute positively to students’ understanding in mathematics. Student
achievement and student efficacy will have a reciprocal effect on the
faculty’s self-efficacy. In other words, teaching matters, and effective
instruction matters. Effective instruction, not efficient instruction, produces
desired learning (Friedman, Harwell, & Schnepel, 2006). Teaching
significantly matters because it influences the overall function of the nation’s
performance. If there is a positive relationship between the self-efficacy of
community mathematics faculty and their instructional practice, the faculty’s
pedagogical knowledge and skills along with other instructional strategies
can create avenues for the mastery of students’ mathematical content
knowledge. The mastery of students’ mathematical understanding is the
output of the faculty’s input of effective instructional practice of the function
called teaching.

8
A publication by the Research and Planning Group of California
Community Colleges indicates that not all students pass their classes in the
initial attempt. Some classes, like elementary algebra, have a 50% pass
rate, with 50% of the failing or withdrawing students repeating the course.
Given that a total of 25% of the elementary algebra population repeats the
class, success in their following attempts becomes an important issue
(Spurling, 2006). The failure rate of these mathematics classes speaks
loudly that somehow these students are not able to retain the information in
long term memory. They have been exposed to the elementary algebra
from sixth grade. After having been exposed to the concepts again in
grades 7, 8, 9, 10, 11, and 12, they are still struggling to understand the
concepts. Although student motivation to learn and master this content
knowledge is one of the factors that inhibit their mastery, it is imperative that
educators examine closely what they teach, how they teach, and why they
teach the way they teach. Obviously, the data reveal that the current
pedagogical approaches are not producing a result of student mastery in
mathematics
In California, the overall student transfer rate is compounded by
other factors that are described by three reports that utilize three different
approaches to assessing the California Community Colleges. For example,
the Public Policy Institute of California (PPIC) concludes that the community
colleges have a completion rate of 25% for transfer students and 12% for
students earning a certificate/award. The Institute for Higher Education and

9
Leadership Policy (IHELP) that published Rules of the Game notes that the
community colleges have a 24% completion rate of transferring students to
higher education. Also, the publication from the System Office indicates in
its first Accountability Report on the Community Colleges (ARCC) that the
colleges have a 51% achievement rate (RP Group Perspectives, 2007).
There are many inhibiting variables that contribute to the low transfer
rate. Often, this low transfer rate is a result of poor mastery of content
knowledge. This low student performance happens more frequently in
mathematics classes than any other discipline. The outcome of the poor
mastery of content knowledge can be attributed to the inability by students
to retain the concepts that were taught in K-12. These students have
difficulty visualizing, remembering, and understanding basic skills. This
means that they must take basic skills mathematics classes again at a
community college. A problem is that they are more likely to be exposed to
the same type of teaching that is very procedural that does not promote
their conceptual understanding.
To bridge the students’ learning gap, the faculty is a critical element.
Community college mathematics teachers are the crucial factor in the
students’ learning. Stigler and Hiebert (1999) describe in the book, The
Teaching Gap, that Americans focus on the competence of teachers while
decrying the quality of applicants for teaching positions and criticizing the
talent of the current teaching corps. However, Stigler and Hiebert conclude
that although variability in competence is certainly visible in the videos they

10
collected, such differences are dwarfed by the differences in teaching
methods in Germany, Japan, and the United States. Stigler and Hiebert
(1999) find,
What we can see clearly is that American mathematics
teaching is limited, focused for the most part on a very narrow
band of procedural skills. Whether students are in rows
working individually or sitting in groups, whether they have
access to the latest technology or are working only with paper
and pencil, they spend most of their time acquiring isolated
skills through repeated practice. Japanese teaching is
distinguished not so much by the competence of the teachers
as by the images it provides of what it can look like to teach
mathematics in a deeper way, teaching for conceptual
understanding. Students in Japanese classrooms spend as
much time solving challenging problems and discussing
mathematical concepts as they do practicing skills ( pp. 10-
11).

The poor learning can be attributed to teaching methodology. In order to
overcome the poor teaching, teachers need to teach mathematics in a
deeper way to promote conceptual understanding. Teachers are the ones
who have to make that commitment to teach mathematics conceptually as
well as procedurally to promote student mastery in problem solving.
According to Marzano, Pickering, and Pollock (2001), the faculty is the most
important factor in student learning (Marzano, Pickering, & Pollock, 2001).
Teacher characteristics have the most significant impact on achievement
(Friedman, Harwell, & Schnepel, 2006).
The community college faculty members face mounting challenges.
There will be continuing conflict between the demand for short-term
responsive programs and the emerging need for greater global

11
competencies more typical general education that includes languages,
critical and creative thinking, and knowledge of other cultures and countries
(Dellow & Romano, 2006). Dellow and Romano (2006) emphasize,
While some global forces will drive community colleges to
expand their transfer functions, others will require a greater
use of the short-term corporate training model. Can the
colleges do both? The shifting job market will require us to
develop more opportunities for life-long learning and to teach
students how to better engage as self-directed learners.
Maintaining flexibility will require more systematic and
frequent assessment of business and industry needs, and
these assessments will need to include more analysis of
global trends. The traditional method of curriculum
development will not result in viable programs with reasonable
shelf lives unless the process takes into account trends in the
global economy (p. 22).

Fourthly, this study is important because the findings of this research
could inform the educational community on how to integrate theory and
practice in teaching and learning. Findings about the relationship between
teachers’ efficacy and their instructional practice in teaching mathematics
could help educators and researchers to look at scientifically based
instructional strategies. As a researcher, I find that the knowledge
generated from this research could create opportunities for community
college faculty, administrators, and policy makers to positively influence
students’ retention rate, transfer rate to four year institutions, employment
rate, and eventually impact the nation’s economy positively within the global
market by improving the overall mathematics teaching practice.
Matsumoto (2000) finds that research is the primary way in which
scholars and scientists generate knowledge about the world. The author

12
states, “Replicated findings and knowledge form the basis for what we know
as ‘truth’ about the world. It is this truth that is taught to you in school and
conveyed everyday in the classroom (Matsumoto, 2000).” Mathematical
faculty members deliver this knowledge to assist students to define how
mathematics can make sense not only in the classroom, but also in the
context of everyday life applications.
Fifthly, this study is important because it could explain the
relationship between the motivational construct of teacher efficacy and
research based effective strategies of instructional practice. Although
motivational researchers have always emphasized rigorous scientific design
and methods, theory and research in motivation have not been integrated
well into theories of learning and instruction (Boekaerts, 2002). Realizing
this challenge, if there is a positive relationship between mathematics
faculty’s self-efficacy and their instructional practice, this study could
promote various ways for promoting teacher efficacy as a motivational
variable. As a result, this study could encourage other researchers to
research how teacher self-efficacy can contribute to the knowledge base of
mathematics teacher/faculty education. Looking at faculty development
through the lens of instructional practice can have a positive impact upon
students’ mastery of content knowledge and promote matriculation to a four
year learning institution. Student achievement can be improved by raising
mathematics faculty’s efficacy levels by understanding the building blocks
of efficacy and effective instruction.

13
Lastly, this study is important because it explores research-based
instructional strategies as a tool for measuring effective instruction in
relation to the community college mathematics faculty’s efficacy. This may
result in good teachers to become great teachers through effective
instruction. When finding a positive relationship between the self-efficacy of
faculty and instructional practice, it could increase the organizational focus
on the faculty’s professional development. This in turn will fine-tune
instructional practice by seeking ways to improve the faculty’s individual
and collective efficacy. Through professional development, mathematics
faculty can gain effective strategies and practices and implement them in
classrooms that can directly impact the nation’s economy by preparing the
future work force. This mastery and modeling experiences of effective
practices through the professional development will cause faculty self-
efficacy to be raised. The importance of teacher self-efficacy cannot be
overstated when America faces a dire need for an economic labor force that
requires highly educated workers, especially in the areas of mathematics
and science.
In conclusion, the study could contribute by reigniting the faculty’s
passion for teaching because the twenty-first century needs teaching
professionals who are willing to take teaching to higher dimension in order
to prepare the work force for globalization. As a consequence of
globalization, information and communications technologies and the shift to
a knowledge society, new approaches of learning are needed in this

emerging global society (O'Hara, 2007). This requires a paradigm shift in
teaching. This will require teachers/faculty who are bold, courageous,
movers and shakers committed to effective teaching that equip students
with excellent knowledge and skills in problem solving (see figure 1).
Figure 1, The Significance of This Study

1. This study is
important because it
is about community
college mathematics
faculty who function
as mediators for
student learning..
5. This study is
important because it
could explain the
relationship between
the motivational
construct and
instructional practice.
6. This study is
important because it
explores research
based instructional
strategies as a tool for
effective instruction.
2. This study is
important because it
could improve the
knowledge of the
labor force and raise
the efficacy of
faculty.
3. This study is
important because
the faculty’s
efficacy can
influence the mastery
of instructional
strategies.
4. This study is
important because it
could inform the
educational
community about
integrating theory
and practice.

The Significance
of This Study:
What Is the
Relationship between
Community College
Mathematics Faculty
and Instructional
Practice?

The above figure shows that this study is important because community
college mathematics faculties function as mediators for student learning.
This impacts the knowledge of the labor force and at the same time raises
the efficacy of the faculty. The efficacy of faculty can influence their
14

15
mastering of instructional strategies. The relationship between the
motivational construct and instructional practice explore research-based
instructional strategies as a tool for effective instruction.
The community college faculty who educate the most needy students
of diverse backgrounds are the foundation of this nation’s economic, social,
and political stability. Raising academic achievement means providing
opportunities, for young people to pursue their careers that will strengthen
the country’s existence in a swiftly changing twenty-first century global
economy. Empowering faculty’s self-efficacy could create ways for
empowering students to gain mastery of basic skills. Education as an
equalizer might apply to many of our future generations regardless of their
subgroup status: socioeconomic status, ethnicity, race, gender, special
education, or English language learner. Therefore, understanding the
conceptual framework through gap analysis in relation to the faculty’s
knowledge and skills, motivation, and organizational barriers can make a
difference as the challenge of teaching multi-subgroup, diverse learning
needs, and multicultural students increase in America.
II. From Conceptual Framework to the Research Question through
Gap Analysis
The conceptual framework of this research originates from Clark and
Estes’(2002) three factors to analyze performance gaps: knowledge/skills,
motivation, and organization. The three layers of gap-analysis uses a lens
looking at knowledge/skills of teachers’ instructional practice and motivation

16
of teachers’ self-efficacy within community college context. Clark and Estes
(2002) point out that the gaps occur between goals and current
performances. The analysis of gaps includes identifying the knowledge,
motivation, and organizational barriers to their achievement. Clark and
Estes (2002) also recommend to gather information on the three big causes
of knowledge/skills, motivational, and organizational performance gaps.
This information can be collected by interviewing groups and individuals,
looking at work records, and observing work processes. The information
gained at this stage can be used to decide whether additional support is
needed and to identify the types of support required to achieve goals.
Knowledge/Skills, Motivation, and Organizational Barriers
According to Clark and Estes (2002), three critical factors must be
examined during the analysis process. The three factors are as follows:
people’s knowledge/skills, motivation to achieve the goal, and
organizational barriers, such as lack of necessary equipment and missing
or inadequate work processes. The authors state that the purpose of the
individual and team gap analysis is to identify whether all employees have
adequate knowledge, motivation, and organizational support to achieve
important work goals. Clark and Estes point out, “For successful goal
achievement, the researchers emphasize that all three factors must be in
place and aligned with each other (p. 43).” In addition, Clark and Estes
(2002) note,

17
In order to understand why knowledge, motivation, and
organizational factors are important in analyzing gaps, think of
a “people as cars” metaphor. Knowledge is our engine and
transmission system. Motivation is what energizes the system
– fuel and the charge in our batteries. Organizational factors
are the current road conditions that can make it easier or
more difficult to get to your intended destination. All people in
organizations participate in a number of separate but
interacting systems – but the knowledge and motivation
systems are the most vital facilitators or inhibitors of work
performance (pp. 43-44).

In other words, the two critical factors of faculty knowledge and
motivation can create a synergetic affect in teaching which creates
momentum for student learning. The authors also point out that, “These
internal systems must cooperate effectively to handle events that occur in
the organizational environment. A focus on one of the systems or on the
organizational environment alone will only capture part of the cause and,
eventually, provide only part of the solution (p. 44).” Since knowledge and
motivation systems are the most vital facilitators or inhibitors of work
performance (Clark and Estes, 2002), this dissertation focuses on self-
efficacy practiced by faculty as a motivational facilitator or inhibitor. Also,
effective instructional practice is a work performance variable as facilitators
or inhibitors for knowledge/skills. Like wise, mathematics faculty is a work
performance variable because they function as facilitators or inhibitors of
the performance of the organization. Gap analysis by Clark and Estes
indicates an important fact that performance is largely governed by people’s
beliefs about themselves and their environment. Clark and Estes (2002)
note,

18
To redirect performance to new goals or to improve
performance, begin by learning the beliefs and perceptions of
the people doing the work- the people on the front lines. What
do they believe is blocking them or their team from reaching
goals? What kind of support do they believe they need? This
is the type of information that is crucial to uncovering the
causes of performance gaps (p. 45).

Studying faculty’s self-efficacy as a motivational variable is to learn
about their belief-system and perceptions. Self-efficacy is one’s belief
system (Bandura, 1997). This belief system could either narrow or broaden
the gaps in performance. Teachers’ belief-system can be measured by
their sense of efficacy. Researchers (Tschannen-Moran & Hoy, 2001)
believe that teachers’ sense of efficacy has a strong positive link to student
performance.
III. Leading to the Problem
Why Is Mathematics Faculty’s Self-efficacy Important?
Self-efficacy of mathematics teachers is critical because it affects
student learning. Teachers’ sense of efficacy has a strong positive link to
student performance (Tschannen-Moran & Hoy, 2001) and proves to be
significantly related to teachers’ success (Armor et al., 1976). Teachers
high in self-efficacy are found to sacrifice more leisure time for their
students than their less self-efficacious counterparts (Schwarzer & Schmitz,
2000). Marzano (2006) points out that educators have experimented with
such things as changing the schedule, decreasing the student-to-teacher
ratio, increasing the availability and use of technology, and so on. All of
these innovations have merit. However, Marzano (2006) finds that, “not

19
even the best has demonstrated the impact on student achievement of the
most intuitively important variable in the educational system – the
classroom teacher (p. 1).” A teacher’s self-efficacy tends to make a
difference in the curriculum and instruction work of what the classroom
teacher does to impact students’ learning through his/her belief system.
Bandura (1997) defines self-efficacy as an individual’s belief about
her or his capacity to organize and execute the actions required to produce
a given level of attainment. People with high self-efficacy choose to
perform challenging tasks. This could mean that teachers with high self-
efficacy choose rigorous and challenging tasks for instruction. These
teachers are likely to provide opportunities for students to work on
challenging tasks that are not just “drill and kill.” At the same time, they
tend to expect their students to challenge themselves in developing
academic understanding.
Teacher efficacy has proved to be powerfully related to many
meaningful educational outcomes such as teachers’ persistence,
enthusiasm, commitment, and instructional behavior. Also, it has proved to
be related to student outcomes such as achievement, motivation, and self-
efficacy beliefs (Tschannen-Moran & Woolfolk Hoy, 2001). Rotter found,
Teachers who concur that the influence of the environment
overwhelms a teacher’s ability to have an impact on a
student’s learning exhibit a belief that reinforcement of their
teaching efforts lies outside their control or is external to them.
Teachers who express confidence in their ability to teach
difficult or unmotivated students evidence a belief that

20
reinforcement of teaching activities lies within the teacher’s
control or is internal (Rotter, 1966).

In other words, teachers’ belief systems and student learning are
related. Student achievement and sense of efficacy are related (Hoy,
Tarter, and Woolfolk Hoy, 2006). Researchers have found positive
associations between student achievement and three kinds of efficacy
beliefs: self-efficacy beliefs of students (Pajares, 1994, 1997), self-efficacy
beliefs of teachers (Tschannen-Moran, Woolfolk Hoy, & Hoy, 1998), and
teachers’ collective efficacy beliefs about the school (Goddard, Hoy, &
Woolfolk Hoy, 2004).
Teachers’ belief system makes a difference in student achievement
(LaBouff, 1996). Teaching at-risk students can be a labor-intensive
rigorous process. Educating high-risk developmental students is time
consuming and requires a committed staff that provides a safe, nurturing
yet highly structured environment while persisting through the challenges
that occur in a Mathematics classroom. Bustillos states,
Mathematics competency is a precursor to access and
success in college and beyond. Without a solid mathematical
foundation, individuals will not only be prevented from
attaining a baccalaureate degree, but will fail to secure
employment within a knowledge economy (2006, p. 9).

Realizing the importance of the mathematics competency, I believe
that mathematics faculty members are active dream catchers by helping
students to comprehend the subject by instilling a deep content knowledge
that helps them to transfer to a four-year university. On the other hand, the

21
faculty members who are apathetic dream watchers just stand by allowing
students’ dreams to go through the holes of the dream catcher. A faculty
who has a strong belief system to assist students to catch their dreams is
more likely to develop strategies to assist students on how to tighten their
dream catcher to ensure that the dream within their reach is caught.
The Affect of Faculty’s Belief System for Student Learning

The belief system of mathematics faculty can make a difference in
assisting students to understand the content knowledge. To teach
effectively, it requires the teacher to learn and reflect to prepare and
evaluate one’s teaching performance. Learning the skills of pedagogy
takes three motivational tools: active choice, mental effort, and persistence
(Clark & Estes, 2002). Among these three motivational tools, researchers
have validated the effect of believing in the importance of effort (Covington,
1985; Harter, 1980; Marzano, Pickering, & Pollock, 2001). Marzano and his
colleagues (2001) find,
…people generally attribute success at any given task to one
of four causes: ability, effort, other people, and luck. Three of
these four beliefs ultimately inhibit achievement. On the
surface, a belief in ability seems relatively useful – if you
believe you have ability, you can tackle anything. Regardless
of how much ability you think you have, however, there will
inevitably be tasks for which you do not believe you have the
requisite skill…. Belief in effort is clearly the most useful
attribution. If you believe that effort is the most important
factor in achievement, you have a motivational tool that can
apply to any situation (p. 50).

It seems there is an interactive circle between effort as a motivational
tool and one’s belief system. Self-efficacy as a belief system tends to affect

22
the motivation as well. Schunk (1989) finds that self-efficacy beliefs instill
not only greater motivation to learn, but also greater motivation to self-
regulate one’s learning (as cited in Schunk & Zimmerman, 1998). For
example, self-efficacious learners are more likely to set high goals for
themselves, to self-monitor accurately, and to self-react in a positive
manner than learners who lack self-efficacy (Schunk & Zimmerman,1998;
Zimmerman, 1995).
Teachers’ belief systems and pedagogical orientations are related to
teaching mathematics for understanding (LaBouff, 1996). LaBouff’s study
indicates that although all teachers in the study had integrated into their
practice teaching strategies associated with the math reform movement, the
majority of teachers possess little knowledge of expert conceptions of
teaching for understanding. Again, it distinguishes two styles of teaching
between transmission style of teaching from teaching for understanding by
identifying beliefs and practices (1996). Another study reveals that the
factors that influence teachers’ reasoned intentions operate differently in the
traditional and reformed instructional models and experiences gained
through practical application and attitudes work reciprocally to produce
changes in teachers’ belief systems (Carson, 1997).
A cause for the reasoned intentions operating differently is that
current teachers’ learning has been modeled by the traditional learned
behavior which is driven by procedural understanding of problem solving
rather than focusing on conceptual understanding of mathematical problem

23
solving while seeking to integrate real life applications. Mingus (1996)
urges that mathematics educators need to take responsibility to interrupt
the process of teaching as they have been taught and need to lessen the
risk of handing down to future generations of teachers poor attitudes about
mathematics and teaching mathematics. This requires teaching practice
that takes much effort and reflection to impact student learning positively.
Teaching differently from what teachers have been taught requires a
paradigm shift in teachers’ belief system in how to teach mathematics. This
demands active choice, effort, and persistent practice of seeking ideas on
teaching mathematics for understanding in addition to teaching students
how to solve problems procedurally. The integration of conceptual
knowledge of teaching mathematics and procedural knowledge requires a
change in teaching behavior. Often to change the behavior, it requires the
teacher to change the practice.
I believe that the physical, emotional, social, and cultural learning
classroom environment of self-efficacious teachers tend to create a belief
system that they can make a difference in student learning. At the same
time, these teachers strive to engage every student and create a
relationship between the teacher and student. Noting the importance of
each student’s learning is like placing a mark on the student’s heart that
says how important he/she is to the teacher. Teaching with a heart
becomes a critical component in a teacher’s belief system because it is the

24
foundation of the motivational tools of active choice, mental effort, and
persistence.
As the teacher builds this relationship with students while delivering
content knowledge, student learning is more likely to be achieved. I believe
that the fertile ground for content knowledge takes root in the soil of caring
teacher’s pedagogy. This takes a lot of effort from the teacher as an
instructional coach. I find that creating a culture of caring and nurturing
environment by lowering students’ affective filter, the teacher teaches to
increase student content knowledge by creating a structure of academic
knowledge with a tool called instructional strategies. When a student
perceives that the instructor cares enough about him/her and teaches to
increase student comprehension with a variety of approaches, the student
is likely to persist in the learning process by trusting the teacher. This
affects student’s perceived ability that influences their ability to regulate
their learning.
Efficacy beliefs are central mechanisms in humans. Efficacy beliefs
promote the intentional pursuit of a course of action. Individuals and groups
are unlikely to initiate action without a positive sense of efficacy. The
strength of efficacy beliefs affects the choices individuals and schools make
about future plans and actions (Hoy, Tarter, & Woolfolk Hoy, 2006). Self-
efficacy is the perceived ability to succeed at a specific task (Bandura,
1986, 1997, as cited in (Pintrich & Maehr, 2004).

25
A teacher’s belief system influences goal seeking behavior in student
achievement. A teacher who has the intentional goal of improving student
learning is likely to provide feedback on the students’ performance by
actively seeking opportunities to develop lesson plans that promote student
learning. To maximize students’ brain growth (Jensen, 1998), it takes two
components: challenge and feedback. The challenge includes problem
solving, critical thinking, relevant projects, and complex activities while
feedback has to be specific, multi-modal, timely, and learner controlled (p.
33). Jensen (1998) advocates that feedback reduces uncertainty, it
increases coping abilities while lowering the pituitary-adrenal stress
responses. Even in the absence of control, feedback has value (Hennessy,
1977). Again, creating learning situations that are challenging and
providing feedback takes active choice and consistent effort from
mathematics teachers.
When a group of mathematics instructors perceives that their effort
makes a difference in student achievement, it creates a construct called
collective self-efficacy. Goddard, Hoy, and Woolfolk Hoy (2004) share this
finding that perceived collective efficacy in schools represents judgments
about the performance capability of the social system as a whole.
Goddard, Hoy, and Woolfolk Hoy believe that teachers have efficacy beliefs
about themselves as well as the entire faculty. In addition to this, other
researchers find that perceived collective efficacy is the judgment of
teachers that the faculty as a whole can organize and execute the actions

26
required to have positive effects on students (Hoy, Tarter, & Woolkfolk Hoy,
2006). Perceived collective efficacy represents judgments about the
performance capability of the social system as a whole (Bandura, 1997). In
other words, perceived collective efficacy is the judgment of teachers that
the faculty as a whole can organize and execute the actions required to
have positive effects on students (Goddard, Hoy, & Woofolk Hoy, 2004).
In addition to looking at student achievement through the construct
called, collective self-efficacy, researchers have been challenged to go
beyond socioeconomic status in the search for school-level characteristics
that makes a difference in student achievement (Hoy, Tarter, & Woolkfolk
Hoy, 2006). Another finding reveals that self-efficacious teachers tend to
set for themselves higher goals and stick to them:
Actions are pre-shaped in thought, and people anticipate
either optimistic or pessimistic scenarios in line with their level
of self-efficacy. Once an action has been taken, highly self-
efficacious people invest more effort and persist longer than
those low in self-efficacy. When setbacks occur, they recover
more quickly and maintain commitment to their goals. High
self-efficacy also allows people to select challenging settings,
explore their environment, or create new ones (Schwarzer &
Schmitz, 2000).

The last quality that makes a difference in the teachers’ belief system
for student achievement is faculty trust in parents and students. Faculty
trust in parents and students is a collective school property in the same
fashion as collective efficacy and academic emphasis (Hoy, Tarter, &
Woolfolk Hoy, 2006). Tschannen-Moran and Hoy believe that trust is one’s
vulnerability to another in terms of the belief that the other will act in one’s

27
best interests. Trust is a general concept with five facets: benevolence,
reliability, competence, honesty, and openness (Tscannen-Moran & Hoy,
2000). Researchers find that there is a direct relationship between faculty
trust in students and parents and higher student achievement. Faculty trust
is a key property enabling schools to overcome some of the disadvantages
of low socioeconomic status (Goddard, Tschannen-Moran, & Hoy, 2001).
Each community college instructor plays a critical role in students’
learning. Self-efficacy of mathematics educators is vital because it directly
impacts student learning. Efficacy and achievement are strongly related
and teachers who believe they can affect positive changes in students are
more likely to engage in outcome-sensitive instructional behaviors (Moore &
Esselman, 1994). The outcome-sensitive instructional behaviors are what
students learn, understand, retain, and problem solve. Faculty instructional
behavior makes a huge difference because their perceived ability, efficacy
beliefs affect motivation to learn (Zimmerman, 2002, p. 202, as cited in
Bandura, 2002) to teach effectively.
The Role of Community College in Student Achievement
Community colleges provide unique learning opportunities for a vast
and varied population of learners. Since the 1960s, community colleges in
America have served the most needy adult learners (Boylan, 2004). The
community college population continues to diversify, with an increasing
number of students of racial, ethnic, linguistic minorities and low
socioeconomic status, first in their families to attend college, and those who

28
are considerably older than traditional college age (Perin, 2005). There is
no other learning institution in this nation or other countries where an adult
learner can enroll in college and can try a second or third time at learning
the basic skills regardless of age or past academic record (Cain, 1999).
Community colleges are a dream come true to many remedial students who
have been struggling in K-12.
In fact, there is no other American educational institution that can
take a young man or woman with a truly dismal previous school record and
no academic accomplishment at all and offer him or her a chance to
overcome all of that history, to become a different and better person
academically and personally (Cain, 1999). Also, community colleges are
known to provide educational opportunities for low achievers and minority
students (Seidman, 1985). They often provide basic skills classes for
struggling learners with low academic achievement. Basic skills classes
include pre-college reading, writing, and math (Perin, 2005). These classes
became a necessity in community colleges, as their doors began to open to
all students, whatever their level of academic preparedness (Perin, 2005).
The Urgent Growing Problems in Community Colleges
Although community colleges in America perform and create unique
access and equity for learning by diverse ethnic and racial students and
have impacted and changed lives, there is much concern about
remedial/developmental education in community colleges (Dougherty &
Reid, 2006; Arendale, 2005; Boylan, 2004; Grubb, 2001: Levin, 2001,

29
Tinto, 1998, and McGrath & Spear,1991). Traditionally, graduation from
high school meant that certain skills have been mastered and that students
were prepared for college-level work (Stevenson, 1998): however, the
number of students who need to take remedial classes has increased over
the years.
There seems to be an ongoing need for remedial education in all two
year junior or community colleges. The 2006 Community College Survey of
Student Engagement (CCSSE) reveals the magnitude of current
remedial/developmental education that about half of first-time community
college students are under-prepared for college. Fifty-three percent of
CCSSE respondents had taken, or were planning to take, at least one
developmental education class. Many under-prepared students do not finish
their first semester at college, let alone return for a second. In addition, the
more developmental courses or subjects a student is referred to, the more
likely he or she is to drop out. Furthermore, close to half of the students
referred to developmental education classes do not even attempt them
(2006).
There is a learning gap in students who are under-prepared and who
do not finish their first semester at college, let alone return for a second
developmental mathematics class. Often these students experience low
motivation that accelerates the curve of the learning gap.
The data from CCSSE (2006) points out that the more
developmental courses a student is referred to, the more likely he or she is

30
to drop out. About 50% of the students who are referred to developmental
education classes do not even attempt them. This could be for a variety of
reasons: low student motivation, unstable home environment, demands to
work full time, failing repeatedly to learn basic skills of mathematics,
learning the same concepts over and over since third grade, learning
disability, low self-perception of ability in learning mathematics, and not
being able to comprehend and retain the concepts that are taught by the
community college mathematics faculty.
In addition to lack of motivation, other empirical evidence shows that
a low GPA from K-12 contributes to low student performance. The National
Center for Education Statistics (NCES, 2004) states that 76 percent of all
higher education institutions offer some form of remediation. Another
NCES report (2004) on remedial education at degree-granting
postsecondary institutions in Fall 2000 indicates that 98 percent of
community colleges offered remediation in reading, writing, and
mathematics, with 42 percent of first-year students enrolled in at least one
pre-collegiate course. First time freshmen students with an astonishing 2.0
GPA at public four-year universities enrolled in at least one remedial course
in the fall of 2000 (McDaniel, 2004). In 2002, the Education Commission of
the States explains that many of the community college students who
require remedial instruction are recent high school graduates. Others are
working adults who have been out of school for some time or are
immigrants or refugees.

31
Supporting Student Learning
The data collected by the National Center for Educational Statistics
(NCES, 1996) reveal that first-year students at public community colleges
were twice as likely to be enrolled in remedial education courses than their
public four-year counterparts (Young, 2002). Adelman (1996) found that
the more remedial courses students are required to take, the less likely they
are to earn degrees. The Center for Student Success (2005) finds,
Many students entering the California Community College
System are in need of developmental or remedial coursework
in English, in math or in both. This has serious consequences
for the ability of students to succeed in other college level
courses, requires devoting significant resources to support
services, and extends the time to program completion and to
transfer. And, unfortunately, it also decreases the likelihood
of such outcomes. Critical to the success of many students in
their programs of study is attention to finding ways of
enhancing the skill development necessary for college work
(CSS, July 2005).

This report also states that more than one of every three students in
California community colleges enrolls in a basic skills class and the
proportion of students enrolling is ever-increasing (Center for Student
Success, 2005). With the changing demographics in California, the current
need for academic support is not going to decrease. The Center for
Student Success also points out that basic skills students traditionally
require high levels of student support services. There is likely to be a need
for increased support services and for alternative approaches to basic skill
education to further enhance student success (CSS, 2005). By giving this
support, there should be a higher rate of graduation while minimizing the

32
attrition rate; however, the current data do not support that the support
students are receiving influences the productive outcome of their academic
achievement.
High Drop-out Rate of First-year Students
In addition to the challenge of supporting student learning, other
empirical evidence suggests that the drop out rate of first-year community
college students is a problem. According to Measuring Up (2006), the
National Report Card on Higher Education, in the best-performing states,
only 65% of first-year community college students return for their second
year, and only 67% of students at four-year institutions complete a
bachelor’s degree within six years of enrolling.
Based upon this data, a question needs to be raised about what
happened to the 35% of first-year community college students who did not
return for the second year. One of the reasons could be their inability to
understand the mathematics content that they have been exposed to since
upper elementary school and that still remains incomprehensible to them.
This learning gap has direct linkage to a teaching gap by the inability to
teach effectively to make the concept comprehensible for students. The
learning gap of these academically struggling students even at the
community college level can be daunting when facing limited career choices
with adult responsibilities.
All these variables, low student motivation, lack of academic
preparation, diverse social and cultural backgrounds, and the deficient

33
capacity of an organizational support system create a vivid picture of how
helpless a faculty is in educating the student to overcome the status quo of
low attrition rate to transfer out from a community college to pursue a
baccalaureate degree. What each student brings into a community college
classroom is beyond the faculty’s control; however, there is one variable
that makes a difference. It is instructional practice. Instructional practice is
what the faculty does as a teacher in the classroom. It is the faculty’s role
as an instructor by imparting knowledge while deepening students’ content
understanding that results in gaining knowledge and skills. When a faculty
includes diverse strategies to reach all students in the classroom, it is likely
to influence the ability of students to promote their motivational level to
persist through the learning process. When students perceive that they
have the ability to make a difference in their own learning process, they are
likely to set attainable goals to graduate and set higher goals of learning at
a four-year institution.
This investigator finds that there is a relationship between an
instructor’s perceived efficacy and instructional practice which plays a very
important role in students’ learning. The objective of this study is to gauge
how important is the efficacy of mathematics faculty in educating
community college students who lack basic skills.
The Conceptualization of Remedial Education at Community Colleges
Community college mathematics remediation has been
conceptualized by many stakeholders. Student remediation is a concern for

34
governors, business, and educational leaders who need to develop a
comprehensive plan, such as holding high schools and colleges
accountable for student success. This accountability includes setting
meaningful benchmarks, intervening in low-performing schools, demanding
increased accountability of postsecondary institutions, and streamlining
education governance so that the K-12 and postsecondary systems work
more closely together (Conklin et al., 2005). Also, student remediation has
been considered as a current educational reform movement of overall
student achievement while reducing achievement gaps among racial and
ethnic groups (Treisman & Surles, 2001).
Researchers have conceptualized community college math
remediation through different lenses: (1) improving two-year mathematics
instruction with new standards (Schwartz, 2007); (2) improving adult
education through a wide array of discourses and theoretical tools (Chaves,
2006); (3) looking at returning adult students as tenacious persisters (Kinser
& Deitchman, 2007/2008); (4) fusing academic support programming and
mentoring for adult learners as retention tool (Scott & Homant, 2007/2008);
(5) measuring efficacy of participating in a first-year seminar on student
satisfaction and retention (Hendel, 2006/2007); (6) applying a motivational
and empowerment model including individual and group interactions as well
as personal responsibility; (7) positive affirmations, goal setting and life
planning and self-management (Kamphoff et al., 2006/2007); (8) examining
learning-style preferences of a diverse freshmen population (Reese &

35
Dunn, 2007/2008); (9) building pathways to success for low-skill adult
students (WSBCTC, 2005); (10) teaching using computer assisted
instruction (Glickman & Dixon, 2002); and (11) mastery learning strategies
(Fawzy Ghobrial, 1992).
It should be noted that the above studies focus on remediation
approaches outside of classroom instructional practice. Although
community college instructor effectiveness has been conceptualized by
many researchers, the number of studies is quite limited in comparison to
K-12 mathematics teacher effectiveness. Also, many remediation studies
focus on students and institutions rather than instructors. Measuring
instructor effectiveness through the lens of examining community college
teachers’ belief on making a difference in student learning has not been
explored in depth.
Studies Lacking in Instructor Effectiveness
There are studies that measure effectiveness of two-year college
mathematics instructors; however, the limited studies do not supply an
ample amount of evidence to gather information on community college
instructor effectiveness. One study measures two-year college
mathematics instructors and their relationship to the American
Mathematical Association of two-year colleges instructional standards by
investigating the instructional attitudes and planning practices (Jonson-
Reid, Davis, Saunders, Williams, & Williams, 2005). Davis finds that there
is no significant difference in participants’ attitudes based on gender, length

36
of teaching experience, or status as either full-time or part-time instructors.
However, Davis (2005) finds that the textbook plays a critical role in the
instructional planning process of two-year college mathematics instruction.
Another study (Kizemien, 2003) examines the gain scores of
students from a pretest-posttest administration in both a computer-mediated
setting and a traditional lecture-discussion setting for an entry-level
arithmetic course at a community college. Kizemien states that the results
of this analysis reveal that presentation method was the only independent
variable that produced a significant effect on gain score. The fact that the
other independent variables did not produce a significant effect would
suggest that the greatest determining factor of student success is the
classroom experience, not factors such as age, gender, number of hours
working per week or previous experience using a computer.
The examination of community college mathematics teachers’
classroom practices is almost non-existent. The inquiry about the
community college classroom experiences needs to stay on the level of
what a teacher does to promote student learning to take place. The what of
a lesson, the how of the lesson delivery, and the why of the anticipated
questions to enhance problem solving depend exclusively on the teacher as
a practitioner to impact student learning through student engagement within
the where of the four walls of the classroom.
Another researcher (Bensimon, 2007) discusses the invisibility of
practitioners in the discourse on student success . The author frames

37
student success as a learning problem of practitioners and institutions and
urges to place responsibility on the practitioner to become an institutional
agent. Bensimon (2007) asserts that the dominant paradigm of student
success is based exclusively on personal characteristics of students that
have been found to correlate with persistence and graduation. In addition,
Bensimon (2007) adds that practitioners are missing from the most familiar
way of conceptualizing empirical studies of student success; when scholars
attempt to translate their findings into recommendations for actions,
practitioners are rarely ever the target of change or intervention.
In addition to this, the faculty’s role in college students’ experiences
has not been closely examined, even though faculty members are the most
consistent point of contact with students (Stage & Hubbard, 2007). Also
student success models and studies place a great deal of emphasis on the
benefit of faculty and student interaction, yet there is practically no research
on the value of “informal communication (born of relationship) between
faculty and students (Martinez Aleman, 2007; Martinez Aleman, 2005).
Although teacher expectations are closely tied to eventual student
achievement since the 60’s and 70’s (Bloom, 1964; Rosenthal, 1968;
Roueche & Kirk, 1973), many authors have emphasized the importance of
community college faculty in students’ learning (Astin, 1985; Cohen &
Brawer, 1972; Grubb & Worthen, 1999a; Perin, 2005; Shulock & Moore,
2007; Tinto, 1998), using self-monitoring scale to predict academic and
social integration among community college students (Guarino et al., 1998),

38
and exploring the relations among ethnicity, effort, self-efficacy, worry, and
statistics achievement (Awang-Hashim et al., 2002). However, not much
research has been done on what makes the faculty to be effective or how
successful instructors are being made or what conditions foster the
successful teaching for students to continue within a community college.
O’Banion describes the personality of the successful instructors as,
Kind of person who has been described by Abraham Maslow
as self-actualizing, by Karen Horney as self-realizing, by
Gayle Privette as transcendent functioning, and by Carl
Rogers as fully functioning. Other humanistic psychologists
have described such healthy personalities as open to
experience, democratic, accepting, understanding, caring,
supporting, approving, loving, non-judgmental. They tolerate
ambiguity; their decisions come from within rather than
without; they have a zest for life, for experiencing, for
touching, tasting, feeling, knowing. They risk involvement;
they reach out for experiences; they are not afraid to
encounter others or themselves. They believe that man is
basically good, and given the right conditions, will move in
positive directions (O'Banion, 1971, p. 45).

Realizing the successful instructor attributes, I find that it is critically
important to look at effective instructional practice because researchers find
that the most important factor affecting student learning is the teacher
(Marzano, Pickering, & Pollock, 2001). Marzano and his colleagues point
out that effective teachers appear to be effective with students of all
achievement levels. When the teacher is ineffective, the students show
inadequate progress academically regardless of how similar or different
they are regarding their academic achievement (Wright, Horn, & Sanders,
1997).

39
Community college teachers are change agents. They function as
classroom practitioners in teaching and making changes in student content
understanding and changing their future. These teachers serve the
students as institutional agents. Therefore, their self-efficacy is a
component of effectiveness in conceptualizing mathematics remediation at
community colleges.

40
Chapter Two
Literature Review
Self-efficacy of Community College s Mathematics Teachers and
Effective Instructional Practice
The Roadmap of the Literature Review
The purpose of this chapter is to provide the background and
rationale (Galvan, 2006) of the relationship between self-efficacy of
mathematics faculty and effective instructional practice. After looking at the
larger context of community colleges though the three components of
knowledge economy, current crises in promoting talents, and situation in
California, the foundational framework for self-efficacy will be introduced.
Teacher self-efficacy includes the theoretical background, four sources of
self-efficacy, the importance of self-efficacy, difference between individual
and collective teacher self-efficacy, and studies on the self-efficacy of
developmental instructors. Then, the challenges of mathematics faculty
who teach basic skills in developmental classes to remedy student
academic achievement in community college will be described. Following
this, effective instructional practice using standards of American
Mathematical Association of Two-Year Colleges (AMATYC), Marzano
research- based strategies, direct instruction, Sheltered Instruction
Observation Protocol (SIOP), and dimensions of knowledge and cognitive

41
process will be explored through three motivational constructs: student
engagement, instructional strategies, and classroom management.
The Larger Context of Community Colleges
Community colleges offer a variety of learning opportunities from
vocational training, community services, to remedial/developmental
education. Among its diverse role of preparing adults to be ready for
employment, the other role is to transfer students to a 4-year college which
remains a central characteristic of community colleges (Brint & Karable,
1989). This preparation for transfer is key to the community college’s role
in higher education because it affirms the community college’s claim to a
collegiate, academic identity and to a role in broadening access for those
historically excluded from a college education (Bradburn & Hurst, 2001). In
the twenty-first century, the community colleges in America face
unprecedented challenges.
Knowledge Economy
America as a whole faces diverse educational challenges in teaching
and learning. The economy of the nation runs by the knowledge of its
citizens. The knowledge of workers is the engine of the economy that
causes the nation to be innovative, creative, and safe. Mathematics is
essential in a knowledge economy.
A report from the National Leadership Council for Liberal Education
& America’s Promise (2007) indicates that only a few year’s ago, Americans
envisioned a future in which their nation would be the world’s only

42
superpower. However, today, it is clear that the United States is challenged
in unprecedented ways by the global community. The report reveals that
students’ choices and their lives is one of disruption rather than certainty,
and of insularity rather than interdependence. This volatility also applies to
careers.
Also, the National Academies’ (2007) report reveals that there is an
alarming trend in knowledge economy which needs the urgent intervention
from government. The report states,
This nation must prepare with great urgency to preserve its
strategic and economic security. Because other nations
have, and probably will continue to have, the competitive
advantage of a low wage structure, the United States must
compete by optimizing its knowledge-based resources,
particularly in science and technology, and by sustaining the
most fertile environment for new and revitalized industries
and the well-paying jobs they bring. We have already seen
that capital, factories, and laboratories readily move wherever
they are thought to have the greatest promise of return to
investors (National Academies, 2007).

The report by the National Center for Public Policy and Higher
Education (Hayward, Jones, McGuinness, Timar, & Schulock, 2004)
indicates that the demand for higher education is at the minimum level while
the knowledge-based economy requires an education and training beyond
high school. The gap between the demand for a knowledge-based
economy and the supply of a qualified work force is huge.
The competitiveness indicators that are listed below from the
National Academies (2007) paints a gloomy picture of the nation’s future for
the US economy, such as the United States is today a net importer of high-

43
technology products. Its trade balance in high-technology manufactured
goods shifted from plus $54 billion in 1990 to negative $50 billion in 2001.
Also, it has been estimated that within a decade nearly 80% of the world’s
middle-income consumers would live in nations outside the currently
industrialized world. China alone could have 595 million middle-income
consumers and 82 million upper-middle-income consumers. The total
population of the United States is currently 300 million and is projected to
be 315 million in a decade.
In addition, the same report (National Academies, 2007) gives a
picture of current trends in Comparative Economics, such as chemical
companies closed 70 facilities in the United States in 2004 and tagged 40
more for shutdown. Of 120 chemical plants being built around the world
with price tags of $1 billion or more, one is in the United States and 50 are
in China. No new refineries have been built in the United States since
1976. Additionally, a company can hire nine factory workers in Mexico for
the cost of one in America, and a company can hire eight young
professional engineers in India for the cost of one in America. During 2004,
China overtook the Unites States to become the leading exporter of
information-technology products, according to the Organization for
Economic Co-operation and Development (OECD).
These trends in knowledge economy sounds a very loud warning
that America is not doing well in producing people who will lead the world
economy in the 21
st
century. The current crisis in knowledge economy can

44
be attributed to the lack of a significant number of young people who desire
to major in Science, Technology, Engineering, and Mathematics (STEM).
Current Crises in Producing STEM Talent
Shirley Ann Jackson, the 2004 president of the American Association
for the Advancement of Science and president of Rensselaer Polytechnic
Institute, sounds an alarm that America is in a quiet crisis now in science
and technology. She says,
“The shrinking of the pool of young people with the knowledge
skills to innovate won’t shrink our standard of living overnight.
It will be felt only in fifteen or twenty years, when we discover
we have a critical shortage of scientists and engineers
capable of doing innovation or even just high-value-added
technology work (Friedman, 2005).”

The National Academies (2007) find that in 2000 that 38% of the
doctoral degrees in the US science and technology workforce were foreign-
born. In 2004, China graduated about 350,000 engineers, computer
scientists, and information technologists with 4-year degrees, while the
United States graduated about 140,000. China also graduated about
290,000 with 3-year degrees in these same fields, while the US graduated
about 85,000 with 2-or 3-year degrees. Over the past 3 years alone, both
China and India have doubled their production of 3-and 4-year degrees in
these fields, while the United States production of engineers is stagnant
and the rate of production of computer scientists and information
technologists only doubled. In addition to this, about one-third of US
students intending to major in engineering switch majors before graduating.

45
Some 34% of doctoral degrees in natural sciences and 56% of engineering
PhDs in the United States are awarded to foreign-born students. There
were almost twice as many US physics bachelor’s degrees awarded in
1956, the last graduating class before Sputnik, than in 2004. Senator Enzi
says, “ For America to retain its competitive edge in the global economy, we
need to find ways to encourage high school students to stay in school and
prepare for and enter high-skill fields, like math, science, engineering,
health, technology, and foreign languages (Pascarella & Terenzini, 1991).
In meeting global competition and adapting to new technologies,
America will look even more to the community colleges (Hughes,
2006/2007). Hughes asserts that community colleges already create a
ladder to four-year degrees and help students who need to add and
improve skills after leaving high school. The community college faces a
challenge that dates back to the original basics of American education, the
proverbial reading, writing, and arithmetic (Hughes, 2006/2007). However,
the 21
st
century version is considerably more demanding. Community
colleges must help students achieve competence in mathematics, mastery
of specific scientific knowledge, and an ability to combine the two to solve
problems in a technologically demanding economy.
Situation in California
In addition to the national crisis of young people’s knowledge skills,
California’s community colleges face the crisis of access to a quality
education. National Center for Public Policy and Higher Education reports

46
in the document, Ensuring Access with Quality to California’s Community
Colleges, that there are seven major contextual conditions that demand
attention: enrollment increase, shifting demographics, low public visibility,
need for an educated populace, poor preparation, hemorrhaging
educational pipeline, and state budgetary difficulties (Hayward, Jones,
McGuinness, Timar, & Shulock, 2004). The authors of the document
emphasize the urgency in community colleges and point out that California
is well behind the national average in baccalaureate degree attainment. In
1997, California ranked 33
rd
in the ratio of baccalaureate degrees awarded
compared to high school graduates six years earlier. By 2000, the state
ranked 36
th
. In 1997, California was 4.3 percentage points behind the
national average on this measure, by 2000, the gap had grown to 5.9
percentage points. This reveals that the Master Plan for Higher Education
that was established in 1961 is not functioning as intended.
Another finding of this report (Hayward et al., 2004) is that the seven
conditions will challenge all sectors of California higher education, but their
cumulative impact will fall most heavily on the community colleges. Two-
thirds of the 700,000 new enrollees will attend a community college as the
initial entry point. The increase of Hispanic students, who are first-
generation college students from low-income families, will impact the
situation immensely (see tables 1, 2, and 3). For example, the statewide
for 2006 - 2007student headcounts by ethnicity, age group, and gender
reveal the following data (CCCCC., 2008).

Table1, Student Headcount by Ethnicity
Ethnicity Student Headcount by Ethnicity,
CA Statewide for 2006-2007
African-American 196,467
American Indian/Alaskan Native 22,429
Asian 321,004
Filipino 90,405
Hispanic 754,729
Other Non-white 51,994
Pacific Islander 18,499
Unknown/Non-Respondent 237,878
White Non-Hispanic 928, 081
Grand Total 2, 621, 481

Table2, Student Headcount by Age Group

Age Group Student Headcount by Age Group, CA
Statewide for 2006-2007
19 or less 642,369
20 to 24 683,214
25 to 29 323,932
30 to 34 207,827
35 to 39 172,838
40 to 49 270,314
50 + 311,966
Unknown 9,021
Grand Total 2,621,481
Table 3, Student Headcount by Gender
Gender Student Headcount by Gender, CA Statewide for
2006-2007
Female 1,436,569
Male 1,155,192
Unknown 29,720
Grand Total 2,621,481

The above data describe adult learners with diverse language background.
Many of these adult learners have poor academic preparation. This
condition directly affects how mathematics teachers teach. These students
have not understood the abstract mathematical concepts well in the past;
47

48
therefore, they are placed in basic skills classes. In addition to academic
inadequacy, many of these students are second language learners who
need instructional intervention beyond lecture. Teaching these students
poses a challenge because these students do not fully understand the
academic language, yet; therefore, it requires other strategies of learning,
such as using non-linguistic representations, graphic organizers, and
interactive activities to help them understand mathematics. This difficulty
demands a close examination of how these instructors teach these students
in order for students to understand the basic skills of mathematics and
ultimately graduate from community college.
Also, the report (Hayward et al., 2004) includes data that the state
government is in financial crisis. California faces unprecedented demands
by higher education enrollment with declining state financial resources.
Along with the deficiency in financial resources, two curriculum related
challenges stand out for the students who will be placed in developmental
classes. The report indicates that many college students and prospective
college students are inadequately prepared for college-level academic
work. Hayward, Jones, McGuinness, Timar, & Schulock (2004) describe
the hemorrhaging educational pipeline of California. For example, for every
100 ninth graders, 70 graduate from high school four years later; of these
70 graduates, 37 enroll in college; of the 37 who enter college, 25 are still
enrolled in the sophomore year; and of these 25, 19 graduate with an

associate’s degree within three years or a bachelor’s degree within six
years (see figure 2).
Figure 2, Hemorrhaging Educational Pipeline of California
19
Twenty-five are
still enrolled in the
sophomore year
Thirty-seven students enroll in
college
Seventy students graduate
One hundred 9
th
graders enter school

Nineteen students
graduate with an
associate’s degree
within three years
or a baccalaureate
degree within six
years.
Hemorrhaging Educational Pipeline of California (Hayward et. a
2004
l.,
)

49
California is experiencing an academic crisis. This is a crisis due to
the lack of student learning which attributes to many factors. Among these
many factors, teachers’ instructional practice plays a key role as a school
factor that influences student achievement (Friedman, Harwell, & Schnepel,

50
2006; Hargreaves, 2003; Hunt, Touzel, & Wiseman, 1999; Joyce, Weil, &
Calhoun, 2004; Klein et al., 2000; Martinez-Miller & Cervone, 2008;
Marzano, 2003; Price & Nelson, 2007).
When looking at figure two (p. 49), only thirty-seven students enroll
at institutions of higher education out of 70 high school graduates. This
means only 53% pursue a college education. The fact that nineteen
students graduate from 37 entering college students reveals that about 51%
of students obtain an associate’s degree in three years or a bachelor’s
degree in six years. Twelve students decide not to enroll and six
discontinue pursuing the degree out of the original 70 graduates. This
means 18 students who might have the potential to work on a higher
education degree choose not to continue leaving for a variety of reasons.
One of these reasons could be the students’ level of academic inadequacy.
Another reason could be their lack of access to information or people who
could function as institutional agents to mediate or promote learning
opportunities. Of course, other causes can be attributed to the
demographic, socioeconomic, and family backgrounds. The bottom line is
that the community college educational system needs to do something
about the inadequate number of graduates or transferring students to four
year universities.
America with inadequate preparation for the twenty-first century will
continue to experience a gap between the knowledge base of human
resources and the adequacy of graduates who could meet the changing

51
needs of the nation’s economic needs. Higher education’s performance in
preparing future citizens cannot be overemphasized. For example,
California’s rate of enrollment for those young adults’ ages, 18 to 24, is
about 35%, while the top performing nation, Korea, is about 72%. Also,
California is surpassed by Greece, Finland, and Belgium (Measuring Up,
2006).
The above is supported by the following quote from the State Report
Card on Higher Education,
California’s underperformance in educating its young
population could limit the state’s access to a competitive
workforce and weaken its economy over time. As the well-
educated baby boomer generation begins to retire, the diverse
young population that will replace them does not appear
prepared educationally to maintain the state’s edge in a global
economy. Compared with leading states, relatively few
students in California graduate from high school on time or
are adequately prepared to succeed in college. Moreover,
California has made little progress in improving its poor
performance in the proportion of 9
th
graders who enroll in
college by age 19. Those who do enroll do not perform well in
completing certificates or degrees. Internationally, California
ranks very low in the number of certificates and degrees
produced, and is outpaced by such low performing nations as
the Czech Republic, Hungary, and Spain (NCPPHE, 2006).

Additionally, Schulock and Moore (2007) find that low rates of degree
completion and student success are threats to California’s future. Studies
project a shortage of college-educated workers to meet the demands of the
state’s growing knowledge-based economy. About 40 percent of first-time
students in the California community colleges are not seeking a degree or
certificate, but are pursuing basic skills, job skills, or personal enrichment

(Schulock & Moore, 2007). Of the 60 percent who are seeking a degree or
certificate, only about one-fourth succeeds in transferring to a university
and/or earning an associate’s degree or a certificate within six years
(Schulock & Moore, 2007). Without big gains in educational attainment,
especially among the growing Latino population, the state’s per capita
income will soon fall below the national average, and the average education
level of California’s workforce will decline (see Figure 3).
Figure 3, The shortage of College-Educated Workers

52

The shortage of college-educated workers to meet the demands of the CA’s
economy (Schulock & Moore, 2007)

60 % of students seek
a degree or certificate

40 % of first-time student do
not seek a degree or
certificate, but are pursuing
basic skills, job skills, or
personal enrichment
(29 % attempt 6 to 12 units
and 32 % attempt 6 units or
less)
15 % of students
succeed in transferring
to a university and/or
earn an associate’s
degree or a certificate
within six years

Based upon Schulock and Moore (2007), the following data tell a
story about which population is more likely not to seek a degree from a
community college. The non-degree seeker’s under age 30 is 21% while
those over 30 is 79 %. There are more female (61%) non-degree seekers
than male (39%). Also, there is an overwhelming large population of
Latino/a non-degree seekers (51%) that is more than any other

53
race/ethnicity: White (19%), Asian (19%), Black (9%), and other (2 %). The
average ratio for course completion of non-degree seekers is 45%. It is
interesting to note that for units attempted, 40% of non-degree seekers
attempt greater than 12 units, 29% attempt between 6 and 12 units, and
32% try 6 units or less. For the number of terms attended, 45% attended 1
term, 34% completed 2 to 3 terms, 12% managed 4 to 5 terms, and 9%
finished less than 5 terms. The data reveal that Latina females who are
over 30 is likely to attempt 6 units and choose to discontinue the
matriculation process after the initial term (Schulock & Moore, 2007).
It is evident that California faces the brutal fact of a shortage of
knowledge economy. Unless the whole community of the state chooses to
take proactive approaches to problem solve this learning deficiency, the
state’s economy will compound its economic challenges in the future.
Within a few decades, those economic problems will create negative
consequences on social and cultural aspects of the states’ citizens. For this
reason, educating community college students must be a priority for the
state’s economy. It is going to take all sectors of the leaders.
In order to encourage minority students to stay in school, it is
essential that a community college in the first term provide needed support
by assisting them socially, emotionally, academically, and financially while
providing support in basic skills classes. In these classes, it is crucial what
teachers do. The learning environment of classroom atmospheres is partly

54
determined by teachers’ beliefs in their instructional efficacy (Bandura,
2002).
Teacher Self-Efficacy

Self-efficacy of Teachers

Bandura (2002) believes that the task of creating environments
conducive to learning rests heavily on the talents and self-efficacy of
teachers. Teachers who believe strongly in their instructional efficacy
create mastery experiences for their students (Gibson & Dembo, 1984, as
cited in Bandura, 2002). Those who have low self-efficacy in their
instructional capacity generate negative classroom environments that are
likely to undermine students’ sense of efficacy and cognitive development.
Bandura believes that teachers’ beliefs in their personal efficacy
affect their general orientation toward the educational process as well as
their specific instructional activities. Those who have a low sense of
instructional efficacy favor a custodial orientation that relies on extrinsic
inducements and negative sanctions to get students to study. Teachers
who believe strongly in the instructional efficacy support development of
students’ intrinsic interests and academic self-directness (Woolfolk & Hoy,
1990, as cited in Bandura, 2002).
Definitions of Self-efficacy and Beliefs

Albert Bandura, a social cognitive theorist, defines self-efficacy as an
individual’s belief about her or his capacity to organize and execute the
actions required to produce a given level of attainment (Bandura, 1997).

55
Pajares (2002) defines beliefs as what individuals create, develop, and hold
to be true about themselves and which form the very foundation of human
agency, and these are vital forces in their success or failure in all endeavors
(school). Bandura believes that people’s beliefs in their capabilities have a
powerful effect on their choice behavior. They choose to engage in
activities that they believe they can master and tend to avoid activities and
situations that exceed their coping capabilities (Evans, 1989).
Self-efficacy beliefs determine how people feel, think,
motivate themselves and behave. Such beliefs produce these
diverse effects through four major processes. They include
cognitive, motivational, affective, and selection processes. A
strong sense of efficacy enhances human accomplishment
and personal well-being in many ways. People with high
assurance in their capabilities approach difficult tasks as
challenges to be mastered rather than as threats to be
avoided. Such an efficacious outlook fosters intrinsic interest
and deep engrossment in activities. They set themselves
challenging goals and maintain strong commitment to them.
They heighten and sustain their efforts in the face of failure.
They quickly recover their sense of efficacy after failures or
setbacks. They attribute failure to insufficient effort or
deficient knowledge and skills which are acquirable. They
approach threatening situations with assurance that they can
exercise control over them. Such an efficacious outlook
produces personal accomplishments, reduces stress and
lowers vulnerability to depression (Bandura, 1994, p. 71).

In contrast, Bandura (1994) believes that people who doubt their
capabilities shy away from difficult tasks which they view as personal
threats. They have low aspirations and weak commitment to the goals they
choose to pursue. When faced with difficult tasks, they dwell on their
personal deficiencies, on the obstacles they encounter, and all kinds of
adverse outcomes rather than concentrating on how to perform the task

56
successfully. They slacken their efforts and give up quickly in the face of
difficulties. They are slow to recover their sense of efficacy following failure
or setbacks. Because they view insufficient performance as deficient
aptitude, it does not require much failure for them to lose faith in their
capabilities. They fall easily to stress and depression.
Also, Bandura (2004) states that belief in one’s efficacy is a key
personal resource in self-development, successful adaptation, and change.
It operates through its impact on cognitive, motivational, affective, and
decisional processes. Efficacy beliefs affect whether individuals think
optimistically or pessimistically, in self-enhancing or self-debilitating ways.
Such beliefs affect people’s goals and aspirations, how well they motivate
themselves, and their perseverance in the face of difficulties and adversity.
Efficacy beliefs also shape people’s outcome expectations – whether they
expect their efforts to produce favorable outcomes or adverse ones. In
addition, efficacy beliefs determine how environmental opportunities and
impediments are viewed. Bandura (2004) suggests that people of low
efficacy are easily convinced of the futility of effort in the face of difficulties.
They quickly give up trying. Those with high efficacy view impediments as
surmountable by self-development and perseverant effort. They stay the
course in the face of difficulties and remain resilient to adversity.

57

Theoretical Background on Self-efficacy

At the turn of the 20
th
century, American psychology began to take its
place among the other academic disciplines, there was much interest in
both the self and in the role that self-beliefs play in human conduct
(Pajares, 2000). Since then, psychological theory has always had a strong
influence on education. Teachers have followed the prescriptions of
psychologists, from William James with his emphasis on habit, to Freud
with his focus on unconscious motivations, to Watson and Skinner with their
stress on observable and measurable behavior (Pajares, 2002). Another
influential name that must be added to the above list of important
psychologist that has influenced education through social cognitive theory
and self-efficacy is Professor Albert Bandura. Today, it is simply not
possible to explain phenomena such as human motivation, learning, self-
regulation, and accomplishment without discussing the role played by self-
efficacy beliefs ((Pajares & Urdan, 2006).
The construct of self-efficacy stems from Bandura’s social-cognitive
theory. From the social cognitive perspective, Bandura describes various
distinctive human attributes: symbolization, forethought, vicarious learning
capacity, self-regulatory capability, and self-reflection (Evans, 1989). First,
Bandura believes that humans have tremendous capacity for symbolization.
Symbol systems provide the vehicle for thought. By representing their
experiences symbolically, people can give meaning and continuity to their

58
lives. Through symbol systems, they can communicate across time and
space (p. 34). Secondly, another distinctive human attribute is our
forethought capability. Bandura states that,
Because people can project into the future, they can regulate
and motivate themselves by anticipated outcomes and
aspirations. They anticipate likely consequences of possible
actions, set goals for themselves, and otherwise plan courses
of action that lead to valued futures. Forethought often saves
us from the perils of a foreshortened perspective (Evans,
1989, p. 34).

The forethought capability affects self-efficacy because it assists to regulate
and motivate oneself by anticipating outcomes and aspirations. It is likely to
assist the individual to set goals and plan courses of action that lead to the
future goals.
Thirdly, according to Bandura, the basic human attribute is our
advanced vicarious learning capacity. People have a capacity to acquire
patterns of behavior, attitudes, and emotional proclivities through
observation without having to go through the tedious trial-and-error process
Also, Bandura indicates that another distinctive human attribute is our self-
regulatory capabilities. People are not only reactors to external events, but
also they are self-reactors with some capacity for self-directedness and
self-evaluation. Self-regulatory capabilities enable people to exercise some
control over their own motivation and actions. Lastly, another distinctive
human characteristic is the capacity for self-reflection. People can reflect
on their own experiences, they can think about their own thought processes
and behavior. They can act on their ideas or predict occurrences from

59
them, judge from the results the adequacy of their thoughts and change
them accordingly (Evans, 1989).
Bandura asserts that social cognitive theory presents a cognitive
interactional model of human functioning. Thought and other personal
factors, behavior, and other environments all operate as interacting
determinants. Psychosocial functioning is improved by altering faulty
thought patterns, by increasing behavioral competencies and skills in
dealing with situational demands, and by altering adverse social conditions
(Evans, 1989).
In the unifying theory of behavior change, Bandura hypothesizes that
expectations of self-efficacy determine whether instrumental actions will be
initiated, how much effort will be expended, and how long it will be
sustained in the face of obstacles and failures (Schwarzer & Schmitz,
2000). Bandura identifies several different ways in which self-beliefs of
efficacy affect psychological functioning. People’s beliefs in their
capabilities have a powerful effect on their choice behavior. They choose to
engage in activities that they believe they can master and they tend to avoid
activities and situations they believe exceed their coping capabilities
(Evans, 1989). Because people’s self-beliefs in their capabilities enable
them to exercise some control over events that affect their lives and how
self-belief translates into human accomplishments, motivation, and personal
well-being (Evans, 1989), self-efficacy plays a crucial role in students’
learning capacity as well as teachers’ teaching capacity.

60
Four Sources of Self-efficacy
Self-efficacy beliefs among teachers develop from four sources. The
most influential source of self-efficacy is teachers’ mastery experience
which is a result of one’s own performance. Success typically raises self-
efficacy; failure lowers it (Pajares, 2000). Bandura believes that by
providing modeling, one can transmit skills, attitudes, values, and emotional
proclivities (Evans, 1989). He calls this process the acquisition function –
the teaching function of modeling.
Modeling can also reduce or strengthen inhibitions over
preexisting behavior. If people observe a model’s action
resulting in punishing consequences, this discourages them
from using that pattern of behavior. However, if they observe
that modeling results in positive consequences, this
encourages them to adopt similar behavior (Evans, 1989.
p.5).

The second source is the vicarious experiences of the effects
produced by the actions of others by social models, such as seeing people
similar to oneself manage task demands successfully. Seeing people
similar to oneself succeed by sustained effort raises observers’ beliefs that
they too possess the capabilities master comparable activities to succeed
(Bandura, 1994). Bandura emphasizes that the greater the assumed
similarity, the more persuasive are the models’ successes and failures. If
people see the models as very different from themselves, their perceived
self-efficacy is not influenced much by the models’ behavior and the results
it produces.

61
Next, individuals also create and develop self-efficacy beliefs as a
result of the social messages, persuasions, and dispersuasions they
receive from others (Pajares, 2000). Social persuasion is a way of
strengthening people’s beliefs that they have what it takes to succeed.
People who are persuaded verbally that they possess the capabilities to
master given activities are likely to mobilize greater effort and sustain it than
if they harbor self-doubts and dwell on personal deficiencies when problems
arise (Bandura, 1994). The social cognitive theorist, Bandura (1994) adds
that it is more difficult to instill high beliefs of personal efficacy by social
persuasion alone than to undermine it. Unrealistic boosts in efficacy are
quickly disconfirmed by disappointing results of one’s efforts. But people
who have been persuaded that they lack capabilities tend to avoid
challenging activities that cultivate potentialities and give up quickly in the
face of difficulties. By constructing activities and undermining motivation,
disbelief in one’s capabilities creates its own behavioral validation.
Lastly, physiological states such as anxiety, stress, arousal, fatigue,
and mood states also provide us with information about self-efficacy beliefs
(Pajares, 2000). People rely partly on their somatic and emotional states in
judging their capabilities. They interpret their stress reactions and tension
as signs of vulnerability to poor performance. In activities involving strength
and stamina, people judge their fatigue, aches and pains as signs of
physical debility. Mood also affects people’s judgments about their
personal efficacy. Positive mood enhances perceived self-efficacy,

62
despondent mood diminishes it. This way of modifying self-beliefs of
efficacy is to reduce people’s stress reactions and alter their negative
emotional proclivities and interpretations of their physical states (Bandura,
1994).
The Importance of Self-Efficacy
Self-efficacy is a key predictor of achievement and retention in most
academic areas (Fenci & Scheel, 2005). Academic self-efficacy is a robust
and consistent predictor (Zajacova, Lynch, & Espenshade, 2005) of college
students’ academic performance. Self-efficacy is a stronger predictor of
cumulative college GPA (Hackett, Betz, Casa, & Rocha-Singh, 1992). For
example, women’s physics self-efficacy correlates with course grade in an
algebra-based physics course (Shaw, 2004). Also, collaborative learning is
positively related to the self-efficacy of students in introductory physics
(Fenci & Scheel, 2004).
Efficacy beliefs affect human functioning through four intervening
processes: motivational, cognitive, affective, and choice processes
(Bandura, 1986). Each intervening process has different effects on human
functioning. Zimmerman (2002) reports that the motivational effects are
rooted in goal setting and outcome expectations. The cognitive effects
include among other things the anticipatory success and failure scenarios
people generate and the acquisition and deployment of strategies for
managing environmental demands (p. 224). As a result of motivational,
cognitive, affective, and choice processes, self-efficacy beliefs are strong

63
determinants and predictors of the level of accomplishments that a teacher
finally attains. The teacher’s behavior in assisting students to obtain
mathematical mastery and vicarious experiences can often be better
predicted by his or her beliefs about pedagogical capabilities.
Researchers found positive associations between student
achievement and three kinds of efficacy beliefs (Hoy, Tarter, & Woolfolk
Hoy, 2006): self-efficacy beliefs of students (Pajares, 1994,1997), self-
efficacy beliefs of teachers (Tschannen-Moran, Woolfolk Hoy, & Hoy,
1998), and teachers’ collective efficacy beliefs about the school (Goddard,
Hoy, & Woofolk Hoy, 2004). Goddard, Hoy, and Woolfolk Hoy inquired that
collective efficacy would enhance student achievement in mathematics and
reading. They found that collective efficacy was significantly related to
student achievement after controlling for SES and using hierarchical linear
modeling (2004).
Teachers with a high sense of efficacy feel personal
accomplishment, have high expectations for students, feel responsibility for
student learning, have strategies for achieving objectives, and a positive
attitude about teaching and believe they can influence student learning
(Ashton & Webb, 1986). Teachers have the challenge of improving the
academic learning and confidence of the students in their charge. Using
social cognitive theory as a framework, teachers can work to improve their
students’ emotional states, correct their faculty self-beliefs and habits of
thinking (personal factors), improve their academic skills and self-regulatory

64
practices (behavior), and alter the school and classroom structures that
may work to undermine student success which are environmental factors
(Pajares, 2002).
Pajares and Urdan (2006) believe, “Those who are more self-
efficacious about being able to effectively manage and cope are expected
to have a higher probability of succeeding, even if others have the same
inherent ability or skill level (p. 53).” This means that teachers who are self-
efficacious can manage and cope with individual students’ differences and
gaps in learning to assist them in students’ understanding. Kazdin (1974)
believes that observing a model perform disinhibited behavior that results in
beneficial consequences produces greater improvements than witnessing
the same performance without any evident consequences.
Pajares (2006) states the most influential source of self-efficacy has
important implications to increase student achievement in schools. This
author indicates that for most people, the most influential source is the
interpreted result of one’s own performance, or mastery experience. In
other words, individuals gauge the effects of their actions, and their
interpretations of these effects help create their efficacy beliefs
… self-enhancement model of academic achievement that
contends that, to increase student achievement in school,
educational efforts should focus on enhancing students’ self-
conceptions. Traditional efforts to accomplish this have
included programs that emphasize building self-esteem
through praise or self-persuasion methods. Self-efficacy
theorists shift the emphasis from self-enhancement to skill
development to raising competence through genuine success
experiences with the performance at hand, through authentic

65
mastery experiences. Educational interventions should be
designed with this critical point in mind. Students’ self-efficacy
beliefs develop primarily through actual success on
challenging academic tasks (Pajares, 2006, as cited in
Pajares & Urdan, 2006, p. 344).

Difference between Individual and Collective Teacher Self-efficacy
Individual self-efficacy is generated by one person while collective
self-efficacy is the byproduct of the collaboration of a group of people. The
magnitude of collection of individual self-efficacy can create a synergetic
movement within a learning organization as individuals retain and recreate
its high level of capacity to sort through actions to achieve the desired
goals. However, the organic culture within the learning institution often is
made-up of various levels of self-efficacy among teachers.
Schwarzer and Schmitz (2000) find that some teachers succeed in
being good teachers, in continuously enhancing students’ achievements, in
setting high goals for themselves and pursuing them persistently, while
others cannot meet expectations imposed on them and tend to collapse
under the burden of everyday stress. Academic emphasis, collective
efficacy, and faculty trust seem to reinforce each other as school properties
work together as a single powerful force explaining school performance.
This force is called academic optimism (Hoy, Tater et al, 2006). In a
longitudinal field study to measure individual and collective teacher self-
efficacy, teachers high in self-efficacy are found to sacrifice more leisure
time for their students than their less self-efficacious counterparts.

66
Also, the level of academic optimism among students can influence
teachers’ level of efficacy. Student characteristics affect school
achievement by altering the teachers’ beliefs in their collective instructional
efficacy (Bandura, 1993). In other words, there is a reciprocal and
interdependent relationship between student performance and teacher
performance. For example, Bandura (2002) finds the higher the proportion
of students from lower socioeconomic levels and of minority status, the
lower the staff’s collective beliefs in their efficacy to achieve academic
progress. Student absenteeism, low achievement, and high turnover also
take a toll on collective school efficacy.
Bandura (2002) reports that the schools’ collective sense of efficacy
at the beginning of the academic year predicts a school’s level of academic
achievement at the end of the year when the effects of the characteristics of
the student bodies, their prior level of academic achievement, and the
staff’s experiential level are factored out. Additionally, he asserts that with
staffs who firmly believe that students are motivatable and teachable,
schools heavily populated with poor and minority students achieve high
levels on standardized measures of academic competencies.
Pajares (2002) believes the higher the sense of efficacy, the greater
the effort, persistence, and resilience. This means that the effects of self-
efficacy influences the choices teachers make and the course of action they
pursue; teacher efficacy also help determine how much effort the teacher
will expend on an activity. A strong sense of efficacy enhances teachers’

67
accomplishment and personal well-being. Confident teachers approach
difficult tasks as challenges to be mastered rather than as threats to be
avoided. They have greater intrinsic interest and deep engrossment in
activities. They quickly recover their confidence after failures or setbacks.
They attribute failure to insufficient effort or deficient knowledge and skills
which are acquirable. In other words, based on Pajares’ findings, for
confident teachers, failure is a healthy reminder that they need to work
harder.
Conversely, teachers with low self-efficacy may believe that things
are tougher than they really are, a belief that fosters stress, depression, and
a narrow vision of how best to solve a problem (Pajares, 2000). When
teachers lack confidence in their capabilities, they are likely to attribute their
failure to low ability which they perceive as inborn and permanent. For
them, failure is just another reminder that they are incapable. This means
that teachers with low self-efficacy are unsure about their pedagogical and
content ability that influences students’ self-efficacy to doubt their academic
capacity. However, not all teachers attribute their failure to their own inborn
and permanent low ability, but rather to other factors, such as lack of
support by the administration, parents, and the inability of their students to
perform successfully.
Studies on the Self-efficacy of Developmental Instructors
The self-efficacy of developmental instructors can have a significant
impact on students’ learning. Bandura (1977) states that people organize

68
and regulate their behavior largely on the basis of individualized
experience; likewise, developmental instructors organize and regulate their
instructional practices based on their classroom experiences. Bandura
(2006) believes that the task of creating productive learning environments
rests heavily on the talents and efficacy of teachers. Bandura reveals that
teachers’ beliefs in their instructional efficacy partly determine how they
structure academic activities in their classrooms. This affects students’
academic development and judgment of their intellectual capabilities.
Teachers with high self-efficacy create mastery experiences for their
students. On the other hand, teachers with self-doubt construct classroom
environments that are likely to undermine students’ judgments about their
abilities and their cognitive development (Gibson & Dembo, 1984; Pajares
& Urdan, 2006; Woolfolk, Rosoff, & Hoy, 1990, as cited in Pajares & Urdan,
2006).
Bandura states, “Rate of learning is also markedly affected by
experiential preparedness. Experience makes predictive stimuli more
distinctive, furnishes prerequisite competencies, creates incentives, and
instills habits that may either facilitate or retard learning of new behavior
patterns (Bandura, 1977, p.75).” Variations in ease of learning do not
necessarily reflect inborn preparedness. Some contingencies are learned
more readily than others because the events covary in time and space in
ways that facilitate recognition of causal relationships (Testa, 1974).
Bandura asserts,

69
Cognitive events are induced and altered most readily by
experiences of mastery arising from successful performance.
Psychological procedures, whatever their form, alter
expectations of personal efficacy. Within this analysis, efficacy
and outcome expectations are distinguished. An outcome
expectancy is defined here as a person’s estimate that a
given behavior will lead to certain outcomes. An efficacy
expectation is the conviction that one can successfully
execute the behavior required to produce the outcomes.
Outcome and efficacy expectations are differentiated because
individuals can come to believe that a particular course of
action will produce certain outcomes, but question whether
they can perform those actions. The strength of people’s
convictions in their own effectiveness determines whether
they will even try to cope with difficult situations. People fear
and avoid threatening situations they believe themselves
unable to handle, whereas they behave affirmatively when
they judge themselves capable of handling successfully
situations that would otherwise intimidate them (Bandura,
1977, pp. 79-80).

Perceived self-efficacy not only reduces anticipatory fears and
inhibitions, but through expectations of eventual success, it affects coping
efforts once they are initiated. Efficacy expectations determine how much
effort people will expend, and how long they will persist in the face of
obstacles and aversive experiences - the stronger the efficacy or mastery
expectations, the more active the efforts. Those who persist in performing
activities that are subjectively threatening but relatively safe objectively will
gain corrective experiences that further reinforce their sense of efficacy
thereby eventually eliminating their fears and defensive behavior. Those
who give up prematurely will retain their self-debilitating expectations and
fears for a long time (Bandura, 1977).

70
Bandura suggests that perceived efficacy plays a critical role in
whether skills are used well, poorly, or extraordinarily (Evans, 1989).
Additionally, Bandura finds,
Performance accomplishments provide the most dependable
source of efficacy expectations because they are based on
one’s own personal experiences. Successes raise mastery
expectations; repeated failures lower them, especially if the
mishaps occur early in the course of events. After strong
efficacy expectations are developed through repeated
success, the negative impact of occasional failures is likely to
be reduced. Indeed occasional failures that are later
overcome by determined effort can strengthen self-motivated
persistence through experience that even the most difficult of
obstacles can be mastered by sustained effort. The effects of
failure on personal efficacy therefore partly depend upon the
timing and the total pattern of experiences in which they
occur. Once established, efficacy expectancies tend to
generalize to related situations (Bandura, 1977, p. 81).

Self-efficacy of Teachers Who Teach Minority, Low Income, and First
Generation Students
It is beneficial for teachers who teach minority, low income, and first
generation students to focus on building students’ self-efficacy rather than
self-esteem. Researchers find that academic self-efficacy rather than self-
esteem is the critical factor for school success (Jonson-Reid et al, 2005).
Bandura differentiates between self-efficacy and self-esteem,
The concepts of self-esteem and perceived self-efficacy are
often used interchangeably as though they represented the
same phenomenon. In fact, they refer to entirely different
things. Perceived self-efficacy is concerned with judgments of
personal capability, whereas self-esteem is concerned with
judgments of self-worth. There is no fixed relationship
between beliefs about one’s capabilities and whether one
likes or dislikes oneself (Bandura, 1997, p.11).

71
Strategies that build a students’ belief in the importance of education may
do more to increase academic self-efficacy among African American youths
than a focus on self-esteem (Jonson-Reid, Davis, Saunders, Williams, &
Williams, 2005). The teachers with high self efficacy provide a model for
these students who are not likely to have similar role models in their family.
These teachers’ role can not be overemphasized.
Teachers who teach minority, low income, and first generation
students function as institutional agents for these students to attain higher
education. In order to have a deep level of self-efficacy, the teacher must
have a profound level of empathy for students’ personal, social,
socioeconomic, ethnic, racial, and cultural understanding. Valuing a
student’s personal space, not crossing the boundary of self-respect for
another’s human dignity, the teacher needs to develop pedagogical skills
and hone content knowledge. Also, the teacher needs to have the desire to
make a positive difference in students’ lives with self- efficacy by
appreciating students’ individual backgrounds.
The teachers who have high self-efficacy are more likely to persist in
assisting minority students. Teachers with high self-efficacy are likely to
perceive working with minority students as a challenge, and therefore, will
do everything within their power to help these students to succeed.
However, teachers with low self-efficacy are likely to avoid dealing with the
difficulties associated with these students, and in turn experience much
stress, frustration, depression, and possibly a severe burn out.

72
Importance of Self-efficacy in Developmental Math Teachers
Self-efficacy is critically important for developmental math teachers
who teach minority students. These minority students interpret the behavior
of faculty and staff cognitively and affectively. Often, the choices of what
they learn are impacted by how they learn which in turn is influenced by
how they are being taught the “what” of content. In addition to this, their
motivation to learn is closely tied to how the faculty and staff perceive them
as individuals who bring with them their own distinct and unique cultural
experiences. When a teacher lacks respect and sensitivity for students’
ethnic and racial background, a teacher can form an environmental learning
culture that is toxic and that impedes the teacher’s capacity in delivering the
content knowledge. Teaching minority students require efficacious
teachers who are keenly aware of not only how the students learn, but who
are multi-culturally sensitive in creating the affective motivational force to
make choices in learning. Bandura says,
Humans do not simply respond to stimuli; they interpret them.
Stimuli influence the likelihood of particular behaviors through
their predictive function, not because they are automatically
linked to responses by occurring together. In the social
leaning view, contingent experiences create expectations
rather than stimulus-response connections. Environmental
events can predict either other environmental occurrences, or
serve as predictors of the relation between actions and
outcomes (Bandura,1977, p.59).

Teachers create learning experiences for all students. This is
especially true for the teachers of minority students. These teachers shape
the learning experiences that create expectations for student learning

73
explicitly and implicitly in conveying the content knowledge and the norms
of mainstream society. In this learning environment, the student predicts
the outcome of their capacity to attain the desired content knowledge.
Sometimes, teachers fail to state explicit expectations. Often, teachers
make assumptions that students have similar life experiences as theirs, and
that can be fatal in preparing and delivering the pedagogy.
Teachers function as models for all students, including minority
students. Zimmerman & Ringle (1981) find that models who express
confidence in the face of difficulties instill a higher sense of efficacy and
perseverance in others than do models who begin to doubt themselves as
they encounter problems ( as citied in Bandura, 1997). Bandura (1997)
identifies that if people see the models as very different from themselves,
their beliefs of personal efficacy are not much influenced by the models’
behavior and the results it produces. Schunck & Hanson (1989) describe
that self-modeling, strengthens beliefs in personal efficacy. Schunck &
Hanson note, “Self-modeling is directly diagnostic of what they are capable
of doing, in which people observe their own successful attainments
achieved under specially arranged conditions that bring out their best (p.
87).”
A minority student who does not fully understand the expectations of
the teacher if the teacher does not explicitly state what those expectations
are with the vocabulary that the student could understand clearly is likely to
be in danger of not developing the affective capacity to work with the

74
teacher. This condition influences the student not wanting to learn from the
teacher. Eventually, the student is likely to be in danger of failing the class
due to low motivation to activate the cognitive domain in making choices to
regulate the learning. Without the intervention of the teacher in a variety of
attempts with interactive strategies, the student is at the mercy of the
learning system within the classroom that impacts the pathways of
succeeding or failing as a productive citizen. The teacher plays a role of an
artisan to create the learning capacity for minority students. With the
scientific features of pedagogy and teaching strategies, the teacher of
minority students equip these students with tools: knowledge of content,
understanding of how to work with people from different cultures, desire of
learning, and yearning for the American dream in this land of opportunity as
a functional citizen.
According to Zimmerman (2002), the poorer performance and lower
self-concept of collegiate women in comparison with men were largely due
to lower judgments of self-efficacy (as cited in Bandura, 2002).
Developmental math teachers can provide engaging learning experiences
and performance-based expectations to influence minority students to attain
positive learning experiences to create self expectations of developing the
content knowledge to graduate from the community college. The
environmental culture in basic skills classrooms can affect certain outcomes
of students’ achievement through a faculty’s level of self-efficacy to create
academic optimism for minority students.

75

Self-efficacy of Teachers in Urban Community Colleges
Efficacy beliefs play a critical role for urban teachers. Often, the role
of the urban community college instructors depends on how well he or she
could assist students to tap into their own motivation in learning by having
them regulate their own learning. However, the reality is that not too many
students are prepared for this task of practicing self-regulated learning.
Students who enter urban community colleges carry the work habits
of their K-12 educational system that focused heavily on standards-based
content knowledge. Dembo (2004) states that the standards-based reform
movement could learn a great deal from the theory and research generated
by the learner-centered approach and use that knowledge to improve the
implementation of standards-based strategies. Fuhrman (2001)
differentiates that the intent of standards-based reform is to integrate key
aspects of policy in curriculum, assessment, teacher education, and
professional development while learned-centered education reform focuses
more on the learner than instruction, curriculum development, or the
administrative structure of the school. Dembo (2004) emphasizes two
important areas of learner-centered principles: strategic processing (self-
regulated learning) and motivational and affect. Dembo defines self-
regulated learning as the ability to take charge of one’s own learning or the
ability of students to control the factors or conditions that affect their
learning. Other researchers also support that students’ self-regulatory

76
beliefs and processes are highly correlated with academic achievement
(Zimmerman, 1977; Zimmerman, 1990, as cited in Dembo, 2004).
According to Bandura (2002), efficacy beliefs regulate stress and
anxiety through their impact on coping behavior. The stronger the sense of
efficacy, the bolder people are, in taking on problematic situations that
generate stress and the greater their success in shaping them. This means
teachers who have strong efficacy in their capacity to organize the
curriculum and execute the courses of action required to teach basic skills
mathematics are more likely to take on the challenge in urban setting
despite the stress and other conditional difficulties, such as the school
neighborhood and lack of signs of tender loving care of the site. However,
Bandura (2002) suggests that major changes in aversive social conditions
are usually achieved through the exercise of efficacy collectively rather than
just individually.
Self-efficacy of Mathematics Faculty
The self-efficacy of Math faculty is the foundation of classroom
learning environment in basic skills mathematics classes because the
faculty members play the role of institutional agents. Teachers are the
agents in delivering mathematics knowledge to students through direct
instruction within the classroom. The role of mathematics faculties as
learning agent is vital in promoting the mental effort and achievement in
diffusing the level of difficulty in problem solving through modeling and
providing vicarious experiences to the students. Salomon (1984) finds that

77
self-efficacy is positively related to self-rated mental effort and achievement
during students’ learning from text material that was perceived as difficult
(Zimmerman, 2002).
Although course work is linked to learning across the curriculum, the
strongest link may be with mathematics because students have little access
to learning in this subject outside school (Lee, 1998). A low sense of
efficacy to exercise control breeds depression as well as anxiety (Bandura,
2002). One route to depression is through unfulfilled aspiration. People
who impose on themselves standards of self-worth they judge that they
cannot attain which drive themselves to bouts of depression (Bandura,
1991 a; Kanfer & Zeiss, 1983, as cited in Bandura, 2002).
Higbee (2001) state that educators must view themselves as
ongoing agents of transformation, and that they are in the most important
position for illuminating future goals. Likewise, math educators must
envision themselves as change agents of transforming current conditions of
students’ mathematical performance. Silverman and Casazza address,
Change agents challenge the status quo. They are not
satisfied with repeating past successes or accepting failures.
Most important, they motivate themselves and others,
including students, administrators, and colleagues, to explore
new directions and take risks (Silverman & Casazza, 2000, p.
260).

Academic Optimism and Developmental Basic Skills Math Teachers
Collins (1982) found that self-efficacy was a better predictor of
positive attitudes to mathematics than was actual ability. Collins noticed

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that students display high and low perceived math self-efficacy within each
of three levels of math ability: high, intermediate, and low. At each level of
math ability, students who were assured of their self-efficacy discarded
faulty solution strategies more quickly, reworked more failed problems, and
achieved higher math performance than did students who were low in their
sense of self-efficacy (Pajares & Urdan, 2006, p. 53). Also, Bouffard-
Bourchard (1990) experimentally increased the self-efficacy of students at
two levels of ability on a novel problem-solving task. Regardless of their
pretest level of ability, students whose self-efficacy was raised due to using
more effective strategies and were more successful in their problem solving
than students whose self-efficacy was lowered (as cited in Pajares & Urdan,
2006).
Realizing that students’ self-efficacy affect their performance in
mathematics classes, teachers should inquire about their own level of self-
efficacy in teaching basic skills mathematics. In addition to working on their
individual self-efficacy, it is important for teachers to work on the collective
self-efficacy as they organize and align their departmental and
organizational learning goals. With individual efficacy coupled with
collective efficacy, developmental mathematics teachers function as
practioners of specific skills called, mathematics pedagogy. The need for
collective efficacy is based on raising the social support within a group of
people. Bandura (2006) states, “Social support raises perceived efficacy,

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which, in turn, raises academic achievement and satisfaction with one’s
home and school life (as cited in Pajares & Urdan, 2006, p. 34).”
Pajares and Miller (1994) found that math self-efficacy was more
predictive of problem solving than math self-concept, perceived usefulness
of mathematics, prior experience with mathematics, or gender (Zimmerman,
2002). Zimmerman (2002) finds that the effect of prior math experiences on
math problem solving was mediated primarily by self-efficacy beliefs, not
one’s self-concept. When self-concept and self-efficacy beliefs are
differentiated, self-efficacy beliefs are the principal predictor of math
performance (as cited in Bandura, 2002).
The reflection of individual self-efficacy that increases one’s
teaching capacity to meet the diverse students’ needs to attain their
competent mathematical capacity and collective self-efficacy to achieve the
desired performance as a department within a learning institution creates a
culture of academic emphasis through modeling, observation, and social
persuasion processes. Developmental basic skills math teachers create a
learning environment that increases students’ mathematical achievement
by applying the research-based strategies in teaching. Teachers need to
function as practitioner and researcher (Bensimon, 2004).
Hoy, Tarter, and Woolfolk Hoy (2006) state that three organizational
properties seem to make a difference in student achievement: the
academic emphasis of the school, the collective efficacy of the faulty, and
the faculty’s trust in parents and students. Academic emphasis, collective

80
efficacy, and faculty trust are tightly woven together and seem to reinforce
each other as they positively constrain student performance. Hoy, Tarter,
and Woolfolk Hoy (2006) link the three school properties together as a
single powerful force explaining school performance - academic optimism.
They assert, “Academic optimism is a general latent concept related to
student achievement even after controlling for SES (social economic
status), previous performance, and other demographic variables (Hoy,
Tarter, and Woolfolk Hoy, 2006, p. 427).” Hoy, Tarter, and Woolfolk Hoy
define academic emphasis as the extent to which a school is driven by a
quest for academic excellence. Other researchers discovered these
tendencies: highly achievable academic goals are set for students; the
learning environment is orderly and serious; students are motivated to work
hard; and students respect academic achievement (Hoy, 2005; Hoy, Tarter,
& Kottkamp, 1991, as cited in Hoy, Tarter et al, 2006).
However, the challenge lies in the incorporation of these research
findings in the cognitive, affective, motivational, and choice domains of
developmental mathematics teacher. Knowing such research is one thing
for teachers, but actually making conscious choices to implement the
curriculum and pedagogy is another matter. Unless the teacher is internally
motivated with deeply seated locus of control to find the need for making
meaningful changes to promote students’ learning individually and
collectively, the result in basic skills mathematics classes will continue to
lag behind and matriculation and transfer rate will not improve.

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Hoy, Tarter, & Woolfolk Hoy (2006) find that academic optimism is a
force for student achievement. This force of academic optimism includes
academic emphasis of the school, the collective efficacy of the faculty, and
the faculty’s trust in parents and students. Although socioeconomic factors
are powerful shapers of student performance (Coleman et al., 1966),
Coleman, Campbell, and Hobson find, academic emphasis, collective
efficacy, and faculty trust are tightly woven together and seem to reinforce
each other as they positively constrain student performance when
controlling for socioeconomic factors (Hoy, Tarter, & Woolfolk Hoy, 2006).
When academic emphasis drives a school for academic excellence, these
qualities are found: high but achievable academic goals are set for
students; the learning environment is orderly and serious, students are
motivated to work hard, and students respect academic achievement (Hoy
& Miskel, 2005; Hoy, Tarter, & Kottkamp, 1991). Academic emphasis was
an important element in explaining achievement in mathematics (Goddard,
Sweetland, & Hoy, 2000). In addition to the academic emphasis, another
component that makes a difference in student achievement is collective
efficacy.
Academic optimism could make a difference within a community
college. If the entire learning institution were to emphasize students’
academic success, faculty would work together by creating collective self-
efficacy. Then, the members of the organization would exercise a high
level of trust in assisting students to transfer to four-year universities.

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Community College Mathematics Faculty

Community College Full-time and Part-time Faculty
In 2005, 8,793 full time faculty who taught mathematics in two-year
colleges had the following characteristics: women (44%), ethnic minorities
(13%), above the age of 50 (46%), full-time faculty with a master’s degree
(82%) and with a doctorate (16%), and participation of full-time faculty in
professional development (53%) according to American Mathematical
Association of Two-Year Colleges (AMATYC, 2006). When compared to
percent of sections taught by full-time and adjunct faculty in two-year
colleges in 2004, there were more adjunct faculty who taught
developmental mathematics courses: full-time faculty (42%) and adjunct
faculty (56%) (AMATYC, 2006).
According to AMATYC (2006) data, adjunct faculty taught 44 % of all
two-year college mathematics sections: teach six credit hours or more
(54%), possess a master’s degree (72%) and doctorates (6%), have no
employment outside the college (49%), teach in high school during the day
(25%), and are employed full-time in industry (14%). Although the research
supports that the faculty’s role is critical in student achievement, the current
ratio between part time and full time faculty creates a mounting institutional
concern. The report on part-time faculty compensation of 22 California
community college districts, with a 22 percent response rate reveals the
following: (1) part-time salaries vary among the 22 community college
districts sampled from a low of $29 to a high of $68 per credit hour; (2) the

83
use of part-time instructors differs by discipline with approximately 58% of
part-time instructors teaching in humanities, social sciences, and
business/technical courses; (3) part-time instructors on average earn 50-60
percent of what full-time instructors earn with comparable experience and
educational backgrounds; and (4) approximately 75% of part-time
instructors report additional employment (California State Postsecondary
Education Commission, 2001). A written testimony of Thomas Nussbaum,
Chancellor of the California Community Colleges points out that California’s
community colleges have significantly larger class sizes than the national
average and often use part-time instructors when full-time instructors
should be utilized (Nussbaum, 2001).
The Role of Faculty in Student Remediation
Many developmental educators perceive that they and their work are
the subject of increasingly strident attacks by legislators and policy makers
(Boylan, 1999). Boylan asserts that of the many services provided by
developmental educators, only remedial courses are the target of most
criticism. The author finds that most of the criticisms are directed at the
lowest end of the continuum that are remedial courses. Students, parents,
administrators, faculty, and legislators regularly complain that remedial
courses take too long, cost too much, and keep students from making
progress toward attaining degrees by holding them in several different
levels of noncredit, remedial courses.

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Faculties play a critical role in helping students to matriculate. The
instructors, who understand the need for educating minority students for the
sake of America’s future, are more likely to work closely with struggling
learners. McGrath and Spear (1991) point out as the nation evolved a dual
system offering high quality education to the privileged and an inferior
education to poor and working-class children, the democratic promise of
education has been half realized, or badly compromised. The authors
state,
It is not hard to see that faculty labor under the illusion of
autonomy. They are isolated in their classrooms, individual
faculty members believe themselves completely free to
develop innovative teaching approaches that they experiment
as they will. Ordinary institutional categories encourage that
belief, favorably contrasting it with curriculum “imposed” from
above. Nevertheless, perceived autonomy is constrained
both by institutional structure and organizational culture,
neither of which can be eluded by teachers or students
(McGrath & & Spear, 1991).

The need for change in curriculum and pedagogy (Kissler, 1981) and
the new pedagogical approaches were talked about over two decades ago
in the annual report by Intersegmental Coordinating Council (1989) in
Sacramento. However, the actual implementation in each basic skills
mathematics classroom by faculty seems to lag behind the urgency that is
promoted among policy makers.
Who should be responsible for remedial basic skills students’
learning? Teachers, of course. Karoly (2001) believes that the remedial
students who are at the bottom of the barrel in basic skills must have their

85
needs met because they are a part of the wealth of the nation. Society’s
total wealth is a combination of human and nonhuman capital. Teachers
are the work force who create and mold the capacity of a nation’s wealth. A
teacher who has a belief system that he/she can make a positive difference
is called a self-efficacious educator. Researchers believe,
Teachers with a high sense of efficacy feel a personal
accomplishment, have high expectations for students, feel
responsibility for student learning, have strategies for
achieving objectives, a positive attitude about teaching, and
believe they can influence student learning (Ashton & Webb,
1986).

The faculty’s role plays a critical part in all students’ remediation.
The Center for Student Success (2007) reports that if developmental
courses are designed to develop critical thinking and to scaffold learning in
ways that contribute to increase self-regulation and self-efficacy, such
experiences may instead enhance student preparation for higher-level
study. However, (Boylan, 2002) asserts that students are rarely exposed to
instruction in critical thinking in high school and points out that
developmental students’ particular lack of this key ability leads to increased
failure for these students. As developmental instruction moves away from
simple repetitive practice to a more fully developed focus on critical thinking
and learning strategy development, the acquisition of these foundation skills
has great potential for improving subsequent success in a variety of content
discipline (Boroch et al., 2007).

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According to the California Community College Chancellor's Office,
"Basic Skills Mathematics" courses consist of mathematics courses that are
one or more levels below the level needed to obtain an AA or AS degree
from a college (Maack, 2002). American Mathematical Association of Two-
Year Colleges (AMATYC) finds that the percent of student enrollment in
Mathematics courses at community colleges in 2005 is as follows:
Developmental basic skills mathematics (57%), Precalculus (19%),
Calculus (6%), Statistics (7%), and other mathematics courses (11%).
Since 57% of students are enrolled in developmental basic skills
mathematics, this study takes a close look at the developmental education
in community colleges.
Developmental Education to Remedy Students’ Basic Skills
Some researchers believe that remedial/developmental education is
one of the most controversial aspects of higher education (Grubb &
Worthen, 1999b). Remediation of basic skills is one of the most
widespread yet understudied components of postsecondary education.
Some have called it postsecondary education’s “dirty little secret” while
others believe that remediation serve as the necessary remedy for helping
the under-prepared to meet the challenges of postsecondary learning
(NCPI, 1999).
Within higher education, these two terms, remedial and
developmental, are used interchangeably. However, Boylan (1999) clearly
distinguishes that developmental education is not a euphemism for

87
remediation. It is a far more sophisticated concept involving a combination
of theoretical approaches drawn from cognitive and developmental
psychology. According to the Center for Student Success (CSS),
Remedial is defined as “intended to correct, to supply a
remedy.” This presumes that something is “wrong,” and that
the student must be held responsible for correcting it.
Developmental education does not judge the student or even
the educational experiences of the student prior to entering
the new educational environment. Instead, it views the
current educational process as transformational, taking the
student from one state and developing his or her abilities into
those of a more capable, self-confident, and resourceful
learner (CSS, 2007).

Grubb defines that the “remedial” label implies that such courses
remedy a lack of skills, and the pejorative connotations-blaming students for
their “deficiencies”– have caused many to avoid this term. The alternative
label, “developmental,” stresses the further development of competencies
that students bring to college, and avoids the negative implications of
remediation (Goto, 1995; Grubb, 1999). Roueche & Kirk (1973) note,
The courses with the heaviest enrollments are those that may
be categorized as remedial or compensatory in nature. A
variety of terms have been contrived to describe these special
courses: developmental, directed, compensatory, guided,
basic, and advancement studies. Whatever the
nomenclature, most programs are designed to develop
students’ basic skills to a level from which they can enter
regular college curriculum programs (p. 6).

National Association for Developmental Education (2001) defines
that developmental education is a field of practice and research within
higher education with a theoretical foundation in developmental psychology
and learning theory. It promotes the cognitive and affective growth of all

88
postsecondary learners, at all levels of the learning continuum.
Developmental education refers to all forms of learning assistance, such as
tutoring, mentoring, supplemental instruction, personal, academic, and
career counseling, academic advisement, and coursework.
Definitions of Developmental Education and Goals

According to Greene (2000) remedial education is not a new
concern; it has been part of higher education since the founding of Harvard.
It has grown in importance as the needs of the economy call for a better
educated work force (2000). National Association for Developmental
Education (NADE, 1995, as cited in Higbee, 2001b) defines,
Developmental education is a field of practice and research
within higher education with a theoretical foundation in
developmental psychology and learning theory. It promotes
cognitive and affective growth of all postsecondary learners,
at all levels of the learning continuum. Developmental
education is sensitive and responsible to the individual
differences and special needs among learners.
Developmental education programs and services commonly
address preparedness, diagnostic assessment and
placement, affective barriers to learning, and development of
general and discipline-specific learning strategies
(NADE, 1995).

Higbee (2001) asserts that the richer the range of definitions and
approaches we provide in developmental education, the more responsive
our classrooms and programs can be to the diverse range of students we
serve.
The National Association for Developmental Education (1995) goals
are as following: (1) to preserve and make possible educational opportunity

89
for each postsecondary learner; (2) to develop in each learner the skills and
attitudes necessary for the attainment of academic, career, and life goals;
(3) to ensure proper placement by assessing each learner’s level of
preparedness for college course work; (4) to maintain academic standards
by enabling learners to acquire competencies needed for success in
mainstream college course; and (5) to enhance the retention of students;
and lastly, to promote the continued development and application of
cognitive and affective learning theory (Higbee, 2001).
The Need for Theoretical Frameworks in Developmental Education
The need for theoretical frameworks in developmental education is
mounting. Although recent developmental education publications reflect a
renewed interest in identifying theoretical frameworks (Caverly & Peterson,
1996, as cited in Darby, 1996), current theoretical frameworks are inexplicit
and unintentional and manage to produce a hodge-podge of contingent
local practices(Collins & Bruch, 2000), lacks a theoretical base (Lundell &
Collins, 1999), and has little knowledge of its roots (Spann & McCrimmon,
1998). Collins and Bruch (2000) state that it is important to construct
powerful theories to guide practice in developmental education, not from
various perspectives in isolation, rather from the purposeful interpenetration
of the theories that inform disciplinary practices that the richness of an
interdisciplinary theoretical framework for developmental education might
emerge (as cited in Higbee, 2001).

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Development education deserves much attention and is needed for
the sake of America’s economic, social, and educational well being. One of
the meanings of the word “education” is the ability to think carefully about
things in an objective way and according to abstract, or general, principles
(Greene, 2000). Development educators need to think carefully about the
theoretical frameworks with the data that are generated by the research to
guide the teaching practices, especially in mathematics.
Boylan (1999) points out that an essential component of a successful
program in the future will be research and development. The most
successful programs are theory based. They do not just provide random
intervention they intervene according to the tenets of various theories of
adult intellectual and personal development (Chung, 2001; Stratton, 1998).
In addition to this, Spann and McCrimmon (1998) identify that the field of
developmental education currently faces an identity crises. For the most
part, it has little knowledge of its roots or a widely understood and
articulated philosophy, a body of common knowledge, or a commonly
accepted set of theoretical assumptions congruent with that philosophy
(Spann & McCrimmon, 1998, as cited in Chung, 2001).
Higbee (2001) states that Silverman and Casazza’s model for
integrating a wider range of theories, applied directly to student experiences
through case studies, provides a clear direction and instructive example of
how developmental educators can continue to create change for students
specifically, and the profession more broadly. The vantage points of

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Silverman and Cassazza (2000) include a wider range of theories than
present definitions have outlined, including sociolinguistic theories,
constructivist models, adult learning frameworks, cognitive development
theories, and multicultural education and intercultural communication
theories. Their rich range of applied theories demonstrate that current
individualistic models alone, which presently dominate definitions and
practice in developmental education (Higbee, 2001b; Lundell & Collins,
1999, as cited in Higbee, 2001b) is insufficient.
What is already known about developmental education is that the
theoretical framework for developmental education is important as part of
the foundation of practice (Barajas, 2001). Traditional framework in
developmental education tends to focus on deficit and normative models of
student educational attainment rater than on the struggle for educational
equality and justice for people of color (Ladner, 1972, as cited in Barajas,
2001). These developmental educational concerns are important because
they contribute to student transfer rates and student performance in
community colleges.
Barajas (2001) asserts that what complicates the situation of
developmental education is the rich literature that speaks to how we
practice as educators. The literature contains impressive consideration of
students who do not fit the mainstream picture of education. However, we
seldom utilize theoretical frames that help us explain the experiences of
students of color beyond their skills. The consequences are that we cannot

92
understand how the structure of our relationship with the institution affects
our relationships with our students, regardless of what that institution is,
rather than just exploring the student-institutional fit.
According to the National Association for Developmental Education
(Stream, 1995), students must undergo remediation if they do not get a high
enough score on placement exam. States should consider adding
performance measures addressing transfer and post-transfer success. All
performance measures should be broken down by student income and
race, so that a clear picture can emerge of how higher education is affecting
students with different backgrounds (Dogherty & Reid, 2006). Maxwell
states that developmental education “not only lacks academic standing, but
its practitioners do not have power to set or even contribute to policy
decisions within their academic communities (Maxwell, 2000, as cited in
Barajas, 2001).
Importance of Remedial/Developmental Education

The education of remedial students is the most important educational
problem in America today. Providing effective remedial education would do
more to alleviate our most serious social and economic problems than
almost any other action (Ehrlich, 2000). The literature and findings in
developmental education is growing and some findings are controversial.
Some believe that developmental students are less likely to reach their
degree objectives (Adelman, 1996) while others find that students in
developmental courses are more likely to persist in college and more likely

93
to transfer to a higher level college and obtain a bachelor’s degree
(Bettinger & Long, 2005).
Community colleges and developmental classes are very attractive
to students of financial need. Developmental programs for first-time college
students can be an equalizer for low-income and minority students. College
remediation is not a new phenomenon. In 1889, 80% of all postsecondary
institutions offered some form of a college-preparatory program (Clowes,
1992) and the University of Wisconsin offered the first remedial courses in
1849 (Breneman and Haarlow, 1998 as cited in McDaniel, 2004). Remedial
programs were part of higher education because tax-supported high
schools were uncommon until the early 1900s and their absence made pre-
collegiate training difficult to obtain. In response, colleges offered
preparatory instruction. Even after the advent of tax supported high schools
in the early part of the 20th century, colleges continued to offer remedial
programs (McDaniel, 2004).
According to Enright and Kersteins (1980) in 1942, between 30 to 40
percent of postsecondary institutions reported that they planned to continue
offering remedial programs even though high schools offer these services.
More recently, in the fall of 2000, an alarming 76 % of higher education
institutions offered at least one remedial course (NCES, 2004). During the
establishment of public high schools in the early 1900s participants of
education were the elite of society (Holton, 1969). Thus, high school
education, like higher education was initially accessible only to the

94
privileged -wealthy boys of European descent. The development of the
contemporary or comprehensive high school (Holton, 1969) witnessed
changes not only in student characteristics but also in function (McDaniel,
2004).
During the mid 1900s, colleges also experienced demographic shifts.
For high schools, the primary purpose of preparing students for higher
education slowly expanded to include preparation for work. The changing
economy (from farm to factory labor) requiring a more literate society, and
an influx of students were among the factors contributing to the shift in the
focus of high schools (Turcker, 1999, as cited in McDaniel, 2004).
Remediation in Mathematics
In fall 2000, National Center for Education Statistics reveals that 28
percent of entering freshmen enrolled in one or more remedial reading,
writing, or mathematics courses. The proportion of freshmen who enrolled
in remedial courses was larger for mathematics (22%) than writing (14%)
(NCES, 2004). The most common way to select students for remedial
coursework is to give placement tests to all entering students; 57 to 61
percent of institutions used this approach in fall 2000 for remedial reading,
writing, and mathematics courses. Institutions also tended to have
mandatory placement policies for students who were determined to need
remediation. Seventy-five to eighty-two percent of the institutions required
students who were identified to need remediation to enroll in remedial
reading, writing, or mathematics courses. Thirteen percent of the

95
institutions offered remedial courses in 2004 through distance education,
compared to 3 % in 1995 (NCES, 2004). While remedial education has
become an increasingly common aspect of all sectors of postsecondary
education, recent ideological debates have resulted in state and system-
wide policies that increasingly segregate remediation solely within the
community college sector (Shaw, 1997).
Most colleges assess entry–level proficiency and provide remedial
courses to students. Others offer more comprehensive programs that also
include orientation, advising, tutoring, study skills courses, and additional
personal enrichment activities (OVAE, 2007). There are many accounts of
innovations being tried in individual developmental education classrooms as
instructors struggle to identify effective teaching methods (Perin, 2005).
However, the comprehensive programs and innovations fall on laps of
community college teachers who teach developmental classes to remedy or
bridge the gap of the students’ subject matter content knowledge. The gap
seems to persist at a steeper rate for minority students.
Marti, a community college president shares (Marti et al., 2006) that
under the open-admissions policy, anyone with a high-school degree or
GED is welcome to matriculate in a program of study at a community
college. However, all matriculated students must take a battery of basic
skills-placement examinations to demonstrate proficiency in reading,
writing, and mathematics. In addition, Marti (2006) points out that students
who do not demonstrate the required competence must enroll in a

96
developmental or “remedial” course designed to provide concentrated
assistance to bring them quickly up to college-level work. These authors
emphasize that remedial courses are the foundation for academic quality in
a community college. Without an effective remedial program, the
alternatives are to abandon open admission and become selective, or to
lower academic standards.
The current approaches rely on the use of standardized placement
tests to determine whether students have remedial needs to assist under-
prepared students include the targeted delivery of remedial courses in
math, English, and reading. Based on those placement test scores,
students may have a remedial need in only one of the core academic areas.
Students may concurrently enroll in required remedial courses and college-
level courses unrelated to the area in which they are considered to be
academically under-prepared. College-level pass rates are much lower
among students concurrently enrolled in remedial courses and college-level
courses. These students under-perform irrespective of the type of college-
level course. In contrast, students who pass their remedial courses are
generally successful in their college-level courses (Illich, Hagan, & Leslie,
2004).
Offering remedial classes is one issue, the low success rate in
remedial basic skills math classes identifies another issue. Another issue
that must be considered is what and how full time and adjunct remedial
mathematics faculty teach in basic skills classes. In addition to the

97
pedagogical issues, there are other concerns in remedial math. Many
approaches taken by community colleges are to offer tutoring sessions in
math labs, provide supplementary instruction classes, and have peer tutors
available at convenient hours for students.
Remediation on Basic Skills Mathematics
The Center for Student Success (Boroch et al., 2007) defines, “Basic
skills are those foundation skills in reading, writing, mathematics, and
English as a Second Language, as well as learning skills and study skills
which are necessary for students to succeed in college-level work (p. 13).”
This report (CSS) also reveals that courses designed to develop these skills
are generally classified as pre-collegiate, basic skills, or both, and may be
either credit or non-credit. To remediate the students’ foundational basic
skills, many community colleges seek out best practices in student
remediation. Boylan’s (2002, 2003, as cited in Boroch et al., 2007) definition
of best practices refers to organizational, administrative, instructional, or
support activities engaged in by highly successful programs, as validated by
research and literature sources relating to developmental education.
Research findings reveal the importance of institutional systemic
leadership approach (Roueche & Roueche, 1999), institutional commitment
(Boylan & Saxon, 2002), and support system (Kiemig, 1983) in student
remediation on basic skills mathematics effective practices. The CSS
report points out that there is a strong correlation between the
comprehensiveness of developmental education programs within an

98
institution and positive impacts on student learning (Boroch et al., 2007).
Isolated basic skills courses have been shown to be least likely to produce
long-term gains in student achievement, while those programs that
incorporate an increasing sophistication of learner support and cross-
disciplinary learning “systems” are the most effective (Kiemig, 1983). In
order to create and maintain such systems, institutions must place a high
value on basic skills programs and see them as fundamental to the
institutional mission. In addition, McCabe (2000) recommends that
community colleges give remedial education higher priority and greater
support that successful remediation occurs in direct proportion to priority
given to the program by the college. Most important is a caring staff who
believes in the students and in the importance of their work (as cited in
Boroch et al, 2007).
Research shows when measuring the performance of academically
underprepared students who complete required remediation that students
who completed all remediation earned higher cumulative grade point
averages than those who completed some or none of the remediation.
Likewise, those who completed some remediation earned more
accumulated credit hours than those who completed no remediation
(Cowden, 1997). In addition, the Achieving the Dream Initiative
(McCleanney, 2006) finds that students who successfully completed a
developmental mathematics course in their first term of enrollment are more
likely to persist and succeed from that point forward than those in other

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groups, including those who attempted but did not complete developmental
math, and even those who did not require math remediation. Remediation
represents a critical and decisive step towards academic success, status
attainment, and economic stability (Riley, 2004).
American Mathematical Association of Two- Year Colleges
According to the American Mathematical Association of Two-Year
Colleges (AMATYC, 2006)), there were more than 1,150 two-year colleges
serving 10.1 million students. In the academic year 2001 -2002, community
colleges/ two-year junior colleges served 53% of all undergraduate students
in the United States (AMATYC, 2006). AMATYC (2006) reveals the
following demographic characteristics of the students: the average age was
29, with 36 % of students were 18-21 years old, 15% were 40 years or
older, 58% were women, 33 % were minority students (Black, Native
American, Asian, Pacific Islander, and Hispanic), 61% took a part-time
course load, 41% were employed, and 80% were employed full time. Many
students were in a career change while some had not attended school
recently and others were commuters.
Dotzler (2003) points out that many students arrive at college
underprepared by their high school to succeed in a traditional college-level
academic setting. These students are in need of “Remedial Education”.
That is, they require a “remedy” for their particular academic deficiencies.
However, Dotzler mentions that an increasing number of students for one
reason or another, never completed their secondary education or graduated

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from high school several years before enrolling in post-secondary
education, or graduated from a non-English speaking high school. These
students are in need of “Compensatory Education.” That is, they need to
“compensate” for their personal situation.
Continuing Concerns of Community Colleges
According to American Association of Community Colleges, there
are four reasons for transfer concerns (Nora, 2007). First, over the past 25
years, there is a notable decline in the percentage of community college
students who transfer to senior institutions: Less than 43 percent in 1973,
nearly 30 percent in 1980 (Friedlander, 1980), then 15 to 20 percent in
2007. Secondly, the growth of services in vocation programs, community
services, and remedial education dilute the transfer function. Thirdly, there
is a decline in the academic performance by community college students.
This may be a result of low academic expectations of students by
community college mathematics faculty. The fourth reason is that students
with baccalaureate degrees starting their college careers in two-year
colleges have less of a chance of attaining the degree than comparable
students in four-year institutions (Pascarella & Terenzini, 1991). In the
best-performing states, only 65% of first-year community college students
return for their second year.
According to Pena, Bensimon, and Coylar (2006), one of the most
critical challenges facing institutions of higher education, such as
community colleges in the twenty-first century is the need to be more

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accountable for producing equitable educational outcomes for students of
color.
Although access to higher education has increased
significantly over the past two decades, it has not translated
into equitable educational outcomes for African Americans,
Hispanics, and Native Americans who have lower graduation
rates than whites and Asian Americans. They also
experience inequalities in just about every indicator of
academic success – from earned grade point average to
placement on the dean’s list to graduation rates in competitive
majors (Pena, Bensimon, & Coylar, 2006).

Community colleges serve a disproportionately high percentage of students
of color (Cohen & Brawer, 1977) and women. They educate millions of
students serving the nation’s least privileged citizens who are and will be
the backbone of the economy. Nevertheless, community colleges receive
scant attention in the research literature, especially in studies that marry
two distinct aspects of an institution, such as its faculty and curriculum
(Kisker & Outcalt, 2005). Astin (1985) states in Achieving Educational
excellence, the major purpose of any institution of higher education is to
develop the talents of its faculty and students to their maximum potential
(as cited in Higbee, 2001a). To develop the talents of its faculty, it is
important to look at their instructional practice.
Effective Instructional Practice

American Mathematical Association of Two-Year Colleges (AMATYC)

In order to study the relationship between self-efficacy of community
college mathematics faculty and instructional practice, it is necessary to
take a look at the content standards of American Mathematical Association

102
of Two-Year Colleges (AMATYC, 2006). There are three strands of the
AMATYC: intellectual development, content, and pedagogy. In the
document Beyond Crossroads, there are eight AMATYC standards for
intellectual development: problem solving, modeling, reasoning, connecting
with other disciplines, communicating, using technology, developing
mathematical power, and linking multiple representations. There are seven
AMATYC standards for content: number sense, symbolism and algebra,
geometry and measurement, function sense, continuous and discrete
models, data analysis, statistics, and probability, and deductive proof. For
pedagogy, there are five AMATYC standards: teaching with technology,
active and interactive learning, making connections, using multiple
strategies, and experiencing mathematics (AMATYC, 2006).
It is a difficult task for mathematics faculty to combine the three
strands of intellectual development, pedagogy, and content in teaching
effectively. The process of integrating the strands to produce a meaningful
outcome for student achievement becomes very difficult for the faculty
when students do not have an adequate amount of basic skills. In addition
to the students who lack basic skills, there are a few other layers of
challenges to the faculty. For a lot of students in California, English is their
second language. There are various levels of English language learners.
The important point is that it takes more effort for the faculty to make the
lesson understandable for these students through modeling, guided
instruction, and frequent practice of the subject.

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Teaching requires a deep level of commitment; especially, teaching
students who lack basic skills requires a tremendous level of dedication of
sheer effort from the faculty to raise students’ understanding to gain
mathematical knowledge/skills. It takes a faculty who has the “can – do”
commitment and determination to take on this task. It demands a faculty
who is willing to “just-do” the integrating and implementing approaches with
the desire to ensure students’ learning to take place. It requires the faculty
to learn strategies and research based instruction to raise student
achievement. It takes self-efficacious faculty to do the job of teaching these
students.
Teaching is a complex process. In order to teach effectively a
community college faculty has to not only know the content knowledge
thoroughly, but also be able to weave the components of intellectual
development and pedagogy in a meaningful whole to make sense to
students to attain and master the content knowledge. Effective teaching
involves knowing what works in curriculum and instruction that is supported
by research-based and scientifically proven findings which is supported by
empirical evidence. At the same time, the faculty needs to interject the
scientifically proven information into teaching by integrating the components
of intellectual development and pedagogy of AMATYC’s standards. This
process of integrating, adapting, synthesizing, and creating a lesson that is
tailored for a specific group of students requires a tremendous effort. This is
an artistic and scientific endeavor of the faculty. The word, pedagogy,

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which is defined as the art or profession of teaching (American Heritage
Dictionary, 2001) is truly an art form through inquiry because the faculty has
to integrate all three components of AMATYC’s standards into a coherent
whole to help students comprehend the input of the mathematical
understanding.
Effective Instructional Practice
Although Individual teachers within a school can vary considerably in
terms of their teaching effectiveness (Kauchak & Eggen, 1993; Alexander &
McDill, 1976; Good et al., 1975), many educational researchers have
explored effective practices among various variables. These variables are
as follows: linking teacher action or behaviors and student learning
outcomes (Gage, 1985); correlating teacher content knowledge and
strategies and student achievement (NCES, 1996); making engagement
central with accountability and school reform (Schlechty, 2002); including
four components of high quality instruction: quality of assignments,
coherence of instruction, student choice in curricular and pedagogical
issues, and the content of instruction (Carbonaro, 2002); offering well-
researched comprehensive, and systematic exploration of the knowledge,
skills, and commitments that should enable teachers to be effective
(Darling-Hammond & Bransford, 2005); classroom management as a
critical aspect of effective teaching classroom (Brophy & Evertson, 1976;
Marzano, Marzano, & Pickering, 2003); instruction that works through
research-based strategies (Marzano, Pickering, & Pollock, 2001); making

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content comprehensible through the sheltered instruction observation
protocol (Echevarria, Vogt, & Short, 2008); and implementing effective
instruction into five phases: orientation, presentation, structured practice,
guided practice, and independent practice (Joyce, Weil, & Calhoun, 2004).
Definitions of Effective Instruction
The American Mathematical Association of Two-Year Colleges’
(AMATYC, 2006) document, Beyond Crossroads, defines effective
instruction, “Effective mathematics instruction requires a variety of
resources, materials, technology, and delivery formats that take into
account students’ different learning styles and instructors’ different teaching
styles. Every teaching activity should promote active learning and be
guided by informed decision-making (Ch. 7, p 1).” The document
specifically defines, “teaching style” as an instructor’s content-independent,
persistent qualities, attitudes and traits. This is directly linked to the
instructor’s educational philosophy and a subset of the instructor’s life
philosophy. In addition, the document includes that understanding how
students learn mathematics and knowing which instructional methods are
likely to be successful should inform instructional practice. It notes that
mathematics faculty will use a variety of teaching strategies that reflect the
results of research to enhance student learning (AMATYC, 2006).
Effective instruction not efficient instruction produces desired
learning. Even if effective instruction is costly at first, its efficiency may be
improved over time. Almost all strategies are more costly when they are

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first introduced and become more efficient with experience over time
(Friedman, Harwell, & Schnepel, 2006). Ball and colleagues point out,
“Effective teaching requires an understanding of the underlying meaning
and justifications for the ideas and procedures to be taught and the ability to
make connections among topics (Ball et al., 2005, p. 4).”
In this dissertation, I look at effective instruction through the three
lenses of self-efficacy: student engagement, instructional strategies, and
classroom management. The first construct of student engagement
includes three pedagogical approaches: (1). direct Instruction, (2). the
types of knowledge and cognitive process dimensions of learning, teaching,
and assessing (Anderson & Krathwohl, 2001), and (3). five levels of student
engagement responses (Schlechty, 2002). The second construct of
instructional strategies include Marzano and his colleagues’ research-
based strategies (Marzano, 2006; Marzano, Marzano, & Pickering, 2003;
Marzano, Pickering, & Pollock, 2001) and the scientifically based approach
called, the SIOP (Sheltered Instruction Observation Protocol) model
(Echevarria, Vogt, & Short, 2008). The third construct of classroom
management includes Marzano’s classroom management approaches
(Marzano, Marzano, & Pickering, 2003).
What Is Effective Instruction?
I find that effective instruction is all about good teaching that
engages students in learning through instructional strategies to promote
student comprehension. When good teaching takes place, classroom

107
management is in place, students are engaged in the learning process, and
instructional strategies are used that support the curriculum and make the
lesson understandable. The curriculum is aligned with assessments in
order to provide corrective feedback on student learning. In addition, good
teaching promotes authentic student efficacy, and that in turn, raises
teachers’ efficacy by their knowing that they make the lesson
comprehensible.
In order to impart the three AMATYC’s strands of intellectual
development, content, and pedagogy, mathematics instruction can be
taught effectively with Marzano’s nine research-based strategies and with
the eight components of the SIOP model when the teacher realizes the
dimensions of knowledge and cognitive process of learning, teaching, and
assessing. Mathematics faculty could implement the intellectual
development standards of reasoning, connecting with other disciplines,
communicating, using technology, and linking multiple representations while
using Marzano’s nine research based strategies. Also, the faculty could
integrate the pedagogy standards of teaching with active and interactive
learning, making connections, using multiple strategies, and teaching with
technology with Marzano’s nine strategies as tools to promote students’
understanding. The SIOP model contributes to students’ understanding
through eight components: lesson preparation, building background,
comprehensible input, strategies, interaction, practice and application,
lesson delivery, and review and assessment (Echevarria, Vogt, & Short,

108
2008). When a lesson is taught with these research-based strategies,
students are likely to be engaged in learning.
There are overlapping features among Marzano’s research-based
strategies and the SIOP model as well as three strands of AMATYC. It is a
teacher who decides what strategy to use when teaching a mathematical
concept. This informed decision-making about pedagogy and implementing
the strategy makes the student understanding to be comprehensible.
According to Marzano (2001), effective pedagogy involves three
areas: (1) the instructional strategies used by the teacher, (2) the
management techniques used by the teacher, and (3) the curriculum
designed by the teacher (p. 10). Marzano, Marzano, & Pickering (2003)
point out, “The effective teacher performs many functions: making wise
choices about the most effective instructional strategies to employ,
designing classroom curriculum to facilitate student learning, and making
effective use of classroom management techniques (p.3).” During this
process, the teacher must understand the dynamics of knowledge
acquisition and usage of different types of knowledge in delivering effective
and appropriate strategies in delivering direct instruction. In addition, five
phases of direct instruction adds another layer to promote student
understanding of concepts (Joyce, Weil, & Calhoun, 2004) are added to the
following figure 4. When these components work together targeting for
students’ intellectual development for English only as well as English
learners, mathematics teachers must deliver explicit instruction through

109
presentation and highly structured guided practice to explain and elaborate
on the key features of a lesson. During this time, it is crucial to include
research-based strategies to make the lesson to be cognitively engaging
and demanding (see figure 4).

Figure 4, Effective Community College Mathematics Instruction

110

Direct Instruction:
1. Orientation
2. Presentation
3. Highly Guided
Practice
4. Guided
Practice
5. Independent
Practice
The
Sheltered
Instruction
Observation
Marzano’s
Research Based
Strategies
AMATYC
(American
Mathematics
Association for Two
Year Colleges)
Effective
Community
College
Math tion ematics Instruc
Intellectual
Development
Content
Pedagogy
Building
Background
Comprehensible
Input
Strategies
Interaction
Practice /
Application
Summarizing/ Note taking
Reinforcing effort / Providing recognition
Homework / Practice
Nonlinguistic representation
Cooperative learning
Setting objective / Providing feedback
Generating and testing hypotheses
Cues, questions, and advance organizers
Identifying Similarities / Differences
Lesson
Preparation
Lesson Delivery
Review /
Assessment

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A. Student Engagement
1. Direct Instruction
There are five phases of direct instruction: orientation, presentation,
structured practice, guided practice, and independent practice by Joyce,
Weil, and Calhoun (2004). In the book, Models of Teaching, the authors
define direct instruction as a pattern of teaching that consists of the
teacher’s explaining a new concept or skill to a large group of students,
having them test their understanding by practicing under teacher direction
(that is, controlled practice), and encouraging them to continue to practice
under teacher guidance (guided practice). The authors note that a major
goal of direct instruction is the maximization of student learning time which
is associated with student time on task and student rate of success, which
in turn are associated with student achievement . Joyce, Weil, and Calhoun
(2004) delineate the five phases in a direct instruction lesson (See Table 4):
orientation, presentation, highly guided practice, guided practice, and
independent practice. The authors emphasize these features:
1. Orientation includes teacher clarification of objectives and procedures for
the new learning task while activating prior knowledge and/or connecting to
previous lessons. 2. Presentation is about teacher explanation,
demonstration, and giving examples of concept, skill, or strategy. During
this time, teacher uses a visual representation of the material and checks
for student understanding. 3. Highly guided practice entails teacher

112
leading students through the practice step-by-step, using an overhead
transparency or chart of the practice examples as well as the visual
representation. 4. Guided practice is students practicing on their own but
with the teacher present to monitor and give corrective feedback. 5.
Independent practice is students practicing completely on their own after
reaching 85-90% accuracy with guided practice with delayed feedback. In
addition to the direct instruction phases, it is essential to consider the
dimensions of knowledge and cognitive process when engaging students in
learning to target higher order thinking skills (see Table 4).
Table 4, Five Phases of Direct Instruction
Phases
of Direct Instruction
Direct Instruction Model (Joyce, Weil, & Calhoun, 2004)
Phase One:
Orientation
Teacher establishes content of the lesson.
Teacher reviews previous learning.
Teacher establishes lesson objectives.
Teacher establishes the procedures for the lesson.

Phase Two:
Presentation
Teacher explains/demonstrates new concept or skill.
Teacher provides visual representation of the task.
Teacher checks for understanding.

Phase Three:
Structured Practice
Teacher leads group through practice examples in lock step.
Students respond to questions.
Teacher provides corrective feedback for errors and reinforces correct
practice.

Phase Four:
Guided Practice
Students practice semi-independently.
Teacher circulates, monitoring student practice.
Teacher provides feedback through praise, prompt, and leave.

Phase Five:
Independent Practice
Students practice independently at home or in class.
Feedback is delayed.
Independent practices occur several times over an extended period.

In addition to the above five phases of direct instruction model (Joyce, Weil,
& Calhoun, 2004), dimensions of knowledge and cognitive process
(Anderson & Krathwohl, 2001) contribute positively to student engagement.

113
2. Dimensions of Knowledge and Cognitive Process
Anderson and Krathwohl (2001) describe four dimensions of
knowledge: factual knowledge, conceptual knowledge, procedural
knowledge, and metacognitve knowledge (see Table 5). First, factual
knowledge is the basic elements students must know to be acquainted with
a discipline or solve problems in it, such as knowledge of terminology and
knowledge of specific details and elements. Secondly, conceptual
knowledge involves the interrelationships among the basic elements within
a larger structure that enable them to function together, such as knowledge
of classifications and categories, knowledge of principles and
generalizations, and knowledge of theories, models, and structures.
Thirdly, procedural knowledge is how to do something, methods or inquiry,
and criteria for using skills, algorithms, techniques, and methods, such as
knowledge of subject-specific skills and algorithms, knowledge of subject-
specific techniques and methods, and knowledge of criteria for determining
when to use appropriate procedures. Fourthly, metacognitive knowledge is
knowledge of cognition in general as well as awareness and knowledge of
one’s own cognition, such as strategic knowledge, knowledge about
cognitive tasks, including appropriate contextual and conditional knowledge,
and self-knowledge.
In addition to the four dimensions of knowledge, there are six
categories of the cognitive process (Anderson & Krathwohl, 2001). The six
categories are as follows: remember, understand, apply, analyze, evaluate,

114
and create. The first cognitive process, remember, is to retrieve relevant
knowledge from long-term memory by recognizing and recalling. The
second process, understand, is to construct meaning from instructional
messages, including oral, written, and graphic communication through
interpreting, exemplifying, classifying, summarizing, inferring, comparing,
and explaining. The third process, apply, is to carry out or use a procedure
in a given situation through executing and implementing. The fourth
process, analyze, is to break material into constituent parts and determine
how parts relate to one another and to an overall structure or purpose
through differentiating, organizing, and attributing. The fifth process,
evaluate, is to make judgments based on criteria and standards, such as
checking and critiquing. The last process, create, is to put elements
together to form a coherent or functional whole; reorganize elements into a
new pattern or structure by generating, planning, and producing. When
using these dimensions, it forms a two dimensional shape of an area
model. The vertical columns represent the cognitive process dimension
while the horizontal rows represent the knowledge dimension
(see Table 5).

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Table 5, The Taxonomy of Knowledge and Cognitive Dimensions
(Anderson & Krathwohl, 2001)

The Cognitive Process Dimension The
Knowledge
Dimension
1.Remember 2. Understand 3. Apply 4. Analyze 5. Evaluate 6. Create
A.
Factual
Knowledge

B.
Conceptual
Knowledge

C.
Procedural
Knowledge

D. Meta-
Cognitive
Knowledge

Understanding the four dimensions of knowledge and cognitive process is
important when teachers are planning for their mathematics instruction
because it provides the framework on how different types of knowledge can
be obtained by students at different levels of the cognitive processes.
While Anderson and Krathwohl organize knowledge into four types,
Marzano (2006) points out three types of knowledge: information, mental
procedures, and psychomotor procedures. Based on these three types of
knowledge, he divides assessment items into three categories: (1) type 1
of addressing basic details and skills, (2) type II of addressing more
complex ideas and processes, and (3) type III of requiring students to make
inferences or applications that go beyond what is taught in class.
When mathematics instruction focuses on the procedural knowledge
of algorithms and techniques for determining when to use appropriate
procedures in problem solving, the instruction focuses on the cognitive

116
process of remembering and understanding. In order for the teacher to
bring students’ understanding to the levels of apply, analyze, evaluate, and
create, it requires infusion of conceptual understanding. The instructional
practice that integrates the conceptual understanding in mathematics
pedagogy requires teachers who have a deep level of content and
pedagogical knowledge and skills. To integrate the conceptual
understanding with the mathematics content, it requires a reflective
cognitive process by the teacher, thinking about teaching, which is the
metacognitive knowledge of the pedagogy.
Too often, in mathematics classes, teachers tend to focus more on
factual and procedural knowledge instead of conceptual understanding.
The mathematics faculty feel obligated to cover the material that is required
to ensure that the students are exposed to all the concepts. However,
students are less likely to master the concepts thoroughly and are unable to
retain the information into long-term memory. With the fast pacing to cover
as much as they can, many teachers do not focus on conceptual knowledge
with higher dimension of cognition.
Another layer of this challenge is that this is a pedagogical skill that
is often taught to K-12 teachers who have gone through the teaching
credentialing process; however, this opportunity to learn pedagogy is not
required nor encouraged for community college mathematics faculty.
Learning how to teach requires the building blocks of self-efficacy: mastery

117
experiences , vicarious experiences, social persuasion, and emotional
arousal (Bandura, 2001).
The difficulty of not connecting mathematical learning to conceptual
and metacognitive knowledge causes students to view learning
mathematics as isolated skills and concepts that are void of interrelated
patterns and does not provide meaningful learning experiences. This
process of learning mathematics becomes even more of a challenge for
English Language Learners. These students struggle with the factual
knowledge, such as knowledge of terminology and specific details and
elements. When a teacher realizes the audience of the classroom is made-
up of diverse linguistic and ethnic English as second language students as
well as English only students who struggled with abstract concepts of
learning mathematics, the teacher is in a position of needing to teach a
math lesson by planning and reflecting about how to increase their
mathematics understanding. This involves four types of knowledge that are
factual, conceptual, procedural, and metacognitive in order to raise
students’ cognitive processes from remembering to understanding,
applying, analyzing, evaluating, and creating. Teaching is a complex,
laborious, and consuming experience.
3. Levels of Engagement Responses
Schlechty (2002) notes that “The key to school success is to be
found in identifying or creating engaging schoolwork for students (p. xiv).”
The author explains that it is an unfortunate fact that educators too often fail

118
to differentiate between teachers who are engaging as a person or as a
performer and teachers who are skilled at providing work and activities for
students that the students find to be engaging. Schlechty (2002) denotes,
What is needed are teachers who know how to create, as a
matter of routine practice, schoolwork that engage students.
Schools cannot be made great by great teacher performance.
They will only be made great by great student performance…,
once teachers figure out how to do it, are tasks, assignments,
and activities that students find engaging from which the
students learn those things that teachers and the larger
society believe the students should learn (p.xxiv).

As teachers engage students, Schlechty (2002) identifies five types of
student engagement responses: authentic engagement, ritual engagement,
passive compliance, retreatism, and rebellion (See Figure 5). Authentic
engagement describes an engagement quality that the task, activity, or
work the student is assigned or encouraged to undertake is associated with
a result or outcome that has clear meaning and relatively immediate value
to the student. Ritual engagement takes place when the immediate end of
the assigned work has little or no inherent meaning or direct value to the
student, but the student associates it with extrinsic outcomes and results
that are of value. Passive compliance involves a situation when the student
is willing to expend whatever effort is needed to avoid negative
consequences, although he or she sees little meaning in the tasks assigned
or the consequences of doing those tasks. Retreatism occurs when the
student is disengaged from the tasks, expends no energy in attempting to
comply with the demands of the tasks, but does not act in ways that disrupt

others and does not try to substitute other activities for the assigned task.
Rebellion is when the student summarily refuses to do the task assigned,
acts in ways that disrupt others, or attempts to substitute tasks and
activities to which he or she is committed in lieu of those assigned or
supported by the school and by the teacher. The Figure 5 is an
interpretation of Schlechty’s Five Types of Student Engagement in a
Coordinate Plane (see Figure 5).

Figure 5, Five Types of Student Engagement (Schlechty, 2002)

119

In addition to be able to engage students at authentic level in order to teach
effectively, it takes a deep content knowledge, by linking it with effective
pedagogical skills. This requires explicit training on how to teach. Teacher
Direct Value
Authentic
Engagement
Positive
Direction
Ritual
Engagement
Passive
Compliance
Retreatism
Negative
Direction
Clear meaning
Rebellion
Positive
direction

120
preparation courses prepare teachers to be exposed to the basic elements
of pedagogy. However, the power of pedagogical theory is experienced as
teachers work with students through continuous trials of integrating the
content knowledge, expected curriculum and standards, knowing how much
to teach per class, what to teach, how to include four types of knowledge
and raising the cognition levels from knowledge and understand to apply,
analyze, evaluate, and create. To teach effectively, teachers must know
when to include specific strategies to promote students’ cognitive
processes. In addition, when designing curriculum for AMATYC’s content
standards, using Marzano’s nine research-based instructional strategies
provide tools for the faculty to use in order to make the lesson
understandable by assisting students to process the information in a variety
of ways.
B. Instructional Strategies
Effective teachers make conscientious and proactive choices
resulting in student engagement. Often these choices help students to be
engaged in academic learning time which focuses on students’ time–on–
task (Echevarria, Vogt, & Short, 2008). Researchers point out that there
are three aspects to student engagement: (1) allocated time, (2) engaged
time, and (3) academic learning time (Berliner, 1984). The engaged time
refers to the time students are actively participating in instruction during the
time allocated (Echevarria, Vogt, & Short, 2008). Researchers (Marzano,
Marzano, & Pickering, 2003; Wright, Horn, & Sanders, 1997) find,

121
Effective teachers appear to be effective with students of all
achievement levels regardless of the levels of heterogeneity
in their classes. If the teacher is ineffective, students under
that teacher’s tutelage will achieve inadequate progress
academically, regardless of how similar or different they are
regarding their academic achievement (Marzano et. al., 2003,
p. 1)

The strategies that are used by effective teachers affect all students in a
classroom. According Marzano (2001), there are nine effective strategies
that are research-based strategies for increasing student achievement: (1)
identifying similarities and differences; (2) summarizing and note taking; (3)
reinforcing effort and providing recognition; (4) homework and practice; (5)
nonlinguistic representations; (6) cooperative learning; (7) setting objectives
and providing feedback; (8) generating and testing hypotheses; and (9)
cues, questions, and advance organizers.
Marzano’s Research-based Instructional Strategies
Sanders and his colleagues (Sanders & Horn, 1994; Wright, Horn, &
Sanders, 1997, as cited in Marzano, Pickering, & Pollock, 2001) have noted
that the individual classroom teacher is the most important factor for student
achievement. As a result of analyzing the achievement scores of more than
100,000 students across hundreds of schools, their conclusion is as follows:
…the most important factor affecting student learning is the
teacher. In addition, the results show wide variation in
effectiveness among teachers. The immediate and clear
implication of this finding is that seemingly more can be done
to improve education by improving the effectiveness of
teachers than by any other single factor. Effective teachers
appear to be effective with students of all achievement levels,
regardless of the level of heterogeneity in their classrooms. If
the teacher is ineffective, students under the teacher’s

122
tutelage will show inadequate progress academically
regardless of how similar or different they are regarding their
academic achievement (Wright et al., 1997, p.63).

Other researchers Marzano, Pickering, and Pollock (2001) have identified
instructional strategies that have a high probability of enhancing student
achievement for all students in all subject areas at all grade levels. No
instructional strategy works equally well in all situations. Table 6 describes
the nine categories of instructional strategies that affect student
achievement (Marzano, Pickering, & Pollock, 2001).
Table 6, Nine Research-Based Instructional Strategies (Marzano et al,
2001)

Categories of Instructional Strategies That Affect Student Achievement
(Marzano, Pickering, & Pollock, 2001)
Category Ave.
Effect
Size
(ES)
Percentile
Gain
No. of ESs Standard
Deviation (SD)
1. Identifying similarities
and differences
1.61 45 31 .31

2. Summarizing and note
taking
1.00 34 179 .50
3. Reinforcing effort and
providing recognition
.80 29 21 .35
4. Homework and practice .77 28 134 .36
5. Nonlinguistic
representations
.75 27 246 .40
6. Cooperative learning .73 27 122 .40
7. Setting objectives and
providing feedback
.61 23 408 .28
8. Generating and testing
hypotheses
.61 23 63 .79
9. Questions, cues, and
advance organizers
.59 22 1.251 .26

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(a) Identifying and Similarities and Differences
Marzano and his colleagues (2001) draw four generalizations from
the research and theory on identifying similarities and differences (Ross,
1988; Stahl & Fairbanks, 1986; Stone, 1983). The generalizations are as
follows (Marzano, Pickering, & Pollock, 2001): (1) presenting students with
explicit guidance in identifying similarities and differences (Solomon, 1995;
Ross, 1984; Chen, 1996; Reeves & Weisberg, 1994; Gholson, Smither,
Buhrman, & Duncan 1997; Newby, Ertmer, & Stepich, 1995); (2) asking
students to independently identify similarities and differences (Chen,
Yanowitz, & Daehler, 1996; Flick, 1992; Gick & Holyoak, 1980); (3)
representing similarities and differences in graphic or symbolic form (Chen,
1999; Cole & McLeod, 1999; Glynn & Takahashi, 1998); and (4)
identification of similarities and differences can be accomplished in a variety
of ways: comparing (Chen, Yanowitz, & Daehler, 1996; Flick, 1992; Ross,
1987), classifying (Chi, Feltovich, & Glaser, 1981; English, 1997), creating
metaphors (Chen, 1999; Cole & McLeod, 1999; Dagher, 1995), and
creating analogies (Alexander, 1984; Ratterman & Gentner, 1998).
Marzano and his colleagues (2001) define,
Comparing is the process of identifying similarities and
differences between or among things or ideas. Classifying is
the process of grouping things that are alike into categories on
the basis of their characteristics. Creating metaphors is the
process of identifying a general or basic pattern in a specific
topic and then finding another topic that appears to be quite
different but that has the same general pattern. Creating

124
analogies is the process of identifying relationships between
pairs of concepts - in other words, identifying relationships
between relationships (p. 17).

Technically, the researcher notes that the term comparing refers to
the process of identifying similarities, and the term contrasting refers to the
process of identifying differences. Most educators, however, use the term
comparing to refer to both (Marzano, Pickering, & Pollock, 2001).
(b) Summarizing and Note Taking
Marzano and his colleagues (2001, pp 30-48) extract three
generalizations from researchers (Anderson & Hidi, 1988/1989; Hidi &
Anderson, 1987): (1) to effectively summarize, students must delete some
information, substitute some information, and keep some information
(Kintsch, 1979; van Dijk, 1980); (2) to effectively delete, substitute, and
keep information, students must analyze the information at a fairly deep
level (Rosenshine, Meister, & Chapman, 1996; Rosenshine & Meister,
1994); and (3) being aware of the explicit structure of information is an aid
to summarizing information(Meyer, 1975; Meyer & Freedle, 1984).
(c) Reinforcing Effort and Providing Recognition
The researchers (Marzano, Pickering, & Pollock, 2001) draw two
generalizations from the research on effort: (1) not all students realize the
importance of believing in effort, and (2) Students can learn to change their
beliefs to an emphasis on effort. The research on effort is based on the
psychologist Bernard Weiner (Weiner, 1972; Weiner, 1983) who researched
attribution theory on the notion that a belief in effort ultimately pays off in

125
terms of enhanced achievement. Among four attributes, such as ability,
effort, other people, and luck of success, belief in effort is clearly the most
useful attribution (Marzano et al., 2001, p.50).
(d) Homework and Practice
Researchers find that there are four generalizations that can guide
teachers in the use of homework (Marzano et al., 2001). First, the amount
of homework assigned to students should be different from elementary to
middle school to high school (Cooper, 1989a, 1989b; Cooper, Lindsay, Nye,
& Greathouse, 1998). Secondly, parent involvement in homework should
be kept to a minimum (Balli, Demo, & Wedman, 1998; Balli, Wedman, &
Demo, 1997; Perkins & Milgram, 1996). Thirdly, the purpose of homework
should be identified and articulated (Foyle, Lyman, Tompkins, Perne, &
Foyle, 1990; Foyle & Bailey, 1988). Fourthly, if homework is assigned, it
should be commented on (Walberg, 1999). Marzano and his colleagues
(2001) point out three classroom practice in assigning homework: (1)
establish and communicate a homework policy, (2) design homework
assignments that clearly articulate the purpose and outcome, and (3) vary
the approaches to providing feedback. These researchers also point out
that mastering a skill requires a fair amount of focused practice and while
practicing, students should adapt and shape what they have learned
(Marzano, Pickering, & Pollock, 2001).

126

(e) Nonlinguistic Representations
Research and theory on nonlinguistic representations support two
generalizations (Guezzetti, Snyder, & Glass, 1993; Hattie, Biggs, & Purdie,
1996; Walberg, 1999): a variety of activities produce nonlinguistic
representations and nonlinguistic representations should elaborate on
knowledge. Marzano and his colleagues (2001) emphasize that each of the
following activities enhances the development of nonlinguistic
representations of the content: creating graphic representations (Griffin,
Simmons, & Kameenui, 1992; Horton, Lovitt, & Bergerud, 1990; Robinson &
Kiewra, 1996), making physical models (Welch, 1997), generating mental
pictures (Muehlherr & Siermann, 1996; Wiloughby, Desmarias, Wood,
Slims, & Kalra, 1997), drawing pictures and pictographs (Macklin, 1997;
Newton, 1995), and engaging in kinesthetic activity (Aubusson, Foswill,
Barr, & Perkovic, 1997; Druyan, 1997). Also, researchers note that
nonlinguistic representations should elaborate on knowledge (Wiloughby,
Desmarias, Wood, Slims, & Kalra, 1997; Woloshyn, Wiloughby, Wood, &
Pressley, 1990).
Marzano and his colleagues (2001) state that although graphic
organizers combine the linguistic mode in that they use words and phrases,
the nonlinguistic mode of symbols and arrows represent relationships.
Classroom practice in nonlinguistic representation includes creating graphic
organizers (Hyerle, 1996): descriptive patterns, time-sequence patterns,

127
process/cause-effect patterns, episode patterns, generalization/principle
patterns, and concept patterns. These are important to consider because
they assist students to move from one level of the cognitive process
dimension to another level in acquiring different types of knowledge. As
students move from the acquisition of factual knowledge to procedural
knowledge, the cognitive dimension shifts from remembering to
understanding and from understanding to applying. This experience is
cognitively demanding for students. When using graphic organizers and
nonlinguistic representations to assist students’ to build connections from
one level of knowledge or cognition to another level through visual
representations, this helps them to process new knowledge with explicit
visual representations which makes their understanding of the knowledge to
be comprehensible.
(f) Cooperative Learning
Researchers (Johnson & Johnson, 1999) find that cooperative
learning has an effect size of .78 when compared with instructional
strategies in which students work on tasks individually without competing
with one another. Johnson and Johnson (1999) define five elements of
cooperative learning: positive interdependence, face-to-face promote
interaction, individual and group accountability, interpersonal and small
group skills, and group processing. Three generalizations can be used to
guide the use of cooperative learning (Lou, Abrami, Spence, Paulsen,
Chambers, & d’Apollonio, 1996; Scheerens & Bosker, 1997; Walberg,

128
1999): (1) organizing groups based on ability levels should be done
sparingly, (2) cooperative groups should be kept rather small in size, and
(3) cooperative learning should be applied consistently and systematically,
but not overused. For the grouping patterns, there are three types:
informal, formal, and base groups (Johnson & Johnson, 1999). The
researchers state,
Informal groups (e.g., pair-share, turn-to-your-neighbor) are
ad hoc groups that last from a few minutes to a class period.
They can be used to clarify expectations for tasks, focus
students’ attention, allow students time to more deeply
process information, or to provide time for closure. … Formal
groups are designed to ensure that the students have enough
time to thoroughly complete an academic assignment;
therefore, they may last for several days or even weeks.
When using formal groups, the teacher designs tasks to
include the basic cooperative learning components: positive
interdependence, group processing, appropriate use of social
skills, face-to-face promotive interaction, and individual and
group accountability… Base groups are long-term groups
(e.g. for the semester or year) created to provide students
with support throughout a semester or an academic year
(Johnson & Johnson, 1999, as cited in Marzano et el., 2001,
pp. 89-90).

(g) Setting Objectives and Providing Feedback
From research findings (Lipsey & Wilson, 1993; Walberg, 1999),
Marzano and his colleagues draw three generalizations on goal setting: (1)
Instructional goals narrow what students focus on, (2) Instructional goals
should not be too specific, and (3) Students should be encouraged to
personalize the teacher’s goals. For classroom practice in goal setting,
Marzano and his colleagues (2001) point out that it is certainly important for
a teacher to set goals for students, but it is also important for the goals to

129
be general enough to provide students with some flexibility. One variation
on goal setting is to contract with students for the attainment of specific
goals, for this provides students with a great deal of control over their
learning (Marzano et al., 2001). In addition to the goal setting, Marzano
draw these generalizations to guide the use of feedback: (1) Feedback
should be “corrective” in nature, (2) Feedback should be timely, and (3)
Feedback should be specific to a criterion.
(h) Generating and Testing Hypotheses
The process of generating and testing hypotheses involves the
application of knowledge (Hattie, Biggs, & Purdie, 1996; Lott, 1983; Ross,
1988) and two generalizations can guide the use of hypothesis generation:
(1) Hypothesis generation and testing can be approached in a more
inductive or deductive manner and (2) Teachers should ask students to
clearly explain their hypotheses and their conclusions. Marzano and his
colleagues (2001) recommend using a variety of structured tasks to guide
students through generating and testing hypotheses. There are six types of
tasks all employ hypotheses generation and testing: systems analysis,
problem solving, historical investigation, invention, experimental inquiry,
and decision making (See Table 7).

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Table 7, Six Types of Tasks to Generate and Test Hypotheses (Marzano,
Pickering, and Pollock, 2001)

Systems Analysis
1. Explain the purpose of the system, the parts of the system, and
the function of each part.
2. Describe how the parts affect each other.
3. Identify a part of the system, describe a change in that part, and
then hypothesize what would happen as a result of this change.
4. When possible, test your hypothesis by actually changing the part
or by using a simulation to change the part.
Problem Solving
1. Identify the goal you are tying to accomplish.
2. Describe the barriers or constraints that are preventing you from achieving
your goal - that are creating the problem.
3. Identify different solutions for overcoming the barriers or constraints and
hypothesize which solution is likely to work.
4. Try your solution – either in reality or through a simulation.
5. Explain whether your hypothesis was correct. Determine if you want to
test another hypothesis using a different solution.
Historical Investigation
1. Clearly describe the historical event to be examined.
2. Identify what is known or agreed on and what is not known or about which
there is disagreement.
3. Based on what you understand about the situation, offer a hypothetical
scenario.
4. Seek out and analyze evidence to determine if your hypothetical scenario
is plausible.
Invention
1. Describe a situation you want to improve or a need to which you want to
respond.
2. Identify specific standards for the invention that would improve the
situation or would meet the need.
3. Brainstorm ideas and hypothesize the likelihood that they will work.
4. When your hypothesis suggests that a specific idea might work, begin to
draft, sketch, or actually create the invention.
5. Develop your invention to the point where you can test your hypothesis.
6. If necessary, revise your invention until it reaches the standards you have
set.
Experimental Inquiry
1. Observe something of interest to you and describe what you observe.
2. Apply specific theories or rules to explain what you have observed.
3. Based on your explanation, generate a hypothesis to predict what would
happen if you applied the theories or rules to what you observed or to a
situation related to what you observed.
4. Set up an experiment or engage in an activity to test your hypothesis.
5. Explain the results of your experiment or activity. Decide if your
hypothesis was correct and if you need to conduct additional experiments
or activities or if you need to generate and test an alternative hypothesis.
Decision making
1. Describe the decision you are making and the alternatives you are
considering.
2. Identify the criteria that will influence the selection and indicate the
relative importance of the criteria by assigning an importance
score from a designated scale, for example 1-4.
3. Rate each alternative on a designated scale (e.g., 1-4) to indicate
the extent to which each alternative meets each criterion.
4. For each alternative, multiply the importance score and the rating
and then add the product to assign a score for the alternative.
5. Examine the scores to determine the alternative with the highest
score.
6. Based on your reaction to the selected alternative, determine if
you need to change any importance scores or add or drop criteria.

Finally, Marzano and colleagues (2001) suggest that teachers can
design assignments, so that students know they must be able to describe

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how they generated their hypotheses and to explain what they learned as a
result of testing: (1) provide students with templates for reporting their work
and highlighting the areas in which they will be expected to provide
explanations; (2) provide sentence stems for students, especially for young
students, to help them articulate their explanations; (3) ask students to turn
in audiotapes on which they explain their hypotheses and conclusions; (4)
provide, or develop with students, rubrics so that they know that the criteria
on which they will be evaluated are based on the quality of their
explanations; and (5) set up events during which parents or community
members ask student to explain their thinking.
(i) Cues, Questions, and Advance Organizers
Cues and questions, as well as advance organizers, are techniques
that call on students’ prior knowledge (Marzano et al., 2001). Marzano and
his colleagues point out that cues involve “hints” about what students are
about to experience. These authors also note that cueing and questioning
are at the heart of classroom practice. Research in classroom behavior
indicates that cueing and questioning might account for as much as 80
percent of what occurs in a given classroom in a given day (Davis &
Tinsley, 1967; Fillippone, 1998); however, teachers are largely unaware of
the extent to which they use cueing and questioning. These generalizations
are suggested: (1) Cues and questions should focus on what is important
as opposed to what is unusual (Alexander & Judy, 1988; Alexander,
Kulikowich, & Schulze, 1994; Rinser, Nicholson, & Webb, 1994);

132
(2) “Higher level” questions produce deeper learning than “lower level”
questions (Fillippone, 1998; Redfield & Rousseau, 1981); (3) “Waiting”
briefly before accepting responses from students that has the effect of
increasing the depth of students’ answers (Swift & Gooding, 1983; Tobin,
1987); and (4) Questions are effective learning tools even when asked
before a learning experience (Hamaker, 1986; Osman & Hannafin, 1994;
Pressley, Wood, Woloshyn, Martin, King, & Menke, 1992).
Research and theory on advance organizers reveal these
discoveries: (1) Advance organizers should focus on what is important as
opposed to what is unusual. (2) “Higher level” advance organizers produce
deeper learning than the “lower level” advance organizers. (3) Advance
organizers are most useful with information that is not well organized. (4)
Different types of advance organizers, such as expository, narrative,
skimming, and illustrated, produce different results (Marzano et al., 2001).
In addition to Marzano’s (2001) nine high yielding strategies that are
research based, classroom management techniques that are research
based, and classroom assessment and grading that work that are research
based, the SIOP model (Echevarria, Vogt, & Short, 2008) which is also
scientifically-based and research-based instruction assist the community
college faculty to promote students’ mathematical understanding.

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2. Sheltered Instruction Observation Protocol (SIOP) Model
The Sheltered Instruction Observation Protocol (SIOP) model is an
empirically-tested, research-based model developed by researchers who
integrate best practices (Echevarria, Vogt, & Short, 2008). The authors
distinguish between the SIOP model as the lesson planning and delivery
system and the SIOP protocol as the instrument used to observe, rate, and
provide feedback on lessons. The SIOP protocol provides concrete
examples of the features of sheltered instruction (SI) that can enhance and
expand teachers’ instructional practice in teaching English language
learners.
The protocol is composed of thirty features grouped into eight main
components: lesson preparation, building background, comprehensible
input, strategies, interaction, practice/application, lesson delivery, and
review/assessment. These components emphasize the instructional
practices that are critical for second language learners as well as high-
quality practices that benefit all students (Echevarria, Vogt, & Short, 2008).
The eight components of the SIOP model are listed in the following table 8.

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Table 8, Eight Components of the SIOP Model
Eight Components
of the SIOP Model
Thirty Features of the Sheltered Instruction Observation
Protocol (SIOP) Model
(Echevarria, Vogt, & Short, 2008)
Lesson
Preparation
1. Content objectives clearly defined, displayed, and reviewed with
students
2. Language objective clearly defined, displayed, and reviewed with
students
3. Content concepts appropriate for age and educational background
4. Supplementary materials used to a high degree
5. Adaptation of content to all levels of student proficiency
6. Meaningful activities that integrate lesson concepts
Building
Background
7. Concepts explicitly linked to students’ background experiences
8. Links explicitly made between past learning and new concepts
9. Key vocabulary emphasized
Comprehensible
Input
10. Speech appropriate for students’ proficiency level
11. Clear explanation of academic tasks
12. A variety of techniques used to make content concepts clear
Strategies
13. Ample opportunities provided for students to use learning
strategies
14. Scaffolding techniques consistently used, assisting and
supporting student understanding
15. A variety of questions or tasks that promote higher-order
thinking
Interaction
16. Frequent opportunities for interaction and discussion between
teacher/student and among students, which encourage
elaborated responses about lesson concepts
17. Grouping configurations support language and content
objectives of the lesson
18. Sufficient wait time for student responses consistently
provided
19. Ample opportunities for students to clarify key concepts in L1
as needed with aide, peer, or L1 text
Practice and
Application
20. Hands-on materials and/or manipulatives provided for
students to practice using new content knowledge
21. Activities provided for students to apply content and language
knowledge in the classroom
22. Activities integrate all language skills (i.e, reading, writing,
listening, and speaking)
Lesson
Delivery
23. Content objectives clearly supported by lesson delivery
24. Language objectives clearly supported by lesson delivery
25. Students engaged approximately 90% to100% of the period
26. Pacing of the lesson appropriate to the students ability level
Review and
Assessment
27. Comprehensive review of key vocabulary
28. Comprehensive review of key content concepts
29. Regular feedback provided to students on their output (e.g.,
language, content, work)
30. Assessment of student comprehension and learning of all
lesson objectives (e.g., spot checking, group response)
throughout the lesson

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C. Classroom Management
When comparing classroom management with the solar system
within community college context, a community college faculty is like the
sun who is at the center of the class realizing the objectives of the
AMATYC’s standards of intellectual development, content, and pedagogy to
engage all students in learning. The teacher is like the sun generating
gravity to maintain its functional orderly learning environment. Without the
its gravitational pull of the effective classroom management approaches,
the learning environment will fall into chaos and student learning is less
likely to take place without the effective management techniques. Just like
the entire solar system is engaged in its function and order effectively
through the gravitational force, the classroom management within a
classroom is a powerful force to set the tone of the learning to take place.
The importance of classroom management can not be over emphasized.
The importance of classroom management is emphasized by
Marzano, Marzano, and Pickering (2003),
Effective teaching and learning cannot take place in a poorly
managed classroom. If students are disorderly and
disrespectful, and no apparent rules and procedures guide
behavior, chaos becomes the norm. In these situations, both
teachers and students suffer. Teachers struggle to teach, and
students most likely learn much less than they should. In
contrast well-managed classroom provide an environment in
which teaching and learning can flourish. But a well-managed
classroom doesn’t just appear out of nowhere. It takes a good
deal of effort to create – and the person who is most
responsible for creating it is the teacher (p. 1).

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The core of the teaching process is the arrangement of environments within
which the students can interact and study how to learn (Dewey, 1916, as
cited in Joyce, 1996). To create this environment for students interact and
learn, Marzano, Marzano, and Pickering (2003) recommend these seven
action steps: (1)get off to a great start by beginning with a strong first day of
class, (2) establish specific effective rules and procedures by involving
students, (3) implement appropriate and inappropriate disciplinary
interventions with clear limits, (4) foster productive student-teacher
relationships with the awareness in student needs with techniques, (5)
develop a positive mental set and withitness and maintain a healthy
emotional objectivity, (6) provide students with self-monitoring and control
strategies by helping students to contribute, and (7) activate schoolwide
measures for effective classroom (see Figure 6).

Figure 6, Classroom Management That Works (Marzano et al, 2003)

6. Provide students
with self-monitoring
and control strategies
by helping students to
contribute
5. Develop a positive
mental set and
withitness and
maintain a healthy
emotional objectivity
4. Foster productive
student-teacher
relationships with the
awareness in student
needs with techniques
2. Establish specific
effective rules and
procedures by
involving students
1. Get off to a great
start by beginning with
a strong first day of
class
Classroom
Management That
Works
(Marzano et al.,
2003)
7. Activate
schoolwide measures
for effective classroom
management
3. Implement
appropriate and
inappropriate
disciplinary
interventions with
clear limits

When designing the curriculum, Marzano (2003) considers a
guaranteed and viable curriculum as the first factor having the most impact
on student achievement. The researcher indicates that a guaranteed and
viable curriculum is primarily a combination of two factors called
“opportunity to learn” and “time” (Marzano, 2000a). Marzano defines the
opportunity to learn (OTL) as a prominent factor in student achievement.
Marzano (2003) notes that OTL is the discrepancy between the intended
curriculum and the implemented curriculum. Marzano explains that the
137

138
intended curriculum is content specified by the state, district, or school to be
addressed in a particular course or at a particular grade level. The
implemented curriculum is content actually delivered by the teachers, and
the attained curriculum is content actually learned by students. Marzano
notes, “The viable curriculum is unattainable without the benefit of time.
The content that teachers are expected to address must be adequately
covered in the instructional time teachers have available (pp. 23-24).”
Marzano (2003) emphasizes,
The concept of OTL, then, is a simple but powerful one - if
students do not have the opportunity to learn the content
expected of them, there is little chance that they will. OTL
addresses the extent to which the curriculum in a school is
“guaranteed.” This means that states and districts give clear
guidance to teachers regarding the content to be addressed in
specific courses and at specific grade levels. It also means
that individual teachers do not have the option to disregard or
replace assigned content (p. 24).

Also, in addition to the viable curriculum, Marzano (2006) finds one
aspect of teaching that is frequently overlooks in discussions of ways to
enhance student achievement: classroom assessment. The author finds
that formative assessment does improve learning, and effective formative
assessments should encourage students to improve by involving students
tracking their progress on specific measurement topics using graphs,
engaging students in different forms of self-reflection regarding their
progress on measurement topics, and estimating students’ true scores at
the end of a grading period (see figure 7).

Figure 7, Assessment Items (Marzano et. al, 2003)
Basic
details
and skills
Inferences
or
application
Complex
ideas and
processes
Assessment Items (Marzano et. al.,2003)

Most importantly, Marzano (2006) states that the effective
assessments should encourage students to improve learning and the
positive effects of feedback are not automatic. He asserts that one of the
most powerful and straightforward ways a teacher can provide feedback
that encourages learning is to have students keep track of their own
progress. Another way to encourage student learning is to ensure that
students have an opportunity to reflect on their learning using information
derived from classroom assessments by allowing students to engage in
self-assessment (Stiggins, Arter, Chappuis, & Chappuis, 2004) and
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140
stimulating self-reflection to have students articulate their perceptions
regarding their learning (Cross, 1998) while planning for the ultimate goal of
assessing students on measurement topics is to estimate their learning at
the end of the grading period. When assessing and computing final scores
for grades, Marzano (2006) notes, “Computer software should allow
teachers to easily enter multiple topic scores for an assessment, should
provide for the most accurate estimate of a student’s final score for each
topic, and should provide graphs depicting student progress (p.124).”
Overall, this chapter two focuses on literature review for the demand
of learning within a knowledge economy. Within the knowledge society that
values learning, teaching plays a significant role in student learning.
Teachers who deliver effective teaching provide the knowledge and skills
resources for the knowledge society to students. Realizing the importance
of the teacher’s role, chapter two supports its research evidence on teacher
self-efficacy, community mathematics faculty, and their effective practice.
Many research-based strategies along with the AMATYC’s standards, direct
instruction, and knowledge and cognitive process dimensions are described
to explain the quality of effective instruction. To explore the relationship
among these variables, the next chapter explains about the research design
of the variables.

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Chapter Three

Methodology
Introduction
The purpose of this study is to explore the relationship between the
self-efficacy of community college mathematics faculty and their
instructional practice. The research question I will be addressing is as
follows: What Is the Relationship between Self-efficacy of Community
College Mathematics Faculty and Effective Instructional Practice? After
defining the problem in chapter one and reviewing the literature in chapter
two, the methodology for this study included the following steps: (1) identify
the relevant variable, select appropriate subjects, select or develop
appropriate measuring instruments, and select the approach that fits the
problem; (2) collect the data; (3) and analyze and interpret the results
(Isaac & Michael, 1997). This study will build upon existing knowledge of
the relationship between faculty’s self-efficacy and their instructional
practice. Additionally, this study will be beneficial to educators,
researchers, the lay public, and policymakers in assisting faculty to expand
their repertoire of pedagogical skills and exploring effective research based
instructional strategies to meet the needs of diverse students.
Research Objectives and Background
Current researchers are challenged to go beyond socioeconomic
status in the search for school-level characteristics that makes a difference

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in student achievement (Hoy, Tarter, & Woolfolk Hoy, 2006). Highly self-
efficacious teachers tend to invest more effort and persist longer than those
low in self-efficacy (Schwarzer & Schmitz, 2000). When setbacks occur,
these teachers recover more quickly and maintain commitment to their
goals by allowing people to select challenging settings, explore their
environment, or create new ones. Schwarzer and Schmitz (2000) believe
that teachers high in self-efficacy are found to sacrifice more leisure time for
their students than their less self-efficacious counterparts. Teachers’ sense
of efficacy has a strong positive link to student performance (Tschannen-
Moran & Hoy, 2001) and is related significantly to teachers’ success (Armor
et el., 1976).
A Description of the Research Design
The design of this study included a mixed methodology of
quantitative and qualitative approaches. This is a correlational study to
investigate the extent to which variations in one factor correspond with
variations in one or more other factors based on correlation coefficients
(Isaac & Michael, 1997). The quantitative study used three surveys:
demographic, self-efficacy, and faculty perceived ability and effectiveness
on three strands of American Mathematics Association of Two-Year
Colleges’ (AMATYC) and Marzano’s instructional strategies. Each survey
took about ten to fifteen minutes to complete. The qualitative study was
based upon observations and interviews. The observations consisted of six

143
faculty members during their mathematics class session, and that was
followed by interviews of the same faculty.
The purpose and rationale of these surveys were to generalize from
a sample to a population, so that inferences can be made about some
characteristic, attitude, or behavior of this population (Babbie, 1990, as
cited in Creswell, 2003) by correlating between the self-efficacy of
mathematics community college faculty and their instructional practices.
The surveys were selected for these reasons: the economy of the design,
the rapid turn around, analysis of returns, check for response bias, capacity
to run a descriptive analysis, capability to collapse items into scales, check
for reliability of scales, and run inferential statistics to answer the research
questions (Creswell, 2003).
The surveys included cross-sectional data collected during the Fall
semester 2007 and Winter 2008. The form of random data collection was
self-administered questionnaires. The survey design provided a
quantitative description by using Likert-like scale of numerical values to
measure community college mathematics teachers’ self-efficacy in the
population of community college mathematics part time and full time
teachers. This survey design provided a quantitative or numeric description
of trends, attitudes, or opinions of a population of community college
faculty. From the sample results, I can generalize or make claims about the
population (Creswell, 2003).

144
1. Demographic Survey
The purpose of the demographic survey is to discover the
relationship between the faculty’s demographic information and their level
of self-efficacy. The demographic survey incorporated these items: number
of years in teaching, education level, gender, full time or part time status,
age range, ethnicity, number of years in teaching, K-12 experience, highest
degree, number of units one teaches per semester, type of math course,
department collaboration opportunity, and teaching methods which focuses
on Marzano and his colleagues’ research based strategies.
2. Self-efficacy Survey
The survey instrument for this study was called Teachers’ Sense of
Efficacy Scale (long form). This instrument was designed by Tschannen-
Moran and Woolfolk Hoy in 2001. Permission was obtained to use the
survey instrument. The questionnaire contains 24 items. All the items were
on a Likert scale from “nothing” to “a great deal.” The Likert scale included
the following components:
Nothing Very little Some influence Quite a bit A great deal
(1) (2) (3) (4) (5) (6) (7) (8) (9)
In order to be context specific for the community college setting,
there were three item modifications. These were items 4, 6, and 13 (See
Appendix B). For items 4 and 6, the phrase “school work” was changed to
“learning math.” For item 13, the word “children” was changed to “students”
to target community college students. Therefore, these three questions

145
looked like this: How much can you do to motivate students who show low
interest in learning Math? How much can you do to get students to believe
they can do well learning Math? How much can you do to get students to
follow classroom rules?
Among the 24-items, eight items were to measure efficacy in student
engagement. These items were questions: 1, 2, 4, 6, 9, 12, 14, and 22.
1. How much can you do to get through to the most difficult students?
2. How much can you do to help your students think critically?
4. How much can you do to motivate students who show low interest in
learning Math?
6. How much can you do to get students to believe they can do well
learning Math?
9. How much can you do to help your students value learning?
12. How much can you do to foster student creativity?
14. How much can you do to improve the understanding of a student who
is failing?
22. How much can you assist families in helping their children do well in
school?
To measure efficacy in instructional strategies, there were eight
items: Items 7, 10, 11, 17, 18, 20, 23, and 24.
7. How well can you respond to difficult questions from your students?
10. How much can you gauge student comprehension of what you have
taught?

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11. To what extent can you craft good questions for your students?
17. How much can you do to adjust your lessons to the proper level for
individual students?
18. How much can you use a variety of assessment strategies?
20. To what extent can you provide an alternative explanation or example
when students are confused?
23. How well can you implement alternative strategies in your classroom?
24. How well can you provide appropriate challenges for very capable
students?
To measure efficacy in classroom management, another eight items
were listed: Items 3, 5, 8, 13, 15, 16, 19, and 21.
3. How much can you do to control disruptive behavior in the classroom?
5. To what extent can you make your expectations clear about student
behavior?
8. How well can you establish routines to keep activities running smoothly?
13. How much can you do to get students to follow classroom rules?
15. How much can you do to calm a student who is disruptive or noisy?
16. How well can you establish a classroom management system with
each group of students?
19. How well can you keep a few problem students from ruining an entire
lesson?
21. How well can you respond to defiant students?

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With the second survey, revised survey of Tschannen-Moran and Woolfolk
Hoy, I developed a third survey to measure self-perceived ability and
effectiveness.
3. The Survey to Measure Self-perceived Ability and Effectiveness
with AMATYC Strands and Marzano’s Instructional Strategies
To measure the community college mathematics faculties’ self-
perceived ability and effectiveness, American Mathematical Association of
Two-Year Colleges’ (AMATYC) three strands were integrated into the
survey as key components of delivering effective mathematics instruction.
The strands were as follows: intellectual development, content, and
pedagogy. In addition to these three strands, Marzano’s research based
instructional strategies were used as a barometer for delivering effective
instruction. Then, each construct was divided into three columns on the
survey. The left column described the self-perceived scale about the
faculty’s ability. The middle column included the standards for each strand.
The right column contained the faculty’s effectiveness. Therefore, the eight
constructs were as follows: intellectual ability, intellectual development
effectiveness, content ability, content effectiveness, pedagogy ability,
pedagogy effectiveness, Marzano’s instructional strategy ability, and
Marzano’s instructional strategy effectiveness. These constructs were
chosen because effective community college mathematics instruction
should contain many of the three mathematics standards and research
based high-yielding instructional strategies that moved domains of students’

148
knowledge from factual, conceptual, procedural, to metacognitive and
cognitive processes from the state of knowing, understanding, applying,
analyzing, evaluating, to creating domains (Anderson & Krathwohl, 2001).
Methods and Procedures for the Study
I delivered the surveys to the colleges and gave them to the
department chair to be placed in the faculty’s boxes in a self-addressed and
stamped envelope. When permission was given by the department chair, I
attended a mathematics department meeting at two different campuses to
explain the rationale of the study to the faculty and present the need for the
research in this field.
To describe the quantitative statistical analysis, SPSS software was
used to analyze the data after its collection. Correlation was measured for
the independent variable of self-efficacy: student engagement, classroom
management, and instructional strategy. In addition, correlation was
analyzed with the dependent variable of instructional practices with eight
constructs. Descriptive statistics provided about the demographic survey of
the population. Using correlation analyses, bidirectional relationships
between two variables was explored between constructs of self-efficacy and
AMATYC’s mathematics standards and research based instructional
strategies.
The data analyzed with a series of frequency distributions that
measures reliability analysis scale, correlations, descriptive statistics that
indicated mean, standard deviation, number of participants. It included the

149
Pearson correlations to indicate the strength of the relationship between
two constructs along with the statistical significance. Correlations were
analyzed for the self-reporting three constructs of self-efficacy. Then, these
constructs were correlated with other constructs to measure whether the
constructs of self-efficacy were positively related with the constructs of
mathematics instruction to deliver effective instruction.
Data Analysis Procedures
To analyze the data, I applied Creswell’s (2003) three steps. First, I
reported information about the number of members of the sample who did
return the survey by creating a table with numbers and percentages
describing respondents. This was done via the SPSS software on the data
view. Secondly, I planed to provide a descriptive analysis of data for
independent variables of efficacy in student engagement, instructional
strategies, and classroom management and dependent variable of basic
skills mathematics teachers’ self-efficacy in this study. The analysis
indicated the means, standard deviations and range of scores for three
variables. Thirdly, since the instrument contained scales, I combined items
into scales. I identified the statistical procedure, such as descriptive
analysis of frequencies. I checked for reliability for the internal consistency
of the scales, such as the Cronbach alpha statistic. Lastly, the research
question was tested by using the SPSS software with the significance levels
of reliability and the strength of the correlations. The assumptions
associated with the number of independent and dependent variables was

150
measured and correlated with the constructs of self-efficacy and
instructional practice.
After the collection of the survey data, it was analyzed by using the
SPSS software. Six mathematics teachers were selected for interviews and
classroom observations. After interviewing the faculty members with a set
of pre-developed questions, faculty members’ instructional practice was
observed that was based on the standards of intellectual development and
pedagogy of 2006-2011 AMATYC, direct instruction, and research-based
strategies. In addition, the data analysis involved interpreting the data,
comparing the findings with past literature and theory, raising questions,
and advancing an agenda for reform (Creswell, 2003) with
recommendations.
Interviews of Six Community College Mathematics Faculty
The interview participants were selected by their permission on the
consent form. On the form, it asked the participant’s permission to be
contacted for an interview and classroom observation. If the participant
agreed, he/she checked a box to acknowledge the agreement by identifying
email address. The interview took about 30 to 40 minutes.
The interview questions began with a question that asks for relatively
straight forward descriptions that required minimal recall and interpretation
(Patton, 2002). Questions about the present tended to be easier for
respondents than questions about the past: therefore, the questions used
the present as a baseline; then, the questions extended to the future

151
(Patton, 2002) dealing with what one can do or the institution can do to
improve the current status of instructional practice. After explaining the
background information on AMATYC the interview questions were
composed of the AMATYC’s standards of three mathematics strands:
intellectual development, content, and pedagogy. There were standards for
each strand. For the intellectual development strand, the standards were
as follows: problem solving, modeling, reasoning, connecting with other
disciplines, communicating, using technology, developing mathematical
power, and linking multiple representations. For the content strand, there
were six standards: number sense, symbolism and algebra, geometry and
measurement, function sense, continuous and discrete models, and data
analysis, statistics, and probability. The pedagogy strand included these
standards: teaching with technology, active and interactive learning,
making connections, using multiple strategies, and experiencing
mathematics. In addition, there were open-ended questions that allowed
the interviewee to select from a full repertoire of possible responses those
that are most salient to one’s feelings, thoughts, and experiences (Patton,
2002).
Observations of Six Community College Mathematics Faculty
I focused on four instructional approaches to measure the
instructional effectiveness of six community college mathematics teachers.
In order to collect the qualitative data, I paid close attention to the teachers’
instructional approaches as well as looked at the self-efficacy constructs of

152
student engagement, instructional strategies, and classroom management.
While observing the teaching, I wrote down the specific approach with the
context of the mathematics problem. I also interpreted what was being
taught in terms of the dimensions of knowledge and cognitive processes
(Anderson & Krathwohl, 2001) to measure the depth of the knowledge and
cognition of the input for students.
Each observation page was made of two-columns. One column
occupied two-thirds of the page that included notes on teacher observation
while one-third contained my interpretation and comments. For the teacher
observation, I paid attention to student responses to measure their
understanding. During this observation process, I was reminded about
Patton’s emphasis on several advantages of direct and personal contact for
an observational setting. Patton (2002) pointed out the following: (a)
Through direct observations, the inquirer is better able to understand and
capture the context; (b) Firsthand experience with a setting and the people
in the setting allows an inquirer to be open, discovery oriented, and
inductive; (c) The inquirer has the opportunity to see things that may
routinely escape awareness among people in the setting; and (d) The
chance to learn things that people would be unwilling to talk about in an
interview. At the same time, I made connections that went beyond what
can be fully recorded by an inquirer:
Finally, getting close to the people in a setting though
firsthand experience permits the inquirer to draw on personal
knowledge during the formal interpretation stage of analysis.

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Reflection and introspection are important parts of field
research. The impressions and feelings of the observer
become part of the data to be used in attempting to
understand a setting and the people who inhabit it. The
observer takes in information and forms impressions that go
beyond what can be fully recorded in even the most detailed
field notes (Patton, 2002, p. 264).

The observation began by drawing on my personal knowledge with
reflection and introspection to collect data and infer to make connections
among instructional approaches with self-efficacy constructs. I tried to
maintain objectivity and neutrality by following these instructional
approaches: eight standards of AMATYC’s intellectual development, five
standards of AMATYC’s pedagogy standards, five phases of direct
instruction, and nine research-based instructional strategies of Marzano.
The eight intellectual development standards were as follows:
problem solving, modeling, reasoning, connecting with other discipline,
communication, using technology, developing mathematical power, and
linking multiple representation. Next, five pedagogy standards incorporated
teaching with technology, active and interactive learning, making
connections, using multiple representations, and experiencing mathematics.
In addition, direct instruction included five phases: orientation,
presentation, highly guided practice, guided practice, and independent
practice (Joyce, Weil, & Calhoun, 2004). Lastly, research based strategies
integrated Marzano’s high yielding strategies that work: identifying
similarities and differences, summarizing and note-taking, recognizing effort
and providing recognition, homework and practice, nonlinguistic

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representations, cooperative learning, setting objectives and providing
feedback, testing and generating hypotheses, and questions, cues, and
advance organizers (Marzano, Pickering, & Pollock, 2001). After the written
data were compiled, I checked the frequencies of approaches and
interpreted the data on a scale and added the total value. The mean score
for the instructional approaches were calculated. In addition to the
instructional mean scores, I calculated the mean scores for the teacher’s
self-efficacy by using the exact self-efficacy survey (revised survey of
Tschannen-Moran and Woolfolk Hoy, 2001). This survey is the one that
participants used to measure their efficaciousness.
The Population and Sampling Procedures
The target population sample for this survey was 50 community
college mathematics full and part time instructors who taught mathematics
classes in Southern California. The study took place at five community
colleges that were located in an urban (one college), suburban (three
colleges), and rural (one college) settings. I did not receive, nor did the
institution receive any financial support for conducting this research. The
iStar application for the internal review board of an exempt review for this
study has been requested and approved (USC UPIRB #: UP- 07- 00304).
This research involved the use of survey procedures, observations, and
interview procedures of community college faculty’s instructional practice.
The sampling design for this population was cluster sampling.
Each faculty member in the population had an equal probability of being

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selected due to randomization. However, if faculty members were not
available, then a less desirable non-probability sample that was known as a
convenience sample was used in which respondents were chosen based
on their convenience and availability (Babbie, 1990, as cited in Creswell,
2003).
The Survey Responses from Five Colleges
College A
The department chair of College A suggested that I bring 80 surveys.
Out of the 80 delivered surveys, I received 29 completed surveys. I did not
receive any blank surveys from this college. The department chair provided
an opportunity for me to explain to the math department about this
research. As a result of this presentation and the opportunity to meet with
the faculty to explain my study, I received permission from five mathematics
teachers to interview and observe their classes. Out of the five permission
letters, I chose to interview and observe three faculty members based on
their availability.
College B
Although a phone call was made to the dean of College B asking for
her permission to deliver and leave the surveys with the mathematics
department chair, the reception was very impersonal and cold. The dean
made this comment three times to me with a stern look, “You understand
that everyone is busy that I cannot guarantee that this will be filled out by
the mathematics faulty.” When I replied to the dean that I absolutely

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understand that there are no guarantees of receiving the completed
surveys, but if possible, please have the mathematics department chair
place the surveys in the faculty’s boxes.” It was not so much what the dean
said, but the tone of the voice that was very oppressing and authoritative
that caused me to feel that I was not welcome.
When I walked out of the dean’s office, I felt very small. Somehow, I
felt that as one professional educator to another professional educator, I
would have been treated differently. I was wondering if they treat an
educated professional this way, how will they treat a first generation new
college student or parent who does not speaking the English language
fluently. After receiving an unwelcoming reception by the dean, I stopped
by the president’s office to let the president know how unwelcoming the
dean’s reception was. The secretary introduced me to another dean
because the president was absent. After explaining the situation to the
second dean and exchanging phone numbers, later that day I received a
personal phone call from the second dean that my behavior of wanting to
talk with the president was not appropriate.
I felt helpless and unimportant by the institutional reaction of College
B. The spacious campus layout of various buildings did not look very
cohesive to meet the needs of the public. The buildings looked like they
were empty shells that lacked systemic capacity to allow pearls of student
learning to grow within due to the void of human relationships and caring
culture to the public.

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College C
I received four permission letters from College C and selected three
mathematics teachers to observe and interview based upon their
availability. The faculty members of College C shared their struggles and
challenges willingly and candidly during the interview. Although I am a
visitor to the college, I felt that they valued my presence as a graduate
student. The positive acceptance made a difference in my perception of the
college while I spent the entire day interviewing and gathering observation
data from 8:00 am till 10:00 pm in January. I wondered whether the
positive reception was because I graduated from this college about two
decades ago and taught mathematics classes as a part time adjunct faculty
member five years ago.
College D
Interestingly, this college took the second longest to grant
institutional approval. After contacting the dean, the dean told the
mathematics department chair that the faculty’s cooperation is totally up to
them. It took over a month to speak with the department chair after
numerous attempts with emails and phone calls. Finally, I was asked to
drop off the surveys at his office. It was surprising and exhausting as to
how long and how much effort it took to contact the department chair at the
main campus. Could this slow pace, non-welcoming, isolating, and non-
caring approach be the culture of this college in terms of working with the
public? I wondered about students on this campus. I thought about the

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students in the department chair’s mathematics classes. Walking away
from the concrete building after delivering the surveys where the
department chair office was located on the main campus, the walls looked
so high that almost seemed like that they were blocking the sunlight
causing an environment where nothing can grow under the leadership on
the campus.
College E
The contact process with the institutional dean at one of the satellite
campus took over a month; however, after contacting the department chair,
he was very receptive and invited me to attend a small department meeting
and five faculty members showed interest in completing the surveys at the
satellite campus. I received four surveys from the satellite campus of
College E while I tried to contact the department chair at the main campus.
The academic dean of the main campus was cordial and approachable and
encouraged me to contact the department chair. I sent many emails, made
phone calls, and left notes on the department chair’s desk asking for his
assistance in distributing the surveys. It took more than a month and half
before I finally received a response from him telling me to drop off the
surveys at the dean’s office. Finally, two surveys arrived in my mail box
from the campus.
This experience made me ponder about the difficulty of receiving
cooperation to have the main campus department chair to place the
surveys in the faculty members’ boxes. I, as a researcher, was a total

159
stranger to College E and I understood that they did not have to do anything
for me, but I could not help but to think about the whole culture of the
institution that was portrayed to me by the mathematics department chair.
It was uncooperative, cold, not relational, and not caring to the public.
Again, I wondered about the students in the department chair’s classes. By
the way, from this main campus, I received 11 blank surveys as well. The
juxtaposition of modern buildings and portable buildings on the main
campus seemed disjointed and did not create a harmonious picture in me
about the leadership of the campus.
Special Subject Population
The special subject population, mathematics faculties who were
selected for this study, were not at risk and did not experience coercion to
participate in this study. When taking this survey, the participants were
informed of their right to choose to participate or not to participate. Subjects
were informed of their ability to cease participating at any point if they so
desired. The survey participation was anonymous. All participants were
members or affiliates of a community college faculty in Southern California.
Eligibility for participation was determined by the community college’s
designation as a full time or part time faculty status.
Access to each subject population in this research took place after
receiving the IRB approval at each participating community college in
Southern California. This investigator contacted the institutional
researchers. After contacting them, I sent emails and made phone calls to

160
the department chairs requesting permission to attend a faculty department
meeting in order to deliver the surveys and the consent forms. I made sure
that each survey envelope included a stamped self-addressed envelope to
return to me. Finally, I contacted those participants who agreed to an
interview and observation and arranged appointments.
Financial Obligation, Compensation, and Risk Assessments
Participants did not receive financial compensation for participation.
Also, participants were not required for medical or psychological services as
a consequence of the research. The risk classification for this study was
minimal. There were no known risks associated with participation in this
research study. However, precautions were taken to minimize any harm
from filling out survey forms, observations, and interviews. Although this
study included only minimal risks to participants, this study was monitored
closely by the principal investigator to make sure that the survey was in
working order and that the data were kept securely at all phases of the data
collection.
Potential Benefits and Alternatives
This study was to benefit the community college faculty by increasing
their knowledge of how the self-efficacy of teachers and their instructional
practice are related. This knowledge might influence the faculty’s teaching
to promote student achievement. In addition, it might create an
understanding of the role of community college instructors as mediators
between K-12 and four year higher education learning institutions. All

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participants had a choice to not participate in this study or withdraw from
participation at any phase.
Limitations
The limitations of this study may have been that without the
qualitative observational data, the quantitative survey data alone could have
generated the result of the study that could have been possibly, not reliable,
not correlated, negatively correlated, or statistically insignificant. Another
limitation was that it did not represent everyone who taught community
college Mathematics due to a small sample of fifty instructors. The random
sample population was a ratio of the entire possible selection. Matsumoto
(2000) noted that,
Truth and knowledge are bounded, however, by the
conditions, parameters, and limitations of the studies that
produced that knowledge. All studies are bounded in some
fashion by these parameters, whether established through
conscious decisions or by default. These limitations apply to
all research in all social sciences, regardless of field or
discipline (p. 135).

Realizing this limitation, this study was to find the relationship between self-
efficacy of community college math faculty and their instructional practice.
Based on the mixed methodology of quantitative and qualitative
research finings, I began collecting data. As soon as the quantitative data
arrived, I began inputting the data into SPSS software to identify reliabilities
and correlations. In the meantime, I contacted six faculty members to
arrange for an interview and observation. The results of the qualitative data
presented a different finding from the quantitative data.

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Chapter 4

Results

Introduction
The results of this study stem from contacting five community
colleges in Southern California upon receiving the Institutional Review
Board (IRB) approval from the University Southern California in October
2007 (USC UPIRB #: UP-07-00304). After receiving approval for the
research from each of the five community college institutional boards and
contacting the academic and instructional dean of each college, the
permission to conduct research is granted by the dean. E-mails and phone
calls are used to contact the mathematics department chairs. Then, 277
surveys are delivered with stamped and self-addressed envelopes: 80
surveys for College A, 45 surveys for College B, 12 surveys for College C,
90 surveys for College D, and 50 surveys for College E.
The Survey Responses from Five Community Colleges
College A’s student enrollment is about 14,000 students and located
in an urban setting. It states its primary mission is to prepare students for
successfully transferring to four-year colleges and universities or for
successful placement or advancement in rewarding careers. From this
college, twenty-nine surveys were returned out of a total of 80. This
represented 58% participation.

163
College B is located in a suburban setting and the student enrollment
is about 19,000 students. I delivered 45 surveys. Five surveys were
returned and this represented 10% of the 50 total surveys that I received
from all five colleges.
College C is located in a rural setting in Southern California about
three hours from Los Angeles. The student enrollment is about 6,000
students. After receiving the institutional IRB approval, the dean allowed
me to contact the mathematics faculty and shared their email addresses
with me. Upon contacting the 12 faculty members, 9 full and part time
faculties responded and more than three faculties volunteered to be
interviewed and observed. The participation of nine faculty members out of
the twelve faculty members exceeded my expectation of 75% participation.
The nine survey responses represented 18% of the 50 total number of
surveys from five colleges.
College D is located about an hour from Los Angeles. It has three
campuses and enrolls about 30,000 students. I received back one survey
out of 45 surveys that I delivered to the main campus. At second campus,
a satellite location, as soon as I contacted the department chair, he asked
me to bring the surveys over and I received three surveys back out of 45
surveys I delivered to the satellite campus of College D. These four
surveys from College D represented a participation rate of 8% of the total
50 returned surveys from all five community colleges.

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College E is located in a suburban setting about two hours away
from Los Angeles in Southern California and accommodates about 12,000
students. This college has two other campuses as well. A participation rate
of 2 surveys out of a total of 50 surveys represented 4% participation from
the main campus. Altogether the participation rate from College E was
12%.
All 277 survey envelops include a letter of introduction that
contained a brief introduction of myself and the research and three surveys
which contained the demographic information, self-efficacy survey, and
another survey about the self-perceived ability and effectiveness on
AMATYC’s strands and instructional strategies. From the end of October
2007 to the beginning of February, 2008, I collected survey responses. Out
of 61 surveys, 50 surveys are filled out completely, and eleven surveys are
blank. The blank surveys are not inputted into the SPSS software for data
analysis, for it contained no data.
Reporting of findings

This study is a quasi-experimental design, descriptive, and
correlational case study of Mathematics faculty that includes three surveys,
interviews, and observations. A mixed method of research is used
because this research is testing the relationship between the theory of self-
efficacy and practice of instruction. Creswell asserted,

165
Mixed methods studies many include theory deductively in
theory testing and verification, or inductively as in an
emerging theory or pattern. In either situation, the use of
theory may be directed by the emphasis on either quantitative
or qualitative approaches in the mixed methods research.
Another way to think about theory in mixed methods research
is the use of a theoretical lens or perspective to guide the
study (Creswell, 2003, p.136).

This mixed method study’s purpose is multifold because it includes
the descriptive statistics of summarizing a set of data from three surveys,
interviews, and observations and move beyond to inferential statistics to be
able to generalize the findings from a smaller population of community
mathematics faculty members to a larger population. Babbie (1990)
explains,
Descriptive statistics are statistical computations describing
either the characteristics of a sample or the relationship
among variables in a sample while it summarize a set of
sample observations while inferential statistics move beyond
the description of specific observations to make inferences
about the larger population from which the sample
observations were drawn (p. 370).

Therefore, I find that this study included the qualities of descriptive and
inferential statistics.
Surveys

The heart of survey analysis lies in the twin goals of description and
explanation (Babbie, 1990). The surveys describe the demographics of the
community mathematics faculty population, explains faculty self-efficacy
levels, and describes their self-perceived ability and effectiveness with
AMATYC’s strands and Marzano’s instructional strategies. From 50 survey

166
responses, not all faculty members filled out all of the surveys completely.
Therefore, for student engagement out of eight items, if a faculty member
chose not to fill out at least six items, then the response was considered
invalid. The same approach was applied to other constructs. Therefore,
although there were 50 surveys, the SPSS software data analysis
considered only 45 valid participants. The range in number of participants
varied from 45 to 42 on other constructs: intellectual development ability
(45), intellectual development effectiveness (45), pedagogy ability (44),
pedagogy effectiveness (44), content ability (44), content effectiveness (45),
Marzano’s instructional strategy ability (43), and Marzano’s instructional
strategy effectiveness (42).
Demographic Surveys
The demographic survey indicates that there are more full time
faculty (27) participation in the survey than part time (23) faculty. There are
more male (37) than female (13) mathematics instructors. Their ages’
range from 25 to 66 or older: twenty-two faculty’s age range between 25 to
45, twenty-four faculty’s age range between 46 and 65, and four faculty’s
age is 66 or older. The ethnicity make-up consists of the following:
Caucasian (36), Asian (5), Latina/o (3), Black (1), and other (5).
There are six mathematics faculty with the teaching experience of 1
to 5 years, twenty-one with 6 to 15 years, seven with 16 to 25 years, and
sixteen with 26 or more years in teaching. Among the 50 participants, 21
faculty members do not have any K-12 teaching experience while 27

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teachers indicate having K-12 teaching experience and two do not indicate
anything. Among 27 who express a K-12 teaching background, there are
more community college mathematics teachers who have taught at middle
and high school levels than elementary level.
The educational background reveals that 50% of the mathematics
teachers have Masters of Arts (MA) in Mathematics and 11% have
Doctorate degree either Ed. D. or Ph. D while others have Bachelors in
Mathematics and others. Fifty-four percent of instructors teach three or less
courses per semester while 46% teach four or more courses. Ninety
percent of the faculty teach or have taught basic skills Math classes, such
as Elementary Algebra and Intermediate Algebra at some time while sixty-
two percent have taught Arithmetic, Pre-algebra, Fractions, Intro Decimals,
and others. About 40% of the faculty have taught College Algebra and
Trigonometry classes.
For the question about collaboration during the last year reveals the
following trends: Fifty-two percent of the faculty have met at least once a
month or frequently, thirty-two percent have met once every semester or
once a year, and seven percent mention that they have not met at all as a
department to collaborate. For instructional strategies, 84% have used
problem solving, 52% have included technology, 50% have tried to include
interactive activities, 42% have used modeling while only 10% include
manipulatives in teaching. In terms of infusing Marzano’s strategies, the

168
most frequently used strategy is homework and practice while the least
frequently used strategy is using non-linguistic representation.
Data Analysis of Surveys for Self-efficacy and AMATYC’s Standards
and Research Based Instructional Strategies
The data analysis begins with inputting the data into SPSS software
item by item for the quantitative data. The constructs of self-efficacy and
the AMATYC’s three strands and Marzano’s instructional strategies are
analyzed while keeping in mind of the data analysis process. Creswell
(2003) notes,
Data analysis is an ongoing process during research. It
involves analyzing participant information, and researchers
typically employ the analysis steps found within a specific
strategy of inquiry. More generic steps include organizing and
preparing the data, an initial reading through the information,
coding the data, developing from the codes a description and
thematic analysis, and representing the findings in tables,
graphs, figures. It also involves interpreting the data in the
light of personal lessons learned, comparing the findings with
past literature and theory, raising questions, and/or advancing
an agenda for reform (pp. 205-206).

Realizing the above outline of the data analysis protocol, I have included a
cumulative frequency distribution because the cumulative frequency
allowed me to see the score of constructs in relation to others (Robinson
Kurpius & Stafford, 2006) among eleven variables or constructs. The
eleven constructs are composed of three constructs about student
engagement, student management, and instructional strategy on revised
self-efficacy survey (Tschannen-Moran & Woolfolk Hoy, 2001) and eight
constructs on the ability and effectiveness of AMATYC’s strands and

169
instructional strategies: intellectual development ability, intellectual
development effectiveness, pedagogy ability, pedagogy effectiveness,
content ability, content effectiveness, Marzano’s instructional strategy
ability, and Marzano’s instructional effectiveness (see Table 9).
Table 9, Frequency Distribution of Eleven Constructs

Statistics

ENGAG
E
MANAG
E
STRATEG
Y
INTDEVA
B
INTDEVE
F
PEDAGOA
B
PEDAGOE
F
CONTENA
B
CONTENE
F
MARZAA
B
MARZAE
F
Valid 45 45 45 45 45 44 44 45 45 43 42
N
Missin
g
0 0 0 0 0 1 1 0 0 2 3
Mean 6.1365 7.2340 7.0722 4.0177 3.8874 3.9076 3.7311 4.2911 4.1289 3.8934 3.7143
Std. Error
of Mean
.19404 .20898 .19694 .09222 .09283 .10340 .10732 .09806 .10248 .10931 .11666
Median 6.2500 7.5000 7.5000 4.0000 4.0000 3.8333 3.7500 4.3333 4.1667 4.0000 3.7778
Mode 6.50 7.75 7.50(a) 4.00 3.88(a) 3.67 4.00 4.00(a) 4.00 3.78(a) 3.22(a)
Std.
Deviation
1.30169 1.40188 1.32113 .61861 .62270 .68588 .71186 .65784 .68743 .71681 .75604
Variance 1.69440 1.96527 1.74538 .38267 .38776 .47043 .50674 .43275 .47256 .51381 .57160
Skewness -1.296 -1.988 -2.114 -.908 -.754 -1.174 -.623 -1.143 -.808 -.836 -.298
Std. Error
of
Skewness
.354 .354 .354 .354 .354 .357 .357 .354 .354 .361 .365
Kurtosis 2.854 5.222 5.595 1.226 .507 3.391 .787 1.976 .629 .947 -.192
Std. Error
of Kurtosis
.695 .695 .695 .695 .695 .702 .702 .695 .695 .709 .717
Range 6.13 6.75 6.38 2.88 2.88 3.67 3.33 3.00 3.00 3.33 3.22
Minimum 1.88 2.25 2.25 2.13 2.13 1.33 1.50 2.00 2.00 1.67 1.78
Maximum 8.00 9.00 8.63 5.00 5.00 5.00 4.83 5.00 5.00 5.00 5.00
Sum 276.14 325.53 318.25 180.80 174.93 171.93 164.17 193.10 185.80 167.42 156.00
A Multiple modes exist. The smallest value is shown

The central tendencies of mean, median, and mode from the three
constructs of student engagement, classroom management, and the
instructional strategies indicate high scores. These high values on the
revised Tschannen-Moran and Woolfolk Hoy’s self-efficacy survey reveal
that the faculty’s self-perceived efficacy is higher than average. On the
survey’s Likert scale of 1 to 9, one as nothing, three as very little, five as

170
some influence, seven as quite a bit, and nine as a great deal, the faculty
response on self-efficacy mean score denotes that the mathematics faculty
members perceive themselves to be above the average and somewhat
highly self-efficacious.
For example, the mean score of 6.13 on student engagement
signifies being closer to “can engage students quite a bit” than “having
some influence.” The mean score of 7.23 on student management shows
that mathematics faculties can manage the classroom environment
between “quite a bit and a great deal.” The mean score of 7.07 on
instructional strategies indicates the same tendencies that faculty members
perceive themselves as being quite efficacious “between quite a bit and a
great deal.” I choose to use the mean because averages offer the special
advantage to the reader of reducing the raw data to the most manageable
form, for a single number represents all the detailed data collected in
regards to the variable (Babbie, 1990).
The most frequent attribute, mode, represents 6.50 for student
engagement, 7.75 for classroom management, and 7.50 for instructional
strategy. In addition, the median score for student engagement is 6.25,
classroom management is 7.50, and instructional strategy is 7.50. The
range of student engagement is 6.13 that is the estimated value of the
difference between the minimum value of 1.88 and the maximum value of
8.00. This means that some faculty members perceive themselves as they
could engage students “between quite a bit and a great deal” while a few

171
faculty members perceive that they can engage students “between nothing
to very little.” The range of 6.75 for classroom management is the
difference between the minimum value of 2.25 and 9.00 which means that a
few faculty members perceive that they could manage “very little” while the
rest of the faculty perceive themselves as being able to manage classroom
environment “a great deal.” The range of 6.38 for instructional strategy is
the estimation difference between the minimum value of 2.25 and the
maximum value of 9.00 that includes a few faculty who do not fill out the
items completely. This illustration indicates that a few faculty members
perceive that they can do “very little” while the rest perceive themselves as
making “a great deal of difference” in delivering the instructional strategies.
Based on these high scores of central tendencies, the community
college mathematics faculty members tend to perceive themselves to be
most efficacious on classroom management and least efficacious on
student engagement. In addition, the mathematics faculty members
perceive themselves to be more efficacious in classroom management than
instructional strategies. They see themselves to be more efficacious on
instructional strategies than student engagement. The histograms show
three tendencies. The histograms describe the mean and standard
deviation for three constructs: student engagement, classroom
management, and instructional strategy.

Figure 8, Classroom Management Histogram

The above histogram, Figure 8, is negatively skewed, for the
distribution trails off to the left and has unimodal meaning that a distribution
has one distinct peak (Howell, 2004). The mean score for classroom
management, 7.2 is greater than the averages of instructional strategies or
student engagement. The mode value of 7.55 indicates “quite a bit” in
making a difference with faculty’s perceived efficacy. In addition, it reveals
the range between 2.25 and 9.00 of the construct values that represent the
community college mathematics faculty.

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Figure 9, Instructional Strategy Histogram

The above histogram, Figure 9, it is negatively skewed and unimodal
as well. The mean score for instructional strategy, 7.1 describes that the
community college mathematics faculties believe that they could make a
difference with instructional strategies. Again, on the survey Likert scale,
the scale 7 indicates “quite a bit” of difference. The range value of 6.38
paints a picture how some faculty perceive themselves to be very little
effective while others perceive themselves as effective to a great deal.

173

Figure 10, Student Engagement Histogram

The above histogram, Figure 10, depicts that student engagement
has a bimodal distribution having two distinct peaks and is negatively
skewed because the distribution tails off to the left (Howell, 2004, p. 49).
Although the mean score of 6.14 is the lowest among the three self-efficacy
constructs, it is still above the average. The Likert scale six illustrates that
the community college mathematics teachers believe that they could make
a difference with “some influence and quite a bit.” With a slight variation of
the mean scores, an inequality exists with these three constructs. The
mean score for classroom management is higher than instructional strategy
and student engagement.
174

175
Likewise, for the other constructs, the self-reported score is above
average. The scores for ability and effectiveness are as follows: (1)
intellectual development ability (4.01= slightly effective); (2) intellectual
development effectiveness (3.88= somewhat effective to slightly effective);
(3) pedagogy ability (3.90=somewhat effective to slightly effective); (4)
pedagogy effectiveness (somewhat effective to slightly effective); (5)
content ability (4.29=slightly effective to never effective); (6) content
effectiveness (4.12=slightly effective to never effective); (7) Marzano
strategy ability (3.89= somewhat effective to slightly effective); and (8)
Marzano strategy effectiveness (3.71= somewhat effective to slightly
effective). Among these eight constructs, the community mathematics
faculties are more efficacious with content ability (4.29), content
effectiveness (4.13), and intellectual development ability (4.02) than with
pedagogy ability (3.91), intellectual development effectiveness (3.89),
Marzano’s instructional strategy ability (3.89), pedagogy effectiveness
(3.73), and Marzano’s instructional strategy effectiveness (3.71).
When comparing the median scores, the community college
mathematics faculties see themselves to be more efficacious on content
ability (4.33) and content effectiveness (4.17). These scores are higher
than intellectual development ability (4.00), intellectual development
effectiveness (4.00), and Marzano’s instructional strategy ability (4.00)
constructs. The pedagogy ability (3.83), pedagogy effectiveness (3.75),
and Marzano’s strategy effectiveness (3.78) show that they do “moderately

well and moderately effective” which represent that their self-perception is
above the average in their ability and effectiveness.
The comparison of scores for the mode identifies an interesting
phenomenon on the following constructs. The discrepancy among these
four constructs of intellectual development ability (4.00), pedagogy
effectiveness (4.00), content ability (4.00), and content effectiveness (4.00)
depict a narrow gap from the other four constructs of intellectual
development effectiveness (3.88), pedagogy ability (3.67), Marzano’s
strategy ability (3.78), and Marzano’s strategy effectiveness (3.22) on
faculty’s self-perception of highly efficaciousness tendencies. This self-
reporting efficaciousness illustrates that they perceive to be less self
efficacious with the effectiveness in intellectual development, ability in
teaching (pedagogy), and ability and effectiveness in delivering Marzano’s
research based instructional strategies than other constructs.
Figure 11, Intellectual Development Ability Histogram

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Figure 12, Intellectual Development Effectiveness Histogram

The above histograms, Figure 11 and Figure 12, illustrate unimodal
and negatively skewed distribution that is asymmetrical. The mean scores
for intellectual development for ability and effectiveness are both high. The
community mathematics faculties perceive their ability as between
“moderately well and very well.” Their self-perception of effectiveness is
very close to being “moderately effective.” One should remember during
this interpretation is that although the survey Likert scale represents “Not
Well at All (NWA)” as the scale 5, the syntax code is developed to recode
the AMATYC survey to represent the high numbers symbolizing the high
scores.

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Figure 13, Pedagogy Ability Histogram

Figure 14, Pedagogy Effectiveness Histogram

The above distributions, of Figures 13 and 14, for both pedagogy
ability and effectiveness depict the above average qualities. The self-
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perceived ability for pedagogy is very close to being “moderately well” while
the self-perceived effectiveness is “moderately effective.” They are both
negatively skewed and unimodal.
Figure 15, Content Ability Histogram

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Figure 16, Content Effectiveness Histogram

The scores of the content ability and effectiveness constructs were
the highest of all the constructs of American Mathematical Association of
Two-Year Colleges (AMATYC). This showed that the mathematics faculty’s
self-perception of content ability and effectiveness was the greatest
between “very well” and “moderately well” for content ability and between
“very effective” and “moderately effective” for content effectiveness. In
addition, the distribution was negatively skewed and unimodal.

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Figure 17, Marzano Ability Histogram

Figure 18, Marzano Effectiveness Histogram

The ability and effectiveness constructs of Marzano’s instructional
strategies, Figure 17 and Figure 18, were unimodal. The ability construct
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was slightly negatively skewed while the effectiveness construct described
the normal curve. Again, the faculty’s highly efficacious self-perception was
evidenced by the high mean scores of “moderate well ability” (3.89) and
“moderately effective” (3.71).
Reliability Analysis

Reliability is a matter of whether a particular technique, applied
repeatedly to the same object, would yield the same result each time
(Babbie, 1990, p. 132). “Reliability is that quality of measurement methods
that suggests that the same data would have been collected each time in
repeated observations of the same phenomenon,” states Babbie (1990,
p. 378).” In this case, the significance of reliability analysis is testing the
internal consistency of the item measurement of the constructs to see if
there are problems with the items. The reliabilities show that there is
internal consistency among constructs. It is a reliable survey and measures
what it suppose to measure. An example is as follows (see Table 10).

Table 10, Reliability Analysis Scale

RELIABILITY ANALYSIS – SCALE (engageme)

Item-total Statistics

Scale Scale Corrected

Mean Variance Item- Alpha
if Item if Item Total if Item
Deleted Deleted Correlation Deleted

SE1 42.9048 83.8444 .7545 .8474
SE2 42.1667 90.7764 .6105 .8634
SE4 42.6667 89.3984 .6031 .8643
SE6 42.1905 84.6945 .8110 .8425
SE9 42.2857 85.5261 .7827 .8455
SE12 43.2381 93.9419 .5773 .8668
SE14 42.9762 91.5360 .6967 .8565
SE22 44.2381 91.7956 .3818 .8963

Reliability Coefficients

N of Cases = 42.0 N of Items = 8

Alpha = .8760

The reliability coefficient for the constructs are as follows as shown in Table
10: student engagement (Alpha =. 88), classroom management
(Alpha=.94), instructional strategy (Alpha=.90), intellectual development
ability (Alpha=.86), intellectual development effectiveness (Alpha = .87),
pedagogy ability (Alpha=.83), pedagogy effectiveness (Alpha = .83),
content ability (Alpha=.88), content effectiveness (Alpha=.90), Marzano
strategy ability (Alpha=.89), and Marzano strategy effectiveness (Alpha
=.90). Reliability that measured the internal consistency seemed to be high
among eleven constructs.

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Correlations
The term, correlation, was defined as the relationship between
variables and correlation coefficient (Howell, 2004). Howell also defined
that Pearson product-moment correlation coefficient (r) as the most
common correlation coefficient. The standard correlation coefficient was
Pearson’s r, which applied primarily to variables distributed more or less
along interval or ratio scales of measurement (Howell, 2004). The above
correlation matrix presented the multivariate correlations among three
variables. The rows and the columns contained correlations between two
variables. Howell (2004) delineated,
The correlation coefficient must be interpreted cautiously so
as not to attribute to its meaning that it does not possess.
Specifically, r = - .72 should not be interpreted to mean that
there is 72% of a relationship (whatever that might mean)
between time and errors. The correlation coefficient is simply
a point on the scale between -1.00 and +1.00, and the closer
it is to either of those limits, the stronger is the relationship
between the two variables (p. 177).

The high representation of Pearson correlation coefficient values
illustrated a strong correlation between these constructs: student
engagement and instructional strategy, student engagement and student
management, and instructional strategy and student management. A table
was created for the sake of categorizing the coefficient values into different
categories in order to discriminate the strength of the coefficient values (see
Table 11).

185
Table 11, Pearson Coefficient Correlation and Strength of Scale Values
Pearson Coefficient Correlation Strength of Scale Values
.75 – above Very Strong
.60 - .74 Strong
.46 - .59 Moderately Strong
.30 - . 45 Moderate
.15 - .29 Slight
.00 - .14 Negligible

The below table shows that the observed probability is high among
these constructs between the rows and the columns (See Table 12):
engage and strategy (.001), engage and manage (.001), and strategy and
manage (.001). A correlation of r = .000 indicates the absence of a linear
relationship (Smith & Glass, 1987).
Table 12, Correlations of Self-efficacy Constructs

Correlations

ENGAGE STRATEGY MANAGE
Pearson Correlation 1 .800 .738
Sig. (2-tailed) . .000 .000
ENGAGE
N 45 45 45
Pearson Correlation .800 1 .780
Sig. (2-tailed) .000 . .000
STRATEGY
N 45 45 45
Pearson Correlation .738 .780 1
Sig. (2-tailed) .000 .000 .
MANAGE
N 45 45 45

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These findings suggest strong positive relationships among the four
constructs. First, the statistical significance of the student engagement and
instructional strategy correlation is significant, r (43) = .80, p < .05.
Secondly, the correlation of the student engagement and student
.management is statistically significant as well, r (43) = .73, p < .05. Thirdly,
a statistically significant correlation exist between the instructional strategy
and student management r (43) = .78, p < .05.
Although a construct’s high value does not imply the causality of
another construct, they describe a strong positive association between
constructs. For example, these positive strong correlations are found
between student engagement and instructional strategies, student
engagement and classroom management, instructional strategy and
student engagement, instructional strategy and classroom management,
classroom management and student engagement, and classroom
management and instructional strategy. Experiencing high correlations
among all of the self-efficacy constructs could be due to the community
mathematics faculty having difficulty discriminating one construct from
another while experiencing a very high level of their self-perception of
efficaciousness. However, the positive correlations among these self-
efficacy constructs and high reliability measures describe a strong
relationship among these constructs and their internal consistency. In
addition, the correlation state that most faculties who are strong in one

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construct are strong in the other. Again, this painted a picture of a strong
positive relationship among the constructs (see Table 13).
Table 13, Correlations of Ability and Effectiveness of AMATYC’s Three
Strands and Marzano’s Instructional Strategies

Correlations

INTDEVAB INTDEVEF PEDAGOAB PEDAGOEF CONTENAB CONTENEF MARZAAB MARZAEF
Pearson Correlation 1 .861 .846 .800 .783 .786 .767 .785
Sig. (2-tailed) . .000 .000 .000 .000 .000 .000 .000
INTDEVAB
N 45 45 44 44 45 45 43 42
Pearson Correlation .861 1 .719 .860 .621 .726 .675 .817
Sig. (2-tailed) .000 . .000 .000 .000 .000 .000 .000
INTDEVEF
N 45 45 44 44 45 45 43 42
Pearson Correlation .846 .719 1 .861 .820 .763 .838 .793
Sig. (2-tailed) .000 .000 . .000 .000 .000 .000 .000
PEDAGOAB
N 44 44 44 44 44 44 43 42
Pearson Correlation .800 .860 .861 1 .712 .785 .752 .876
Sig. (2-tailed) .000 .000 .000 . .000 .000 .000 .000
PEDAGOEF
N 44 44 44 44 44 44 43 42
Pearson Correlation .783 .621 .820 .712 1 .881 .725 .671
Sig. (2-tailed) .000 .000 .000 .000 . .000 .000 .000
CONTENAB
N 45 45 44 44 45 45 43 42
Pearson Correlation .786 .726 .763 .785 .881 1 .655 .726
Sig. (2-tailed) .000 .000 .000 .000 .000 . .000 .000
CONTENEF
N 45 45 44 44 45 45 43 42
Pearson Correlation .767 .675 .838 .752 .725 .655 1 .895
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 . .000
MARZAAB
N 43 43 43 43 43 43 43 42
Pearson Correlation .785 .817 .793 .876 .671 .726 .895 1
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .
MARZAEF
N 42 42 42 42 42 42 42 42

The above multivariate matrix revealed high correlations among
variables of American Mathematical Association of Two-Year Colleges
(AMATYC, 2006) as well as Marzano’s research based instructional
strategies (See Table 13). The self-reporting survey of the faculties’ self-
perception on their ability and effectiveness in intellectual development
strand seem to be highly correlated with the other variables: pedagogy
ability, pedagogy effectiveness, content ability, content effectiveness,

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Marzano’s strategy ability, and Marzano’s strategy effectiveness. The
intellectual development strand include these standards: problem solving,
modeling, reasoning, connecting with other disciplines, communicating,
using technology, developing mathematical power, and linking with multiple
representations. The ability and effectiveness of pedagogy strand that
include teaching with technology, active/interactive learning, making
connections, using multiple strategies, and experiencing mathematics seem
to be highly correlated with the rest of the variables. The ability and
effectiveness of content strand include these standards: number sense,
symbolism and algebra, geometry and measurement, function sense,
continuous and discrete models, and data analysis, statistics, and
probability.
There is a positive correlation between the constructs of ability and
effectiveness. First, between intellectual ability and intellectual
development effectiveness, the strength of correlation is significant, r (43) =
.86, p < .05. Secondly, the correlation of pedagogy ability and pedagogy
effectiveness is significant, r (42) = .86, p < .05. Thirdly, content ability and
content effectiveness correlation is significant, r (43) = .88, p < .05.
Fourthly, Marzano instructional strategy effectiveness and Marzano
instructional strategy ability correlation is significant, r (40) = .89, p < .05.
The strength of the correlation is highest between Marzano’s strategy ability
and effectiveness.

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When comparing constructs with the Pearson coefficient correlation’s
strength of scale values from pedagogy effectiveness to pedagogy ability
with other constructs in between, the correlations reveal positive
relationships. For example, between pedagogy effectiveness and
intellectual development effectiveness, the significance is very strong, r (42)
= .86, p < .05. Between intellectual development effectiveness and
Marzano’s instructional strategy effectiveness, the significance is very
strong, r (40) = .81, p < .05. Between Marzano instructional strategy
effectiveness and pedagogy effectiveness is significantly very strong, r (40)
= .87, p < .05. Between pedagogy effectiveness and pedagogy ability, the
significance is very strong, r (42) = .86, p < .05. Between pedagogy ability
and intellectual ability, the significance is very strong, r (42) = .84, p < .05.
Between intellectual development ability and intellectual development
effectiveness, the significance is very strong, r (43) = .86, p < .05. Between
intellectual development effectiveness and content effectiveness, the
significance is strong, r (43) = .72, p < .05. Between content effectiveness
and content ability, the significance is very strong, r (43) = .88, p < .05.
Between content ability and pedagogy ability, the significance is very
strong, r (42) = .82, p < .05. Between pedagogy ability and pedagogy
effectiveness, the significance is very strong, r (42) = .86, p < .05.
Overall, the effective practice in delivering the strands and standards
of AMATYC along with Marzano’s research based instructional strategies
are highly correlated with pedagogy effectiveness. Although this may be

190
good news to this researcher, it raises a cautionary flag and makes me
ponder about whether the high correlation is due to the self-reporting
surveys of the high self-perceptions of participants’ self-efficaciousness.
This raises a caution flag resulting in looking at the relationship between the
constructs of self-efficacy and other constructs.
Table 14, Correlations of Constructs between Self-efficacy and Others
Correlations

ENGAGE STRATEGY MANAGE INTDEVEF PEDAGOAB PEDAGOEF CONTENAB CONTENEF MARZAAB MARZAEF
Pearson Correlation 1 .800 .738 .414 .300 .385 .119 .254 .287 .434
Sig. (2-tailed) . .000 .000 .005 .048 .010 .435 .092 .062 .004
ENGAGE
N 45 45 45 45 44 44 45 45 43 42
Pearson Correlation .800 1 .780 .402 .259 .321 .228 .349 .252 .350
Sig. (2-tailed) .000 . .000 .006 .089 .033 .133 .019 .104 .023
STRATEGY
N 45 45 45 45 44 44 45 45 43 42
Pearson Correlation .738 .780 1 .379 .228 .280 .230 .348 .242 .365
Sig. (2-tailed) .000 .000 . .010 .136 .065 .129 .019 .117 .017
MANAGE
N 45 45 45 45 44 44 45 45 43 42
Pearson Correlation .414 .402 .379 1 .719 .860 .621 .726 .675 .817
Sig. (2-tailed) .005 .006 .010 . .000 .000 .000 .000 .000 .000
INTDEVEF
N 45 45 45 45 44 44 45 45 43 42
Pearson Correlation .300 .259 .228 .719 1 .861 .820 .763 .838 .793
Sig. (2-tailed) .048 .089 .136 .000 . .000 .000 .000 .000 .000
PEDAGOAB
N 44 44 44 44 44 44 44 44 43 42
Pearson Correlation .385 .321 .280 .860 .861 1 .712 .785 .752 .876
Sig. (2-tailed) .010 .033 .065 .000 .000 . .000 .000 .000 .000
PEDAGOEF
N 44 44 44 44 44 44 44 44 43 42
Pearson Correlation .119 .228 .230 .621 .820 .712 1 .881 .725 .671
Sig. (2-tailed) .435 .133 .129 .000 .000 .000 . .000 .000 .000
CONTENAB
N 45 45 45 45 44 44 45 45 43 42
Pearson Correlation .254 .349 .348 .726 .763 .785 .881 1 .655 .726
Sig. (2-tailed) .092 .019 .019 .000 .000 .000 .000 . .000 .000
CONTENEF
N 45 45 45 45 44 44 45 45 43 42
Pearson Correlation .287 .252 .242 .675 .838 .752 .725 .655 1 .895
Sig. (2-tailed) .062 .104 .117 .000 .000 .000 .000 .000 . .000
MARZAAB
N 43 43 43 43 43 43 43 43 43 42
Pearson Correlation .434 .350 .365 .817 .793 .876 .671 .726 .895 1
Sig. (2-tailed) .004 .023 .017 .000 .000 .000 .000 .000 .000 .
MARZAEF
N 42 42 42 42 42 42 42 42 42 42

When correlating the self-efficacy constructs of student engagement,
classroom management, and instructional strategy with the other

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constructs, these correlations are moderate (see Table 14). The moderate
correlation strength for student engagement and other constructs reveal the
following trends: (a) a moderate correlation significance, r (43) = .41, p <
.05 between students engagement and effectiveness of intellectual
development; (b) a moderate correlation significance, r (42) = .30, p < .05
between student engagement and ability of pedagogy; (c) a moderate
correlation significance, r (42) = .38, p < .05 between student engagement
and effectiveness of pedagogy; and (d) a moderate correlation significance,
r (40) = .43, p < .05 between student engagement and effectiveness of
Marzano’s instructional strategy. This means that the survey items in
student engagement are positively moderately correlated with the faculty’s
effectiveness in delivery of the intellectual development standards of
problem solving, modeling, reasoning, connecting with other disciplines,
communicating, developing mathematical power, and linking multiple
representations. The construct, student engagement, includes these items:
(a) getting through to the most difficult students, (b) helping students think
critically, (c) motivating students who show low interest in learning Math, (d)
having students believe they can do well learning Math, (e) helping students
value learning, (f) fostering student creativity, (g) improving the
understanding of failing students, and (h) assigning families to assist their
children do well in school. However, it is surprising to see this moderate
relationship that faculty members feel less efficacious in relating their self-

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reporting self-efficacy with delivering AMATYC mathematics strands and
research based instructional strategy.
Similarly, the faculty’s self-efficacy in student engagement is
moderately correlated with the ability and effectiveness of pedagogy
standards: teaching with technology, active/interactive learning, making
connections, using multiple strategies, and experiencing mathematics.
Additionally, the moderate significance between self-efficacy construct,
student engagement and instructional construct, research based strategies,
reveals that the mathematics faculty members feel moderately efficacious in
delivering these instructional strategies: (1) identifying similarities and
differences, (2) summarizing and note taking, (3) reinforcing effort and
providing recognition, (4) homework and practice, (5) non-linguistic
representations, (6) cooperative learning, (7) setting objectives and
providing feedback, (8) generating and testing hypotheses, and (9)
providing questions, cues, and advance organizers.
When correlating the second self-efficacy construct, instructional
strategy, with other constructs, a similar finding is found. The mathematics
faculty members are moderately efficacious with correlating self-efficacy
instructional strategies with intellectual development effectiveness. This is
a moderate significance, r (43) = .40, p < .05. Between instructional
strategies and pedagogy effectiveness, the significance is moderate, r (42)
= .32, p < .05. Between instructional strategies and content effectiveness,
the significance is moderate, r (43) = .34, p < .05. Between instructional

193
strategies and Marzano’s research based strategy effectiveness, the
significance is moderate as well, r (40) = .35, p < .05. The self-efficacy
instructional strategies include the following items: responding to difficult
questions from students, gauging student comprehension, crafting good
questions for students, adjusting one’s lessons to the proper level for
individual students, using a variety of assessment strategies, providing an
alternative explanation or example when students were confused,
implementing alternative strategies, and providing appropriate challenges
for capable students. The positive moderate correlations between the self-
efficacy instructional strategy with the AMATYC’s constructs describe that
the faculties are less efficacious with instructional strategies in delivering
effective instruction.
The third self-efficacy construct, student classroom management,
has a moderate positive correlation with intellectual development
effectiveness. This significance is as follows, r (43) = .37, p < .05. There is
a moderate strength of correlation between student management and
content effectiveness, r (43) = .34, p < .05. There is a moderate correlation
between student management and Marzano’s strategy effectiveness, r (40)
= .36, p < .05. The student classroom management construct includes
these items: (a) controlling disruptive behavior in the classroom, (b) making
your expectations clear about student behavior, (c) establishing routines to
keep activities running smoothly, (d) getting students to follow classroom
rules, (e)calming a student who is disruptive or noisy, (f) establishing a

classroom management system with each group of students, (g) keeping a
few problem students from running an entire lesson, and (h) being able to
respond to defiant students.
Table 15, Mean and Standard Deviation Scores between Self-efficacy
Constructs and Marzano’s Instructional Strategies

When self-efficacy constructs are correlated with the eight constructs
of Marzano’s strategies in the demographic survey, it shows the following
mean scores from the highest to lowest (see Table 15): homework and
practice (M =.91, SD =.28), summarizing and notetaking (M =.60, SD =.49),
cooperative learning (M=.51, SD=.50), identifying similarities and
differences (M=.51, SD =.50), reinforcing effort and providing recognition
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(M=.44, SD = .50), setting objectives and providing feedback (M=.38, SD =
.49), cues, questions, and advance organizers (M=.31, SD = .46),
generating and testing hypotheses (M=.29, SD = .45), and using non-
linguistic representations (M = .27, SD = .44). The high mean score for the
homework and practice could be interpreted as that the community
mathematics faculty members are more efficacious in using homework and
practice as an instructional strategy than having students to generate and
test hypotheses and use non-linguistic representations. Based on these
correlations, it is obvious that the faculties feel the least efficacious using
non-linguistic representations in teaching mathematics to community
college students. The below correlations matrix described these tendencies
(see table 16).

Table 16, Correlations of Constructs between Self-efficacy and Marzano’s
Instructional

The above correlations of Table 16 support the research question between
self-efficacy and Marzano’s instructional strategies. There are negative
correlations for the following self-efficacy constructs and two of Marzano’s
instructional strategies: (a) student engagement and identifying similarities
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197
and differences with a slight negative insignificant correlation because the
probability value is grater than .05, r (43) = - .21, p › .05; (b) instructional
strategy and identifying similarities and differences with a moderately strong
negative insignificant correlation, r (43) = - .05, p › .05; (c) classroom
management and identifying similarities and differences with a negative
negligible strength of insignificant correlation, r (43) = -.10, p › .05; and (d)
student engagement with summarizing and notetaking with a moderately
strong insignificant negative correlation, r (43) = -.04, p › .05. In conclusion,
although there are negative correlations with a few constructs, the overall
correlations between self-efficacy constructs and Marzano’s instructional
strategy construct are positively associated.
Interviews and Observations

The interviews include six mathematics faculty members who teach
these classes: Intermediate Algebra (2), Elementary Algebra (3), and
Statistics (1). After piloting the interview questions, these questions are
developed. While interviewing six Mathematics faculty members, Clark and
Estes’ (2002) quote is used as a reminder;
Interviewers do not have to agree with all of the views people
will express, but is absolutely necessary to listen actively and
neutrally. While listening, analyze whether people are saying
that their performance gaps are due to a lack of knowledge
and skills, insufficient motivation, some organizational
barriers, or some combination of the three (Clark and Estes,
p. 45).

Considering these three factors of knowledge/skills, motivation, and
organizational gaps, the qualitative data collection process by interviewing

198
six community college mathematics faculties has begun. The faculties
responses indicate that four are motivated to teach because they love
teaching students. Five out of six mention that what they like most about
teaching has to do with students, such as “students’ responses, more
motivated students than high school students, positive attitudes about
learning, helping students, and willing audiences.” What they least like
about teaching has to do with student motivation according to five out of six
faculties, such as “diversity of student background, not being at the course
level, not caring about learning, not serious about learning with unrealistic
ideas, and undecided about learning.”
Interestingly though, when the six faculty members are asked the
question, “Do you consider yourself a highly efficacious teacher (on a Likert
scale, zero being the lowest and five being the highest)?” The mean score
among the six faculty members is 4.5 which is close to being 5. They are
highly efficacious. The dilemma this researcher found is that the interviews
reveal that their self-perceived personal efficacy in teaching is very high;
however, when observing the same faculty during mathematics instruction,
different data are generated.
Among the six faculty members, one faculty member is highly
efficacious (very effective) in delivering the effective instruction while five
faculty members varied from moderately effective, somewhat effective,
slightly effective, and between slightly effective and never effective. The
observation using the same survey instruments to measure the faculty’s

199
efficacy and their instructional practice points out a gap of unexpected
discrepancies. The gap is that highly perceived self-perception in teaching
delivery is not being presented to students. The instruction focuses heavily
on lecture with factual and procedural problem solving processes while not
developing conceptual understanding by using intellectual development and
pedagogy standards. The fast paced lecture does not allow students to
experience mathematics by tapping into the concepts and patterns that are
underneath the rules that are being taught. Five out of six faculty members
are busy covering the content of the book while not providing opportunities
for students to think about the thinking, metacognitive knowledge, of
mathematics. The interaction includes some low level questions that are at
the low domains of cognitive processes of knowing and understanding
instead of applying, analyzing, evaluating, and creating. This could be the
outcome of the gap among knowledge/skills, motivation, and organizational
(Clark & Estes, 2002) lack of emphasis on faculty development of
pedagogy. Interview responses are shown in Table 17.

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Table17, Interview Responses from Six Community College
Mathematics Faculty

Questions Interview Responses from Six Community
College Mathematics Faculty
1. What motivated you to become a community
college faculty?
1. “Community college students need me the most”
2. “Not to be burned out from high school teaching”
3. “Financial need and love teaching”
4. “Fun to teach”
5. “Like teaching, helping students, and helping students”
6. “Teaching math excites me in dealing with people’s fears and giving them
experiences in conquering their fears in learning math”
2. What do you most like about
teaching community college
students?

1. “Students’ responses”
2. “Students are more motivated and mature than high school students”
3. “Does not require parent contact”
4. “Most students have positive attitudes about learning”
5. “Helping students who have experienced failure in the past in learning math”
6. “Willing audiences”

3. What do you least like about
teaching community college
students?
1. “The drudgery of correcting tests and ready for students’ feedback of the graded
tests”
2. “Diversity of student background and organizationally unstructured environment
without any Math curriculum coordinator”
3. “When a student thinks he/she is ready but not ready for the course work due to
lack of basic skills, it slows down the pacing”
4. “Some students don’t care about learning”
5. “Still get a lot of students who are not serious and do not do their work and have
unrealistic ideas on work habits”
6. “Some students are undecided, not too serious, and not very clear about
learning”

4. What does effective instruction mean to you? 1. “You can do it = You can teach.”
2. “Effective instruction equals effective assessment and curriculum”
3. “Being able to teach for the maximum level of student understanding for the most
number of students”
4. “Helping students to think critically and apply the knowledge”
5. ”Whatever you are trying to get across to the students, it has to be palatable and
comprehensible”
6. “Clear communication with the students to be successful”
5. What professional development have you
attended?
1. “One day conference in one year”
2. “One day conference and 12 hours of college flex day staff development (not
related to math) last year”
3. “Six hours of flex day training (not math specific) during last year”
4. “Twelve hours of flex day training on learning styles and creating student learning
outcomes (none on math) last year”
5. “One day per year”
6. “Minimum 30 hour requirement last year”

6. How familiar are you with AMATYC strands
and standards?
1. “Somewhat familiar”
2. “Not at all”
3. “Never heard of it”
4. “Not familiar”
5. “Not much”
6. “Somewhat”
7. AMATYC’s Intellectual Development
Standards:
a) problem solving
b) modeling
c) reasoning
d) connecting with other disciplines
e) communicating
f) using technology
g) developing mathematical power
h) linking multiple representations

7.1 Which one would you feel is the most
important? Why?
1. “Communicating because you have to get the message across”
2. “Modeling”
3. “Reasoning, with the reasoning, problem solving is possible”
4. “Problem solving , but they are all important”
5. “Modeling and reasoning, that’s the heart of math”
6. “Problem solving, math is a skill that could be applied anywhere”

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(Table 17 continued)
7.2 Which one would you feel is the least
Important? Why?
1. “Linking multiple representations because of limited amount of time”
2. “Developing mathematical power due to lack of time”
3. “Using technology, being able to solve basic skills problems without relying on
calculators”
4. “Modeling (thinking about mathematical representation of physical phenomenon)”
5. “Using technology and developing mathematical power”
6. “Linking multiple representations”

7.3 What can the community college leadership
do to assist you to effectively implement the
intellectual development standards?
1. “By providing assistance with clerical work”
2. “Leadership attention for full time faculty, staff development and instructional
technology”
3. “Having math department meetings to talk and discuss about teaching”
4. “Cap the class size to 30, add a little more technology, and provide resources,
such as well functioning copy machine and printers”
5. “Let me teach and leave me alone, don’t bother me with all sorts of busy work.”
6. “Smaller class sizes, from 40 to 35”
8. AMATYC’s Content Standards:
a) Number sense
b) Symbolism and algebra
c) Geometry and measurement
d) Function sense
e) Continuous and discrete models f) Data
analysis, Statistics, and Probability

8.1 Which standard are you most prepared to
teach?
1. “Data analysis, Statistics, and Probability…All of them”
2. “Function sense and geometry and measurement”
3. “All of them except continuous an discrete models”
4. “All of them”
5. “Symbolism and algebra”
6. “All of them, especially symbolism and algebra/data analysis, statistics, and
probability”
8.2 Which one are you least prepared to teach? 1. “None”
2. “Continuous and discrete models”
3. “Continuous and discrete models”
4. “Continuous and discrete models”
5. “Number sense, it falls outside of my area of preparation and never taught
elementary nor junior high”
6. “Geometry and measurement”
9. AMATYC’s Pedagogy Standards: a)
Teaching with technology
b) Active and interactive learning
c) Making connections
d) Using multiple strategies
e) Experiencing mathematics

9.1 What pedagogy standard do you feel most
comfortable using in your classroom?
1. “Active and interactive learning”
2. “Making connections and using multiple strategies”
3. “Using multiple strategies”
4. “Active and interactive learning”
5. “Active and interactive learning”
6. “Active and interactive learning”
9.2 Which pedagogy standard do you feel least
comfortable using in your classroom?
1. “Experiencing mathematics”
2. “Experiencing mathematics”
3. “Active and interactive learning”
4. “Using multiple strategies”
5. “Experiencing mathematics”
6. “Experiencing mathematics”
9.3 What can the community college leadership
do to help increase your ability in teaching?
1. “To relieve me from clerical work”
2. “More staff development for pedagogy and technology”
3. “Be able to have math department meetings and attend professional
development to talk about teaching”
4. “Send me to the conferences to learn about pedagogy”
5. “Make more professional staff development opportunities available”
6. “Increase staff development funds”
10 Marzano’s research-based
Instructional strategies:
a) Identifying similarities and differences
b) Summarizing and note taking
c) Reinforcing effort and providing
recognition
d) Homework and practice
e) Nonlinguistic representation
f) Cooperative learning
g)Setting objectives and providing
feedback
h) Generating and testing
hypotheses
i) Questions, cues, and advance organizers

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(Table 17 continued)
10.1 Which strategy do you most frequently use
in your classroom?
1. “Homework and practice”
2. “Questions, cues, and advance organizers”
3. “Summarizing and note taking, reinforcing effort and providing recognition, and
homework and practice”
4. “Homework and practice”
5. “Identifying similarities and differences and summarizing and note taking”
6. “Identifying similarities and differences and summarizing and note taking”
10.2 Which strategy do you least frequently use
in your classroom?
1. “Nonlinguistic representations”
2. “Cooperative learning”
3. “Cooperative learning”
4. “Generating and testing hypotheses”
5. “Generating and testing hypotheses”
6. “Reinforcing effort and providing recognition”
11. Do you find your belief system makes a
difference in teaching?
1. “Yes, I can make a difference with varying degrees of effectiveness”
2. “Yes, in a positive way”
3. “Yes, by helping students laugh and correlate it with real life examples”
4. “Yes, I can make a positive difference”
5. “Probably”
6. “Yes, anyone can do math, it’s just a matter of time.”
12. Do you find that there is a relationship
between a faculty’s belief system and his or her
instructional practice?
1. “Undoubtly, general attitude of teaching makes
a difference in teachers’ lessons by making a difference”
2. “Absolutely, there is a positive relationship…”
3. “Yes, highly positive”
4. “Yes, absolutely because belief system permeates personality which can’t be
removed from teaching”
5. “I think so, each instructor has to make practical decisions”
6. “Probably so”
13. Do you consider yourself a highly
efficacious teacher? ( On a Likert scale, zero
being the lowest and five being the highest)
1. “Yes (score five)”
2. “Yes (score five)”
3. “Yes (score four)”
4. “Yes (score five)”
5. “Yes (score four)”
6. “Yes (score four)”
14. If you have an opportunity to attend
professional development dealing with these
strands, intellectual development, content, and
pedagogy, which one would you attend? Why?
1. “Three strands can’t be separated because deeper study makes you better
understand the subject which gives you higher power to further understand the
conceptual knowledge”
2. “Pedagogy (relating to technology) and content (statistics)”
3. “Pedagogy”
4. “Pedagogy and intellectual development”
5. “Pedagogy”
6. “Pedagogy, focus on different areas and examples of teaching”
15. If you have one wish as a teacher, what
would that be?
1. “Provide assistance with grading”
2. “Someone who did make a long term difference in student learning”
3. “To work here full time”
4. “ Having self-motivated students who are interested in self-development”
5. “To find ways to be able to make it accessible to all students, make it palatable”
6. “Everyone could succeed”
16. What would you like the community college
leadership to do to assist the mathematics
faculty?
1. “Community college to be more inviting for students”
2. “ Provide staff development to encourage cohesiveness among Math faculty by
creating a level of leadership for curriculum”
3. “Mandate math department meetings”
4. “Where is the relationship among scheduling, funding, and selection of faculty?
Provide more support and work closely with faculty, not autonomously and be
transparent”
5. “Give us more full time faculty”
6. “Smaller class size and more full time math faculty”
17. What should future researchers research
about mathematics faculty and student
achievement?
1. “Find ways and design courses to concentrate on problematic students who are
distracted and turned off from learning”
2. “To see correlation between student achievement and faculty background as it
relates to pedagogy”
3. “Highly qualified teachers of teacher quality and research driven instructional
process”
4. “How an idea, a question, and an answer is found in general principles of a
framework”
5. “Areas of finding ways to help students with major deficiencies”
6. “The influence of carry over behavior from high school and drugs and alcohol in
student learning at community colleges as well as grading variations among full
time and part time instructors and the need for data to communicate”

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Six Case Studies from the Interview and Observation Data

Before beginning the faculty observation to organize the observation
data with consistency and accuracy, these data collection information is
found to be helpful. Three researchers emphasized the importance of
consistency and accuracy of data collection,
Studies often involve creating a record of what is observed in
some sort of code (numbers, word, symbols, or even electrical
traces on a magnetic disc or tape). The recorded code
(collectively called data) is retained for subsequent inspection
and analysis. To accomplish the process of creating data
requires very careful decisions about what to collect and how
to collect…. Consistency and accuracy are not just
necessities in research; they are concerns whenever people
want to obtain a reliable account of what is going on (Locke,
Silverman, & Spirduso, 2004).

In order to have consistency and accuracy of the data collection, a table of
codes is used for the instructional approaches that include the standards of
intellectual development and pedagogy. In addition, the five phases of
direct instruction and the nine Marzano research- based instructional
strategies are included. While observing the faculty, these attributes are
used as a rubric during the observation of the instruction. The following key
is used to measure the instructional approaches: (a) 1 = Very Effective
(VE); (b) 2 = Moderately Effective (ME); (c) 3 = Somewhat Effective (SWE);
(d) 4 = Slightly Effective (SE); (e) 5 = Never Effective (NE). Following this,
a mean score for the instructional observation is developed. Same efficacy
survey instrument is used to measure the efficacy of the faculty to evaluate
their teaching through the three efficacy constructs: student engagement,

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classroom management, and instructional strategies. These observations
are identical to the survey that the faculty members have used to report
their own effectiveness. The following key is used to measure the
effectiveness levels: (a) 1 = Very Effective (VE) = Advanced effectiveness
(100 – 90 %); (b) 2 = Moderately Effective (ME) = Proficient Effectiveness
(89 – 90%); (c) 3 = Somewhat Effective (SWE) = Basic Effectiveness (79 -
70 %); (d) 4 = Slightly Effective (SE) = Below Basic Effectiveness (69-60%);
(e) 5 = Never Effective (NE) = Far Below Basic Effectiveness (59% and
below). After the observation, the values of the effectiveness scales and
developed mean scores are calculated for the six mathematics instructors.
The First Mathematics Instructor Observation
The first instructor is a part-time male teacher who teaches Statistics.
He begins the lesson by stating the lesson objective. He is upbeat, and the
pacing seems appropriate. It is fast enough to teach many new statistical
concepts; at the same time, the instructor is able to include cooperative
interactive activities, such as think-pair-share. During the lesson, he checks
for students’ understanding frequently. He incorporates the intellectual
development standards: problem solving, communication with instructional
technology (calculators), linking with multiple representations, having
students reason and promote mathematics power. In addition, he
demonstrates the pedagogy standards: active and interactive activities,
making connections with other disciplines, using multiple representations,
and having students experience mathematics through real life situations.

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Also, he infuses Marzano’s research-based strategies, such as setting an
objective and providing feedback, asking questions, throwing out cues in
problem solving, identifying similarities and differences, summarizing and
note taking, connecting with cooperative learning, reinforcing effort and
providing recognition, generating and testing hypotheses, and giving
opportunities for independent work through homework and practice.
He engages the students at a high level. He often uses humor and made
connections with real life applications.
During the interview, when asked what the community college
leadership can do to assist the mathematics faculty, his response is that
community colleges should be more inviting. In addition, he expresses that
he has taught at the secondary level in K-12 as a mathematics teacher. He
feels most comfortable in using active and interactive learning and least
comfortable in having students to experience mathematics by having
students work on projects in problem solving during the instruction. He is
efficacious in delivering the active and interactive learning through
cooperative learning activities, such as having students work with partners
to think and share.
Although he feels least comfortable in having students experience
mathematics, he establishes a learning environment that makes Statistics
come alive in the classroom through activities and direct instruction of
orientation, presentation, structured practice, guided practice, and
independent practice. He weaves the modeling process of presentation

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with highly guided practice and guided practice as he draws pictures and
graphic organizers. His questions target the cognitive domains of
remembering and understanding as well as applying and analyzing, the
dimension of higher order thinking skills. The types of knowledge he aims
are factual, procedural, and conceptual.
Occasionally he challenges students to think about why Statistics
work the way it work which measures students’ conceptual and
metacognitive knowledge. After students are asked to think and share with
partners, he calls on student volunteers to share with the entire class. A
sample problem is, “Your chance of passing Mr. A’s first statistics test is
80%. Your chance of passing Mr. A’s second statistics test is 75%. What
are your chances of passing either one or the other or both?” The real life
example seems to spark students’ interest in problem solving and connects
the subject matter with a real life application of experiencing mathematics.
Occasionally, a few disengaged adult learners are noticed not
knowing what to do next due to lack of explicit directions because of the
complexity of the worksheet. For these students, it would been helpful to
have a demonstration of highly structured practice to guide them through
the step-by-step problem solving process before asking them to work with
partners and independently. When the instructor realizes the dilemma that
students do not know what is expected on the worksheet, he encourages
them to work with partners as he walks around to check for their
understanding.

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As he explains the correlation coefficient, he says, “Do your work
together! You’re going to put pieces of this info together. Help each other!”
He recognizes students’ effort, and the recognition of their effort seems to
work well for his students. They seem to thrive on his feedback. However,
some students have difficulty interpreting what the problem is due to a lack
of an explanation of the Statistics content vocabulary. It would have been
helpful to check for students’ understanding before releasing them to do
cooperative activities.
Overall, this instructor creates urgency in delivering the instruction to
cover the material by making comments, such as “We’re on a roll, and time
is short.” As he creates a graph of probability distribution, he creates
numerous tables on the white board to make his point to the students by
scaffolding the previously taught material. The student engagement varies
from authentic engagement, reluctant engagement, to passive compliance.
Evaluating his instruction by using the same survey instruments
along with the five phases of direct instruction, his mean score for
instructional approaches in integrating standards for intellectual
development, pedagogy, direct instruction, and Marzano research-based
strategies is 1.5 that is between very effective and moderately effective.
Based on the self-efficacy survey instrument, his mean score for student
engagement, instructional strategies, and classroom management is 86%
indicating that his self-efficacy is moderately efficacious (see Tables 18, 19,
and 20).

Table 18, Key for Instructional Approaches Scale
Instructional Approaches: Intellectual
Development, Pedagogy, Marzano’s
Strategies, and Direct Instruction

Key:

1= Very Effective (VE)
2=Moderately Effective (ME)
3=Somewhat Effective (SWE)
4=Slightly Effective (SE)
5=Not Effective (NE)
Self-efficacy
Key:
1= N (Nothing)
2
3=VL (Very Little)
4
5=SI (Some Influence)
6
7=QAB (Quite a Bit)
8
9= A Great Deal (AGD)

Table 19, Key for Self-efficacy Scale

Key:

1= Very Efficacious (VE) = Advanced Efficaciousness (100 -90%)
2= Moderately Efficacious (ME) = Proficient Efficaciousness (89-80%)
3=Somewhat Efficacious (SWE) = Basic Efficaciousness (79-70%)
4= Slightly Efficacious (SE) = Below Basic Efficaciousness (69-60%)
5= Not Efficacious (NE) = Far Below Basic Efficaciousness (59% and below)

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209
Table 20, Observations of Six Mathematics Faculty
Instructional Approaches Faculty 1 Faculty 2 Faculty 3 Faculty 4 Faculty 5 Faculty 6
Intellectual Development
(ID)
1. Problem solving

1 (VE)

4 (SE)

1 (VE)

4 (SE)

3 (SWE)

3 (SWE)
2. Modeling 1 (VE) 4 (SE) 1 (VE) 4 (SE) 3 (SWE) 3 (SWE)
3. Reasoning 1 (VE) 4 (SE) 1 (VE) 5 (NE) 4 (SE) 4 (SE)
4. Connecting with other
Discipline
1 (VE)

4 (SE) 1 (VE) 5 (NE) 5 (NE) 5 (NE)
5. Communication 2 (ME) 3 (SWE) 1 (VE) 4 (SE) 3 (SWE) 3 (SWE)
6. Using technology 4 (SE) 3 (SWE) 3 (SWE) 5 (NE) 5 (NE) 5 (NE)
7. Developing mathematical
Power
1 (VE) 3 (SWE) 1 (VE) 5 (NE) 5 (NE) 4 (SE)
8. Linking multiple
representations
1 (VE) 2 (ME) 2 (ME) 5 (NE) 4 (SE) 4 (SE)
Pedagogy (P)
1. Teaching with technology

4 (SE)

3 (SWE)

3 (SWE)

5 (NE)

5 (NE)

5 (NE)
2. Active and interactive
Learning
1 (VE) 3 (SWE) 2 (ME) 4 (SE) 5 (NE) 3 (SWE)
3. Making connections 1 (VE) 3 (SWE) 1 (VE) 4 (SE) 2 (ME) 4 (SE)
4. Using multiple strategies 1 (VE) 3 (SWE) 1 (VE) 4 (SE) 3 (SWE) 4 (SE)
5. Experiencing
Mathematics
1 (VE) 3 (SWE) 1 (VE) 5 (NE) 5 (NE) 4 (SE)
Direct Instruction (DI)
1. Orientation

3 (SWE)

4 (SE)

3 (SWE)

4 (SE)

2 (ME)

4 (SE)
2. Presentation 1 (VE) 4 (SE) 2 (ME) 3 (SWE) 2 (ME) 4 (SE)
3. Highly structured practice 2 (ME) 5 (NE) 2 (ME) 3 (SWE) 3 (SWE) 3 (SWE)
4. Guided practice 1 (VE)

4 (SE) 1 (VE) 2 (ME) 3 (SWE) 4 (SE)
5. Independent practice 2 (ME) 3 (SWE) 2 (ME) 4 (SE) 4 (SE) 4 (SE)
Marzano’s Strategies
1. Identifying similarities and
Differences

1 (VE)

3 (SWE)

2 (ME)

5 (NE)

4 (SE)

4 (SE)
2. Summarizing and note
Taking
2 (ME) 3 (SWE) 2 (ME) 4 (SE) 4 (SE) 5 (NE)
3. Reinforcing effort and
providing recognition
2 (ME)

3 (SWE) 2 (ME) 4 (SE) 3 (SWE) 4 (SE)
4. Homework and practice 1 (VE) 3 (SWE) 1 (VE) 4 (SE) 3 (SWE) 3 (SWE)
5. Nonlinguistic
representations
2 (ME)
diagrams
3 (SWE) 2 (ME) 4 (SE) 3 (SWE) 3 (SWE)
6. Cooperative learning 1 (ME)
Think-
Pair-share
3 (SWE) 2 (ME) 5 (NE) 5 (NE) 5 (NE)
7. Setting objectives and
Providing feedback
1 (VE)

3 (SWE) 2 (ME) 5 (NE) 5 (NE) 5 (NE)
8. Generating and testing
Hypotheses
1 (VE)

2 (ME) 3 (SWE) 5 (NE) 4 (SE) 5 (NE)
9. Questions, cues, and
Advance organizers

1 (VE) 3 (SWE) 2 (ME) 4 (SE) 4 (SE) 4 (SE)
Mean Score for the
Instructional Approaches:
Intellectual development,
Pedagogy, Direct Instruction,
and Marzano’s Strategies
41/27
=1.5
Between
VE and
ME
88/27
=3.3
Between
SWE and
SE
47/27
= 1.7
Between
VE and
ME
115/27
= 4.25
Between
SE and
NE
101/27
=3.74
Between
SWE and
SE
108/27
=4
SE
Teacher Self-efficacy
1. Student engagement:
Items 1,2, 4, 6,9,12, 14, and
22(N/A)
57/ 63
= 90%

47/63
=74%
56/63
=88%
20/63
= 32%
41/63
=65%
35/63
= 56%
2. Instructional strategies:
Items 7, 10, 11, 17, 18, 20,
23, and 24
66/72
= 92%
54/72
=75%
66/72
=92%
15/72
=21%
24/72
=33%
29/72
=40%
3. Classroom management:
Items 3, 5, 8, 13, 15, 16, 19,
and 20
56/72
=77%
53/72
=74%
67/72
= 73%
52/72
=72%
68/72
=94%
42/72
=58%
Mean Score for the
Teacher
Self-efficacy: Student
engagement, instructional
strategies, and classroom
management
90+92+77
=259

259/3
=86 %
74+75+74
=223

223/3
=74 %
88+92+73
=253

253/3
=84 %
32+21+72
= 125

125/3
=42%
65+33+94
=192

192/3
=64%
56+40+58
=154

154/3
=51%

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The second mathematics faculty observation
The second mathematics teacher is a full-time instructor who
teaches Elementary Algebra. During the interview, this instructor expresses
that he feels most comfortable by having students make connections and
use multiple strategies. At the same time, he mentions that he feels the
least comfortable in having students experience mathematics. He has
taught over thirty years in K-12 as a secondary mathematics teacher. With
the question of what can community college leadership do to assist the
mathematics faculty, he expresses encouraging cohesiveness among
mathematics faculty members by providing staff development opportunities.
He says, “Within the mathematics department, there is no one to pull the
faculty together, no active department chair and no division chair, nobody
presides over the curricular matters.”
He begins the lesson by writing down an agenda for the day on the
board and states his objective for the lesson that it is to cover the agenda.
He reviews homework problems and models problem solving process by
using a graphic organizer in a step-by-step manner. After explaining the
process, he asks, “Any questions about that?” A few students responded.
Then, he also asks students to problem solve in alternative ways by using a
graphic organizer. More questions are asked by the instructor. Students
are asked to engage in a cooperative activity to do think-pair-share, but
there are students who do not have any partners. Then, he talks about

211
error analysis of problem solving by asking students to think about whether
the mathematics error occurs due to carelessness, minor math error, or
major deficiency of math concept. On a worksheet, he asks students to
indicate the level of errors next to each problem. To do this, he encourages
students to work with someone. The cooperative activity is arranged
loosely. When some students choose to work independently, he does not
reinforce his expectation of working cooperatively.
For instructional strategies, he uses some of Marzano research-
based strategies, such as identifying similarities and differences, asking
questions, using graphic organizers, drawing pictures which is a form of
using non-linguistic representation, and cooperative learning of think-pair-
share while delivering the procedural mathematics knowledge. His
checking for understanding is based on asking students whether they have
any questions. For intellectual development standards, he focuses on
procedural problem solving and encourages to do error analysis that taps
into the students’ reasoning process. For the pedagogy standards, he uses
think-pair-share for the interactive lesson and tries to include using multiple
strategies in solving one-step equations. About one hour prior to the end of
the instruction time, he gives students a worksheet. Students have a
choice to stay to hear the guided practice or leave. The session begins with
17 students at 1:05 pm. Six students do not come back after the break. By
3:15 pm, only 11 students are working on the problems independently. As
soon as the instructor gives them a choice either to stay for the guided

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practice or leave, nine students left. Of those students who choose to stay,
two students express that they are confused because they do not know how
to do one-step equations. The instructor works with these two students.
Although this faculty member infuses some research based
instructional strategies, the instruction lacks the phases of direct instruction,
such as presentation, highly guided structure, and guided practice. The
ineffective use of direct instruction results in a lack of understanding about
one-step and two-step equations and creates a passive “compliance
engagement” and “retreatism” among many students with a high rate of
absenteeism. The inclusion of types of knowledge varies from factual,
procedural, to conceptual; however, the conceptual knowledge of
mathematics is covered slightly by using visual clues while lacking in depth
reasoning thinking opportunities for the adult learners. The cognitive
demand is at “remembering and understanding” instead of “applying,
analyzing, evaluating, and creating” domains of cognition.
The mean score for integrating the instructional approaches for
intellectual development, pedagogy, direct instruction, and Marzano’s
strategies is 3.3 that is between somewhat effective and slightly effective.
The mean score for the teacher efficacy of student engagement,
instructional strategies, and classroom management is 74% that he is
somewhat efficacious.

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The third mathematics faculty observation
The third instructor is a part-time female teacher who taught
Elementary Algebra. She is a full time high school teacher in K-12, and one
day she wishes to become a community college full-time instructor if the
salary is better than K-12. Her reason for teaching at this community
college is due to financial need and loves teaching community college
students.
She begins the lesson by reviewing the last week’s quiz. There are
18 adult learners. As she goes over the questions that students do not do
well on, she uses diagrams and pictures to explain the algebraic concepts.
She acknowledges the student effort. Modeling the problem solving
process that is highly structured, she often encourages students to link the
problem solving by creating diagrams and non-linguistic representations.
Solving problems with multiple strategies are encouraged by this instructor.
Students brainstorm the problem solving process with a partner by think-
pair-share activity.
During the error analysis, she asks students to analyze their errors.
As she goes over the homework answers, many students ask questions
and make comments freely to reason with the instructor. She frequently
checks for their understanding and encourages them to use calculators for
a five to ten minute period just to make sure that they understand how to
operate the calculators. There is a lot of humor and laughter and a positive
tone between the instructor and the students. She asks questions, such as

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“Does that always work in multiplication?” as well as “Do you think this is
true?”
The direct instruction begins by stating what students are going to
learn, then she begins the presentation on properties of real numbers by
using a graphic organizer. It is highly structured and uses non-linguistic
representations. The step-by-step practice is followed by guided practice
by providing sample problems from the textbook. Although students do not
have much time for independent practice on the newly introduced lesson,
the engagement level varies from authentic engagement, reluctant
engagement, to ritual engagement. The mean score for the instructional
approaches is 1.7 that indicates very effective and moderately effective.
The mean score for the teacher efficacy is 84% that she is moderately
efficacious.
The third faculty’s instructional strategies work for her students to
understand the lesson to be comprehensible. She weaves the direct
instruction phases of modeling and highly guided practice together in the
lesson; however, the types of knowledge that is the focus of the lesson is
focused on factual and procedural knowledge with occasional inclusion of
conceptual and metacognitive knowledge domains. The cognitive process
includes from remembering, understanding, to analyzing. This faculty
includes many of the intellectual development as well as pedagogy
standards.

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The fourth mathematics faculty observation
The fourth instructor teaches Elementary Algebra is a male full-time
teacher. He expresses that it is fun to teach. In his morning class, there
are thirty-nine students. He feels most comfortable using active and
interactive leaning and feels least comfortable with using multiple
strategies. Regarding what the community college leadership can do to
help faculty to increase their ability in teaching, he states the need to attend
conferences to learn about pedagogy. He does not have any K-12 teaching
background.
He begins his lesson and introduces me to the class. Then, he takes
attendance and models properties of real numbers. His instructional
strategies heavily focus on lecture that emphasizes the factual and
procedural knowledge, such as “Convert the negative to a positive and
clear the parentheses by expanding the distributive form”. He encourages
students to write down the process by saying, “The test, if you just write
down the answers with no process, I can’t give you any partial credit.” The
lesson is driven by the teacher without checking for students’ understanding
as he demonstrates the problem solving step by step. Depositing the
teacher content knowledge without any interactive activities nor checking
for understanding of the concept creates student engagement that varies
from ritual engagement, passive compliance, to retreatism.
The faculty’s mean score of the instructional approaches including
intellectual development, pedagogy, direct instruction, and research-based

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strategies is 4.25 that represents between slightly effective and never
effective. The mean score for the teacher self-efficacy is 42% that he is not
efficacious. The low teacher efficacy and the low level of instructional
effectiveness seem to be correlated.
The fifth mathematics faculty observation
The fifth instructor who teaches Intermediate Algebra is a female full-
time teacher. In the past, she has taught high school mathematics in K-12.
She is motivated to teach at the community college because she likes
teaching and helping students. About what can the community college
leadership do to help increase faculty ability in teaching, she responds with
this statement, “Make available of more professional staff development
opportunities.” She feels most comfortable in using active and interactive
learning while feeling least comfortable by having students experience
mathematics.
There are 28 students. She begins the lesson by distributing a
previous quiz, goes over the homework, and passes out another quiz that is
composed of two problems to measure their understanding of the content
that is going to be taught. While she is lecturing, some students seem to
have difficult time writing down all the steps. She comments, “Rational
expressions are hard to do. Make your exponents float… try to make effort,
so the bottom of the fractional exponent does not look like…” She sings a
song for students to remember the process on how to isolate the radicals to
square both sides. Using pictures, encouraging to take notes, making

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connections with problem solving and graphing, using a few nonlinguistic
representations, such as using her fingers, she tries to make the content
knowledge comprehensible. Frantically, there are some students writing
down the processes. The pacing of the lesson appears to be too fast for
the students to understand and to write down lecture notes at the same
time. This instructor incorporates some of the research-based strategies.
There seems to be a positive rapport between the students and the
teacher. However, when a few probing questions are asked by students to
reason the problem solving process, she quickly discourages them by not
explaining the conceptual content while focusing on the procedural
understanding exclusively. For example, when a student asked, “Why do
we write the imaginary ‘i’ like that? Why do we use ‘i’ ?” She responds,
“We just do.” The instruction is focused heavily on factual and procedural
knowledge with the cognitive domains of remembering and understanding.
The low levels of knowledge and cognitive processes do not allow students
to reason through the problem solving process. She often asks, “Any
questions on that?” With only a little wait time, she moves on to the next
problem.
During this time, two students are phone texting and another student
is doodling. The rest of the students are engaged with a varying degree of
engagement, from ritual engagement, passive compliance, and retreatism.
As she continues the lecture that is consist of presentation of modeling
problem solving processes with guided practice, the lesson came to an end.

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This faculty’s mean score for the instructional approaches are rated at 4.25
that represents between somewhat effective and slightly effective. The
mean score for the teacher efficacy is rated at 64% that indicated slightly
efficacious.
The sixth mathematics faculty observation
The sixth instructor who teaches Intermediate Algebra is a male full-
time faculty. At the interview, he states that he became a community
college mathematics teacher, because teaching mathematics excites him.
He wants to help students deal with their fears about learning mathematics
and conquer those fears. He feels most comfortable using active and
interactive learning strategies in teaching and feels least comfortable in
having students experience mathematics. With the prompt about what the
community college leadership can do to help increase the faculty ability in
teaching, he mentions to increase staff development funds.
There are 27 students in the afternoon class. The instructor begins
the lesson by saying, “There are 11 chapters. Next, we’ll do two chapters.
This is where you haven’t had Algebra II. We’re going to encounter new
materials.” He begins by lecturing on completing the square. He asks,
“Which formula am I referring to? What undoes the square?” He talks
about that completing the square becomes useful to us in graphing
parabolas. After that, he mentions about creating a balance of the equation
and demonstrates by using three markers while placing his finger in the
middle of the second marker. His instruction is focused heavily on factual

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and procedural understanding without checking for students’ understanding.
From the content, completing the squares, the instructor moves on to a new
concept, Pythagorean theorem with the direct instruction that includes
presentation and guided practice. The newly introduced concepts make
little connection from one phase to another. They seem segregated and
isolated. The isolated chunks of information are an exercise to instill the
procedural understanding of the Pythagorean formula. The instructor works
very hard continuously solving problems after problems. However, the
process is void of the mathematical reasoning process of conceptual
understanding in encouraging students to think about “why” the
mathematics concept works. He moves on to the next lesson by stating the
need for the quadratic formula.
Many students appear to take notes, but I am not sure their level of
conceptual and procedural understanding of the lesson. Some students in
the back of the classroom look like they are doing homework. After the
break session, a few students’ seats are vacant. However, the majority of
the students seem to be respectful and listen to the lecture quietly. The
student engagement level varies from ritual engagement, passive
compliance, and retreatism. As he ends the class, he encourages students
to work on two different approaches of procedural problem solving
processes.
The mean score for the instructional approaches that include
intellectual development, pedagogy, direct instruction, and Marzano

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research-based strategies is 4 that represents the effectiveness to be
slightly effective. The mean score for the teacher efficacy is 51% which is
not efficacious. It makes me wonder about what motivates the majority of
the students to stay in the class respectfully all the way to the end in
silence.
Finally, contrary to the findings of the high positive correlations
between self-efficacy constructs with the standards of intellectual
development, content, pedagogy, and Marzano’s research based strategies
of the survey data, the high self-reporting efficaciousness is not pervasive
during the classroom observations of six community college mathematics
faculty members. The discrepancy between the quantitative data and
qualitative data results in implications for practice and policy.

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Chapter Five

Findings and Conclusions

Summary of Findings

The research question, “What Is the Relationship between Self-
efficacy of Community College Mathematics Faculty and Effective
Instructional Practice?” examines the variables of self-efficacy and faculty
instructional practice. The constructs of self-efficacy, and the three strands
of American Mathematical Association of Two Year Colleges (AMATYC)
are highly reliable. It is evident from this study that high correlations exist
within the self-efficacy constructs and the instructional strategy constructs.
The high reliabilities and high correlations could be the result of an
exaggerated self-perception of the participants.
The reason for choosing the mixed method of quantitative and
qualitative data is to explore the relationship between self-efficacy and
instructional practice. By collecting data from two other sources to support
the quantitative from alternative viewpoints of multiple sources, the study
conclusions are more valid and credible. Issac and Michael (1997) assert,
Once a proposition has been confirmed by two or more
independent measurement processes, the uncertainty of its
interpretation is greatly reduced. The triangulation of
measurement process is far more powerful evidence
supporting the proposition than any single criterion approach
(p. 97).

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Considering the multiple outcomes- triangulation, data collection for this
research includes the quantitative data collection by three surveys, and two
qualitative data collection by interviews and observations. This approach of
multiple outcomes- triangulation has been encouraged by the assertions of
self-regulated learning (SRL) researchers. Winnie, Jamieson-Noel, and
Muis (2002) believe that studies of the calibration or match between self-
reports and traces are essential to offset the strengths of each kind of data
against weakness of the other.
Realizing the importance of multiple data collections, six faculty
members are chosen for interviews and observations. This purposeful
sampling is based on the availability of mathematics faculty during the
middle of January, 2008. After contacting these faculty members via email
and phone, an interview and an observation were scheduled. Three
community college mathematics teachers who volunteered to be
interviewed and observed taught Winter intercession classes while the
other three began the Spring semester at the end of January. I interviewed
two faculty members before their class began, and the other four were
interviewed after the class session ended.
The qualitative data collection from the interviews supports the
quantitative data; however, a discrepancy is found from the observation
data of the six faculty members who expressed a high level of
efficaciousness from interviews. Contrary to the survey data and interview
data, the observations reveal different results. Their actual instructional

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practice was less efficacious or less effective than their self-reporting
perception of their efficaciousness in instructional effectiveness. Based on
the quantitative self-reporting data and the interview data, I could have
concluded that the mathematics teachers impact student learning positively
since the majority of the community college mathematics faculty survey
participants perceived themselves to be highly efficacious from the
quantitative data analysis.
The quantitative findings of the large positive correlations between
the constructs of ability and effectiveness do not support the qualitative
evidence on actual teaching. The qualitative data of faculty observation
reveal a discrepancy between findings of actual teaching behavior and
teacher self-reports. The faculty’s highly efficacious self-reporting of
instructional effectiveness is indicated by the strength of correlations
between the measures: (a) the significance and size of correlation between
intellectual ability and intellectual development effectiveness is at p = .001, r
(43) = .86; (b) the significance and size of correlation between pedagogy
ability and pedagogy effectiveness is at p = .001, r (42) = .86; (c) the
significance and size of correlation between content ability and content
effectiveness is at p = .001, r (43) = .88; and (d) the significance and size of
correlation of Marzano’s instructional strategy effectiveness and Marzano’s
instructional strategy ability correlation is at p = .001, r (40) = .89. These
strong intra-correlations between ability and effectiveness within AMATYC’s
strands and Marzano’s research based strategies also reveal a perplexing

224
gap between quantitative self-reporting data and the qualitative
observational data.
I discovered this gap when examining the qualitative data of
effectiveness instruction. For example, of the six interviewees, the mean
score was about five on a Likert scale, zero being the lowest and five being
the highest. They all expressed a high level of self-efficacy in delivering
effective mathematics instruction. Four of the six relied heavily on lecture
containing mostly factual and procedural knowledge. The content delivery
consisted of solving problem after problem. The teachers skipped from one
topic to another. They routinely solved these problems without providing
opportunities to discuss the concept within procedural problem solving. Out
of the six instructors, four focused on continuous problem solving without
checking for student understanding, nor making connections with
conceptual understanding. The four faculty’s instruction focused heavily on
factual and procedural knowledge while only including two domains of
cognitive dimension (Anderson & Krathwohl, 2001) of remember and
understand. In general, the instructional strategies of the teacher examined
were mainly teacher talk and asking questions without enough wait time.
Student discussion was almost non-existent. The higher cognitive
processes hardly happened with conceptual and metacognitve knowledge.
The instruction hardly included higher order domains of cognitive
processes, such as apply, analyze, evaluate, and create. The instruction by
four teachers that lacked research based effective instructional strategies

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along with the deficiency in direct instruction resulted in a stagnant learning
environment that was quite different from the two instructors where the
learning environment included a variety of instructional strategies with
enthusiasm, humor, and laughter.
The gap between faculty’s self-perception of what they perceive to
be effective instruction in theory is not practiced through their teaching
behavior. This could mean that the teachers recognize the theoretical
constructs of effective instructional strategies, but they have not
internalized nor integrated it into their teaching practice. This is a gap
between theory and practice. According to Clark and Estes’ (2002) gap
analysis model, this could be a gap between knowledge and skills. This is
the gap of the art and science of teaching.
The survey of quantitative data supports the strong correlations of
the theoretical interpretations of what teachers perceive to be effective
instruction among various constructs. When comparing the statistical
relationship with the Pearson correlation from pedagogy effectiveness
through other AMATYC’s strands and researched based strategies of ability
and effectiveness to pedagogy ability, the correlations reveal strong positive
relationships. These quantitative findings demonstrate that there is a strong
statistical significant relationship between two constructs. These constructs
are strongly correlated to one another, such as from pedagogy
effectiveness to intellectual development effectiveness (p = .001, r (42) =
.86), from intellectual development effectiveness to Marzano’s instructional

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strategy effectiveness (p = .001, r (40) = .81), from Marzano instructional
strategy effectiveness to pedagogy effectiveness (p = .001, r (40) = .87),
from pedagogy effectiveness to pedagogy ability (p = .001, r (42) = .86),
from pedagogy ability to intellectual ability (p = .001, r (42) = .84), from
intellectual development ability to intellectual development effectiveness (p
= .001, r (43) = .86), from intellectual development effectiveness to content
effectiveness (p = .001, r (43) = .72), from content effectiveness to content
ability (p = .001, r (43) = .88), from content ability to pedagogy ability (p =
.001, r (42) = .82), then finally from pedagogy ability to pedagogy
effectiveness (p = .001, r (42) = .86).
Based on this data alone, I could have developed a premature
conclusion that faculty’s theoretical knowledge is transferred in their
teaching practice. Contrary to this, the reality is that strong correlations of
effective instructional strategies constructs do not mean that the
mathematics teachers deliver or implement effective instruction; rather, the
correlations show that community mathematics faculty can identify effective
instruction intellectually and theoretically. Transferring that theoretical
teaching knowledge in teaching practice has not been fully integrated in
community college mathematics classes based on the observations of six
faculty members. This could be the result of a motivational gap.
Learning specific instructional strategies require an extensive
amount of effort to internalize and incorporate in lesson delivery. This effort
of lesson delivery that translates theory into pedagogical practice takes a

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great amount of teacher efficacy. Teacher efficacy demands constant self-
monitoring, self-assessment, and self-reflection in order to improve teaching
practice through student engagement, instructional strategies, and
classroom management that are three constructs of teacher efficacy.
Another reason for this gap could be that teacher knowledge and
skills about what effective instruction is might vary greatly from one
community college mathematics teacher to another. Erickson (1986) says
that teacher effectiveness is a matter of the nature of the social organization
of classroom life—what we have called the enacted curriculum—whose
construction is largely, but not exclusively, the responsibility of the teacher
as instructional leader. When comparing the six community college
mathematics teachers, two teachers are “moderately efficacious” according
to the observational data. One has “very effective” and another has
“moderately effective” instructional practice. Both of these teachers have K-
12 teaching experience. The third mathematics teacher is “somewhat
efficacious.” This teacher has “somewhat effective and slightly effective”
instructional practice and has K- 12 teaching experience as well. The fourth
community college mathematics teacher is “slightly efficacious” and teaches
with “somewhat effective and slightly effective” instructional practice. This
teacher also teaches in K-12 during the day. It should be noted that the fifth
and sixth teachers who are not efficacious, both reveal “slightly effective”
instructional practice while one of them has “not effective” instructional
practice; and, interestingly, these two teachers do not have K-12 teaching

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experience. These two instructors’ ineffective teaching cannot be
attributed solely to a lack of K-12 teaching experience. However, the
variable of not having K-12 teaching experience stands out above all other
variables.
This variable sets them apart from the other more efficacious and
effective teachers as an indicator. This means that a lack of training in
pedagogical knowledge and skills contributes negatively to their
instructional delivery. As a result of not having sufficient teacher training,
their instructional delivery suffers. These instructors deliver ineffective
teaching that affects students’ learning negatively. These teachers need
pedagogical professional development to increase their efficacy of
efficacious teaching in order to deliver effective instruction.
Recommendations for Further Research
Recommendations for further research should include a large scale
study with a greater number of faculty to see whether reliabilities and
correlations can be replicated among the various constructs of self-efficacy
and effective instructional practice. In addition, it will be interesting to find
out whether the similar observational data will be obtained about community
college mathematics instructors with a large scale study. When conducting
research, I would inform the participants about how theory defines self-
efficacy and effective instruction to encourage a more accurate description
of their self-perceptions. For observations, I would go back for a second
time to observe the same faculty member in order to measure their

229
observation data. The data will be compared with the first observation to
find the commonalities and similarities of the observational data. In
addition, I would interview students’ perceptions of the instructor to rate
their effectiveness. Comparing faculty’s self-perception of efficacy and
effective instructional strategies through the students’ perception will create
a set of data on how a lesson is understood by students to find out what
strategies work and what strategies do not work. To measure this, it will be
beneficial to include quantitative and qualitative data. Also, it would be
interesting to see the effective instruction through students’ lens in
measuring the gap analysis. Comparing the gap analysis of the self-
efficacy of students and the self-efficacy of faculty through research-based
instructional strategies might generate data for other inquiries. The options
for further research seem limitless to find relationships between faculty self-
efficacy and their instructional practice with other constructs.
Limitations
The high self-rating about self-efficacy by the participants may be
due to the sources of research error, such as the halo effect. The halo
effect is described as the following,
This is the tendency for an irrelevant feature of a unit of study
to influence the relevant feature in a favorable or unfavorable
direction. Typically, a strong initial positive or negative
impression of a person, group, or event tends to influence
ratings on all subsequent observations. Impressions formed
early in as series of observations often affect later
observations; or impressions based on high or low status
attributes of the unit of study affect observations on unrelated
attributes-quoting a celebrity’s opinion on an educational issue

230
or associating emotionally-loaded labels with candidates in a
hotly contested school board election. The more vague and
impressionistic the variable to be rated, the more powerful is
the effect; the more specific and clearly defined the variable,
the less evident is the effect (Isaac & Michael, 1997, p. 90).

In other words, it is possible that the high efficacious self-rating could be
the result of the participants thinking that the constructs of self-efficacy is
vague and impressionistic which influenced their high rating.
Another research error for the high mean scores could be the result
of the Hawthorne effect. Issac and Michael (1997) point out causes of the
Hawthorne effect: (1) novelty; (2) awareness that one is a participant in an
experiment; (3) a modified environment involving observers, and special
procedures, and new patterns of social interaction; and (4) knowledge of
results in the form of daily productivity figures and other feedback, ordinarily
not systematically available (p. 91). In addition, Boekaerts emphasizes the
limitations of the self-reporting instrument and assessment:
Empirically supported knowledge does not naturally translate
into classroom practice. There are many reasons for the
occurrence of this bottleneck. One of the main reasons is that
teachers and motivation researchers differ in their perceptions
of what happens in the live classroom. A second, closely-
related reason is that there is no common language to talk
about these perceptions and about research findings. Indeed,
the training that teachers have enjoyed is diverse and only a
small percentage of the teachers are acquainted with
motivation theories. Even fewer were trained to use and
interpret psychological research methods to collect and
evaluate information about teacher practice. Another
bottleneck is that theory and research in motivation have not
been integrated well into theories of learning and instruction.
This implies that teachers, but also researchers who
investigate good teaching practice, tend to consider findings

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from motivation research alien to classroom practice
(Boekaerts, 2002).

Boekaerts differentiates how teachers and motivation researchers differ in
their perceptions. The lack of integration between theory and research in
the areas of motivation and theories of learning and instruction is one
example of the gap between scientifically researched findings of theory and
research versus the implementation of these research based instructional
strategies in teaching and learning. Possibly the perception of the research
participants could be different from my perception on self-efficacy and
effective instruction. In addition, the realization there is a lack of a common
language to talk about the perceptions about findings and teacher practice;
possibly, I need to go back to the community colleges and share this finding
of linking this research on motivational construct and classroom practice.
Another limitation could be that due to the small number of 50 participants,
this research also may have limitations for the generalization to a broader
audience of all community college faculty. The data represent a small
population of the community college mathematics faculty in Southern
California.
Implications and Interpretations
The implication of the observational finding is that the K-12 teaching
experience contributes positively to the instructional practice of the
community college mathematics faculty. The teachers who have K-12
education courses are more likely to be exposed to content pedagogy, such

232
as mathematics methodology. This could mean that they are more likely to
be aware of issues and concerns in delivering instruction while raising their
success rates in teaching students that raises their self-efficacy through
classroom management, instructional strategies, and student engagement.
The teachers who are exposed to pedagogical skills are more likely to
perform better in delivering effective instruction than the teachers who do
not have the pedagogical training that affects their level of efficacy.
In addition, the definition of effective instruction by the teachers
seems to have a connection with their K-12 experience. During the
interview, the four community college mathematics teachers with K-12
experience define effective instruction by the following: (a) “You can do it is
same as you can teach”; (b) “Effective instruction is same as effective
assessment and curriculum”; (c) “Being able to teach for the maximum level
of student understanding for the most number of students”; and (d)
“Whatever you are trying to get across to the students, it has to be palatable
and comprehensible.” These comments have one common theme. It is a
linkage of effective instruction with teaching: assessment, curriculum, and
student understanding and comprehension. When a teacher has a specific
objective for a lesson, the teaching is more likely to target for one or more
knowledge dimensions: factual, conceptual, procedural, and metacogntive.
When a teacher knows about teaching, he/she is likely to include the
cognitive process dimensions for students to remember, understand, apply,
analyze, evaluate, and create. The statements by the K-12 experience

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faculty infer that there is an internal efficacy belief. These teachers tend to
teach with a higher perceived efficacy than the teachers who do not have K-
12 experience. Perceived self-efficacy as beliefs in one’s capabilities to
organize and execute the courses of action required to produce given
attainments (Bandura, 1997).
Contrary to the four teachers with the K-12 experience, the two
teachers who do not have K-12 teaching experience equate effective
instruction as “helping students to think critically” and “apply the knowledge
and assisting students with clear communication to be successful.” Their
responses seem to be more general and focus on helping students with
cognitive processes. Although their internal efficacy is within themselves,
the responses seem to have less implication for teaching. The implication
of the observational finding is that the K-12 teaching experience could
contribute positively to the teachers’ instructional practice. The teachers
who have K-12 education courses are more likely to be exposed to content
pedagogy, such as mathematics methodology. This could mean that they
are more likely to be aware of issues and concerns in delivering instruction
while raising their success rates in teaching that raises their self-efficacy
through classroom management, instructional strategies, and student
engagement. The teachers who are exposed to pedagogical skills are
more likely to perform better in delivering effective instruction than the
teachers who do not have the pedagogical training that affects their levels
of efficacy.

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Teaching effective instruction requires a complexity of multi-
dimensions of a teacher’s repertoire. This involves transferring knowledge
into skills, increasing motivation by making active choices to select right
curriculum, applying mental effort in seeking out the best instructional
strategies for engaging students while monitoring students’ performance in
learning, and practicing persistently in maintaining an effective learning
environment to master the pedagogical skills through practice in a
classroom context. The conversion of theory and practice takes a set of
specific content knowledge called, pedagogy. Ball and colleagues
describe, “Effective teaching requires an understanding of the underlying
meaning and justifications for the ideas and procedures to be taught and
the ability to make connections among topics (Ball et al., 2005).”
The implication from the teachers who have K-12 experience and
who perceive effective instruction lies within the ability of what a teacher
does in the classroom suggests that they are more efficacious than the
teachers who do not have the K-12 pedagogical training. This could mean
that explicit pedagogical knowledge contributes to teacher efficacy. This
could mean that the explicit mastery of various instructional strategies has
to be taught, modeled, and observed. Four building blocks of self-efficacy
of mastery experiences, vicarious experiences, social persuasion, and
emotional arousal (Bandura, 1997) can be infused in mathematics faculty’s
professional development programs by making pedagogical knowledge
specific and explicit through modeling effective instructional strategies. This

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would promote teacher efficacy. Observing one another’s teaching and
peer coaching can benefit the faculty through a dialogue of collaboration in
sharing one’s teaching approaches. Observing one another’s instruction
can create opportunities for them to reflect on their instructional practice
that focuses on student learning. This could lead to an awareness or need
for collaboration that might open doors to seek assistance from the
community college leadership.
The culture of faculty learning collectively and interdependently can
change the culture of the department and the academic senate within a
community college. However, this requires the support of the community
college leadership. The leadership that can raise faculty’s efficacy by
empowering them with pedagogical knowledge and skills that will increase
student performance; in turn, this will promote students’ transfer rates and
graduation rates. Student achievement depends heavily on the efficacy of
the ability of teachers to deliver effective instruction, effective pedagogy that
is the art and profession of teaching. Ball and her colleagues point out,
Teaching demands knowing appropriate representations for a
particular mathematical idea, deploying these with precision,
and bridging between teachers’ and students’ understanding.
It requires judgment about how to reduce mathematical
complexity and manage precision in ways that make the
mathematics accessible to students while preserving its
integrity. Well-designed instructional materials, such as
textbooks, teachers’ manuals, and software, may provide
significant mathematical support, but they cannot substitute
for highly qualified, knowledgeable teacher. Teachers’
mathematical knowledge must be developed through solid
initial teacher preparation and ongoing, systematic
professional learning opportunities (Ball et al., 2005, p. 4).

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To raise authentic mathematics faculty’s efficacy, the teachers’
mathematical knowledge must be developed through ongoing and
systematic professional learning opportunities. The community college
mathematics teachers know the content; however, if a teacher does not
have K-12 teaching experience, he/she is less likely to be exposed to
pedagogical knowledge. This lack of exposure impedes their
understanding in “how” to teach. Even among the teachers who have K-12
teaching experience, the level of student engagement varies greatly.
Community college leadership needs to provide opportunities for faculty
professional development that directly affects the faculty’s instruction. This
professional learning has to be meaningful to raise the faculty’s efficacy
with specific student performance data to meet a common goal.
Based on Bandura’s social cognitive learning theory of self-efficacy
(1997), personal efficacy can be interpreted into teacher efficacy.
Teachers’ beliefs determine how teachers feel, think, motivate themselves
and behave. Such beliefs produce diverse effects through four major
processes: cognitive, motivational, affective, and selection processes. A
strong sense of efficacy enhances teacher accomplishments and personal
well-being in many ways. Teachers with high assurance in their capabilities
approach difficult teaching tasks as challenges to be mastered rather than
as threats to be avoided. Such an efficacious outlook fosters intrinsic
interest and deep engrossment in integrating instructional activities. These

237
teachers set for themselves challenging goals and maintain a strong
commitment in delivering effective instruction. They heighten and sustain
their efforts in the face of failure of unsuccessful lessons. They quickly
recover their sense of efficacy after failures or setbacks from student
engagement, classroom management, and instructional strategies. They
attribute failure to insufficient effort or deficient knowledge and skills that are
acquirable.
Contrary to the teachers with high efficacy, Bandura (1997) also
describes another spectrum of efficacy that is low personal efficacy. It can
be expressed as the following. Teachers with low self-efficacy have similar
attributes. Teachers who have low efficacy doubt their capabilities. They
shy away from difficult tasks of integrating instructional strategies for
engaging students. They view difficult students as personal threats. They
have low aspirations and a weak commitment to the goals of maximizing
student engagement; and therefore, they choose not to try to reach a level
of authentic student engagement. They tolerate students who have given
up and manifest apathy and low motivation. These low efficacious teachers
choose not to intervene in these students’ learning. When faced with
difficult tasks of raising student performance, they dwell on student
deficiencies instead of examining within themselves to meet the needs of
the student. The obstacles they encounter in classroom, students’ low
socioeconomic status, low parental support, diverse cultural and ethnic

238
backgrounds, special needs, low teacher morale, and all kinds of adverse
outcomes overwhelm the teacher’s capacity.
As a result of low motivation, teachers with low efficacy have
difficulty developing in themselves the pedagogical abilities and
effectiveness that are needed for student learning. They slacken their
efforts and give up quickly in the face of difficulties with classroom
management, instructional strategies, and student engagement. They are
slow to recover their sense of efficacy following failure or setbacks because
they view insufficient performance as deficient aptitude not in themselves;
but they are likely to attribute the deficient student learning to students’
inability to learn. They lose faith in their capabilities to deliver effective
instruction due to low efficacy. These teachers fall easily to stress and
depression; eventually, they are more likely to experience burnout and
blame academic inadequacies, low aspirations and motivations of students,
and end up not caring and not respecting students.
Therefore, the uncaring teachers affect negatively student
performance. Knowing the teachers do not care, the students rebel, defy,
and become not compliant in these teachers’ classrooms that create a
never ending cycle of inefficacious teachers and unhappy students and
parents with ineffective instructional practice and deficient student
achievement. This affects the future of this nation’s knowledge economy
because the students’ learning have been delayed due to the low teachers’
motivation, knowledge, and skills.

239
In order to raise teachers’ efficacy, teachers need learning
opportunities, it takes professional development in learning and teaching.
Ball and Cohen (1999) urge,
The vision of a better education is complex. Teachers are to
help diverse learners become competent and skilled,
understand what they are doing, and communicate effectively.
Schools are to be connected with their communities, and all
students are to succeed in ways they currently do not and
never have before in the history of American public education.
If such plans are to move in any significant way beyond
rhetoric to permeate practice, significant professional
development will be crucial, for such instruction is not
commonplace. Nor could teachers change instruction in
these ways simply by being told to do so. Teachers would
need opportunities to reconsider their current practices and to
examine others, as well as to learn more about the subjects
and students they teach (p.3)

The opportunities to evaluate current teaching practices in one’s own and
others’ teaching as well as to learn more about the subjects and students
they teach demand personal humility and professional will. To improve
instruction, extraordinary teachers with humility and will are needed in
America who are determined and committed to exercise instructional
leadership. In the book, Good to Great, Collins (2001) describes Level 5
leadership as building enduring greatness though a paradoxical blend of
personal humility and professional will. Collins delineates the Level 5
leadership as having the following attributes: (1) “ordinary people quietly
producing extraordinary results (p. 28”); (2) “equally about ferocious
resolve, an almost stoic determination to do whatever needs to be done (p.
30)”; (3) “channel their ego needs away from themselves and into the larger

240
goal (p. 21)”; and (4) “looking in the mirror to apportion responsibility, never
blaming bad luck when things go poorly (p.35).” Interestingly, Collins’
research team points out that “Level 5 as a key component inside the black
box of what it takes to shift a company from good to great. Yet inside that
black box is another black box – namely, the inner development of a person
to Level 5 (pp. 37-38).” This desire for “inner development of a person” or
“inner development for pedagogy of a teacher” is a motivational construct
that contributes to the teacher’s belief in his/her efficacy.
Bandura (2005) states that beliefs in one’s efficacy is a key personal
resource in self-development, successful adaptation, and change. It
operates through its impact on cognitive, motivational, affective, and
decisional processes. Efficacy beliefs affect whether individuals think
optimistically or pessimistically, in self-enhancing or self-debilitating ways.
Such beliefs affect people’s goals and aspirations, how well they motivate
themselves, and their perseverance in the face of difficulties and adversity.
Efficacy beliefs also shape people’s outcome expectations – whether they
expect their efforts to produce favorable outcomes or adverse ones.
Efficacy beliefs determine how environmental opportunities and
impediments are viewed.
Self-efficacy plays a critical role in teacher education. The primary
purpose of teacher education is to cultivate the knowledge, skills, and
values that will enable teachers to be highly effective in helping students to
learn (Ball & Cohen, 1999). Effective teachers make a significant difference

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in student achievement (Marzano, 2007). Marzano substantiates his
research findings with one key element. The one factor that surfaces as the
single most influential component of an effective school is the individual
teachers within a school.
The most important factor in student learning is also supported by
Nye and colleagues. Their findings reveal students who have a teacher at
the 75
th
percentile in terms of pedagogical competence will outgain students
who have a teacher at the 25
th
percentile by 18 percentile points in
mathematics. Likewise, students who have a 90
th
percentile teacher will
outgain students who have a 50
th
percentile teacher by 18 percentile points
in mathematics (Nye, Konstantopoulos, & Hedges, 2004, as cited in
Marzano, 2007). The researchers note that teacher effects are large
enough effects to have policy significance.
The teachers who believe they can shape their own expectations of
teaching tend to apply more effort to produce outcomes of effective
pedagogical skills. They do this by finding opportunities for professional
development where by they grow and master the skills of pedagogy. These
efficacious teachers think optimistically when encountering difficult students
with severe deficiency in basic skills. They keep themselves motivated by
persevering through difficult teaching situations while raising students’
motivation for learning. They exercise control over their emotions. They
infuse humor in teaching because they realize the power of emotional
arousal in teaching. They have an enclave of supporters to talk about their

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teaching to gather ideas or bounce off their frustrations and difficulties in
teaching. These efficacious teachers are dedicated and committed
teachers.
Although much of their being is so consumed with teaching and
learning, they face students with authentic self-efficacy. They transfer
pedagogical knowledge into skills with the infusion of theory and practice as
they strive to teach effectively. While they carefully balance their personal
lives with their professional lives, they grow wisely by deepening their
compassion for students by building professionally caring relationships with
students and passion for the content and pedagogy knowledge in teaching
as they grow intellectually. They realize that teaching is more than a job.
Teaching is their career and calling.
With this sense of purposefulness in their profession, they improve
continually. Their professional improvement cycles through four
components of plan, teach, assess, and reflect (California Commission on
Teacher Credentialing and the California Department of Education, 1998).
They independently and collectively inquire about teaching while infusing
content knowledge with pedagogy knowledge to promote students’
intellectual development. As they radiate through learning and teaching,
they ignite students’ desire for learning. Their learning energy is
contagious.

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Discussion
Where are highly efficacious and effective mathematics teachers at
community college campuses? My research indicates based upon a small
sample of 50 faculty that about 70% of community college teachers need to
invest their effort in raising their teaching efficacy through professional
development. How do community colleges go about accomplishing in
raising teacher efficacy to implement effective instructional strategies?
Effective collaboration is perhaps the most effective form of staff
development (Schmoker, 1999). Schmoker urges that it is time for a
breakthrough,
With all this knowledge, we are dancing on the edge of a
revolution in the quality of education we can provide, and
arguably, our quality of life. Yet, most schools still do not (1)
conscientiously examine the number of students who can do
such activities as problem-solve, analyze, calculate, and
compose and then (2) adjust instruction and programs
accordingly (1999, p.6).

Collins (2001) encourages the transformation as a process of buildup
followed by breakthrough, broken into three broad stages: disciplined
people, disciplined thought, and disciplined action. Within each of these
three stages, there are two key concepts that wraps around the three
stages. Collins calls this the flywheel, which captures the gestalt of the
entire process of going from good to great. In order for the transformation
to take place, Collins notes on two distinctive forms of disciplined thought:
infusing the entire process with the brutal facts of reality and developing a
simple, yet deeply insightful, frame of reference for all decisions.

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There are number of brutal facts for community college faculty and
administrators, inadequacy in students’ transfer rates to higher education
institutions (Shulock & Moore, 2007), low student graduation rates (RP
Group Perspectives, 2007) , high dropout rates (Boylan, 2004a), non-
returning students to colleges (Olson, 2005), and deficiency of basic skills
knowledge (Boylan, 2004b; Bundy, 2000; Bustillos, 2006; Illich, Hagan, &
Leslie, 2004; Jenkins & Boswell, 2002). Schmoker delineates,
Our best “plan” is to arrange for teachers to analyze their
achievement data, set goals, and then meet at least twice a
month – for 45 minutes or so. That way, they can help one
another ensure that they are teaching essential standards and
using assessment results to improve the quality of their
lessons (Schmoker, 2006, p. 34).

However, realizing the need for the knowledge economy of the
nation, America’s community colleges need to raise the bar of having all
teachers who carry out the effective instruction through learning and
practice. Ball and Cohen (1999) urge the importance of learning in and
from practice,
This is inquiry into teaching in teaching. The knowledge of
subject matter, learning, learners, and pedagogy is essential
territory of teachers’ work if they are to work as reformers
imagine, but such knowledge does not offer clear guidance,
for teaching of the sort that reformers advocate requires that
teachers respond to students’ efforts to make sense of
material. To do so, teachers additionally need to learn how to
investigate what students are doing and thinking, and how
instruction has been understood, as classes unfold.
Conducting such investigations of student learning is essential
to the new pedagogies that reformers urge, as well as to
effective traditional instruction (p. 11).

245
In order for the inquiry into teaching in teaching to take place, it
requires highly efficacious teachers who could regulate learning and
teaching. Bandura describes human attributes: symbolization, forethought,
vicarious learning capacity, self-regulatory capability, and self-reflection
(Evans, 1989). Evans states that because people can project into the
future, they can regulate and motivate themselves by anticipated outcomes
and aspirations. They anticipate likely consequences of possible actions,
set goals for themselves, and otherwise plan courses of action that lead to
valued futures. Forethought often saves us from the perils of a
foreshortened perspective. Evans (1989) points out that this happens
because people’s self-beliefs in their capabilities enable them to exercise
some control over events that affect their lives and how self-belief translates
into human accomplishments, motivation, and personal well-being.
Conclusion
The Need for Effective Instruction
Based on my research, I find that community college mathematics
instructors need to integrate into their teaching a variety of instructional
strategies, such as direct instruction (Joyce, Weil, & Calhoun, 2004),
research-based strategies (Echevarria, Vogt, & Short, 2008; Marzano,
Pickering, & Pollock, 2001), higher order thinking styles by infusing four
types of knowledge dimension with six dimensions of the cognitive process
(Anderson & Krathwohl, 2001). The current teaching focuses heavily upon
factual and procedural knowledge dimension and the cognitive process

246
dimension of remember and understand. In order for community college
mathematics teachers to move from the factual and procedural knowledge
dimension to conceptual and metacognitve knowledge dimension while
incorporating the other dimension of cognitive process, the faculty members
need to raise their teaching performance in order to eliminate the dismal
student achievement in basic skills, transfer rates, and graduation rates. Of
course, they could blame the students’ deficient understanding of basic
skills upon K-12 educators; however, the bottom line is that someone has to
be responsible and accountable for helping these students with academic
deficiency based on where students are.
Effective instruction requires engaging students in learning through
research-based instructional strategies (Echevarria, Vogt, & Short, 2008;
Marzano, Pickering, & Pollock, 2001) while at the same time weaving the
pedagogy and intellectual development standards of AMATYC (American
Mathematical Association of Two Year Colleges) in teaching mathematics
content. To impart content specific mathematics knowledge, the knowledge
must be integrated with four types of knowledge dimensions: factual,
conceptual, procedural, and metacogntive (Anderson & Krathwohl, 2001).
When teaching with direct instruction (Joyce, Weil, & Calhoun, 2004), the
teacher should incorporate the five phases of a lesson: objective of the
lesson (orientation), modeling the concept (presentation), adding structured
input (structured practice), guiding the students’ understanding (guided
practice), and ensuring that students are able to work independently

247
(independent practice). During direct instruction, the teacher delivers the
content knowledge to students through the cognitive process dimensions in
order to move them from a lower level of cognition, such as “remember and
understand” to a higher level of cognition, “apply, analyze, evaluate, and
create” (Anderson & Krathwohl, 2001).
When the teacher works to enhance students’ understanding about
mathematics, the teacher as an inquirer needs to study his/her own
teaching capacity to make the student understanding comprehensible. In
doing so, the teacher continuously reflects and improves. The teacher’s
pedagogical knowledge and skills transform from factual and procedural to
conceptual and metacognitive pedagogy knowledge levels. During this
process, the teacher tries multiple strategies to engage the defiant and
reluctant learners, so students experience mathematics with authentic
engagement (Schlechty, 2002). Therefore, effective teaching requires
much commitment and motivation by the teacher.
The core of effective instruction needs to be planted deeply within
the inner-self of the teacher’s self-efficacy. Highly efficacious teachers are
courageous by trying out new instructional strategies. They are motivated
to respond to the calling of the profession, teaching, that equips students
with content knowledge. They are tenacious and committed to reaching
every student in the classroom.
The teacher knows how to manage his/her classroom with heart
(Ridnouer, 2006). This teacher teaches, so students can remember

248
through seven Rs: reach, reflect, recode, reinforce, rehearse, review,
retrieve, and realization (Sprenger, 2005). The teacher ignites student
learning though research-based strategies: seeking to captivate students’
attention, building dendrites through realizing the power of assessment,
knowing how stress and emotion affect learning, and linking memory,
learning, and test-taking success while making connections as a neurologist
and classroom teacher (Willis, 2006). This teacher strives to activate the
desire to learn by making connection with theory and research and practice
by tapping into understanding the internal motivation of students (Sullo,
2007). To ignite the desire to learn, this teacher creates a need-satisfying
environment, transforms from telling to asking, from enforcing to teaching
responsibility and fostering positive relationships (Sullo, 2007).
Effective teaching is tremendously complex and demands much
effort. With a curriculum, the effective teacher paces the student learning
through effective teaching. Effective teaching looks like it is linear;
however, effective instruction combined with the self-efficacy constructs of
student engagement, instructional strategies, and classroom management
creates a two-dimensional shape with the teacher’s knowledge and skills as
well as motivation that in turn narrows the students’ learning gap. When
organizational support is added to the teacher efficacy and effective
instructional tools, the learning environment creates a three dimensional
form. What moves this three dimensional form with upward mobility is
student learning. The key element of creating this non-linear artistry of

249
combining the science and the art of knowledge and skills is the teacher
who integrates knowledge and cognitive dimensions together. As a result,
the learning organization moves into the fourth dimensions of human
existence into space and time with the mastery of student understanding.
Integrating self-efficacy and effective instructional strategies through the
components of gap analysis: knowledge/skills, motivation, and
organizational barriers are shown in Figure 19.
Teaching is multi-dimensional. Teachers are movers and shakers of
this dimensional learning environment. Effective teachers impact student
learning by assisting them with mastery of knowledge and skills that raises
their efficacy. In turn, raising students’ efficacy affects teachers’ efficacy
positively. Teachers and students are bound together in a wheel of
reciprocity. In this reciprocal relationship, they give and receive. Effective
teachers serve students with respect and professional compassion. This
demands a deep level of humility. Effective teachers empower student
learning by their passion to master the pedagogical knowledge and skills.
This requires professional will to learn. Effective teachers are born while
serving the students, and they are made as they improve their practice of
mastering pedagogical knowledge and skills (See Figure 19).

Figure 19, Integrating Self-efficacy and Effective Instructional Strategies
through the Components of Gap Analysis: Knowledge/Skills,
Motivation, and Organizational Barriers

Student engagement
Instructional
Strategies
factual
procedural
conceptual
metacognitive
remember
understand
apply
analyze
evaluate
create
Classroom Management
Direct instruction
Research
Based
Strategies
(Marzano)
The SIOP
Model
Intellectual Development through Content
Pedagogy
Organizational Systemic Capacity

250

251
Recommendations
There are two layers of recommendations to promote student learning.
One layer is for faculty and the other layer is for college administrators. The
recommendations for community college faculty are as follows: (1) the need
for professional development; (2) the need for a professional learning
community; (3) the need for staff development to raise faculty efficacy; and
(4) the need for data based decision making to produce results. The other
recommendations are two-fold for college administrators. They are what
they can do within and beyond a community college.
Recommendations for Community College Faculty
(1) The Need for Professional Development
The interview findings reveal that community mathematics teachers
need specific mathematics professional development. Five out six (about
83%) interviewed participants desire and plead for more professional
development in pedagogy as well as wanting more opportunities to meet
together to talk about teaching. Yet, the reality is that the current system
only allows them to meet one day per year, 12 hours of college flex day
meeting that is not related to teaching math, or minimum of 30 hour
requirement that has little to do with teaching mathematics. This calls for
support by the administrative leadership in developing a system that
creates opportunities for content specific professional development. To
teach effectively requires serious professional development. Teachers are
the most important element of student achievement (Ball et al., 2005;

252
Marzano, 2003); therefore, professional development is not an option, but a
necessity.
To deliver mathematics content knowledge in order to develop
students’ intellectual development, the mathematics instructors need
professional development opportunities to learn about research-based
pedagogy knowledge and skills. This must be explicitly and systematically
modeled and shared with the faculty members through professional
development. I believe that the majority of community college mathematics
faculty is interested in promoting student achievement. I also believe that
they are capable of motivating themselves to regulate their teaching to
produce effective instruction.
To create the outcome of effective instruction is going to require the
collective efficacy of college faculty and administrators who value
instructional efficacy for every division of the campus. Bandura (1997)
emphasizes that “Collective efficacy is not simply the sum of the efficacy
beliefs of individuals. Rather, it is an emergent group-level attribute that is
the product of coordinative and interactive dynamic (p.7).” The collective
efficacy of the academic senate that focuses on teaching and learning will
increase the teacher efficacy, and it will contribute positively to student
achievement. However, this efficacy building exercise is going to take a
tremendous amount of desire and commitment by the top leadership in
order for every sector of the institution to deeply value learning and
teaching. This commitment has to be deeply engrained in the heart of a

253
president as well as every single faculty and staff member in the institution.
Shulman (1986) points out,
Until faculty members in schools and colleges of education
take responsibility for the demonstrated competence in
content, pedagogy, and performance in the classroom of the
students whom they admit as well as those they graduate,
little progress will be made. Formal assessments for teachers
may well be important in moving us toward those goals, but a
concerted commitment by educators will the real key (p. xiv).

Collective efficacy in learning and teaching at every single division of
the academic senate has to be integrated with the commitment of the
governance of the college. Whether a college has shared governance or
not, the culture of community college must value learning and teaching in
order for faculty to grow together to master effective instruction. This
requires professional development.
(2) The Need for a Professional Learning Community
A professional learning community (PLC) is the byproduct of a
collective efficacy within a learning organization. The efficacy levels might
vary; however, as staff members work together, they focus on common
goals for student learning. When this happens, they more likely to
contribute to the organizational existence in a positive way. In this process,
the school culture changes with the integration of personal efficacy and
collective efficacy. When individual’s efficacy combines with collective
efficacy, it creates a synergistic organization.
Eaker points out that changing the school culture to become a
professional learning community involves many elements: collaboration,

254
developing mission, vision, values, and goals, focusing on learning,
leadership, focused school improvement plan, celebration, and persistence
(Eaker, DuFour, & DuFour, 2002). To be a part of the professional learning
community takes motivation. Clark and Estes (2002) delineate that
motivation is the product of an interaction between people and their work
environment. The two authors point out, “Excellent human performance in
today’s organizations is a complex phenomenon and grows out of passion,
belief, expectation, and expertise (p. 87).” In addition, Clark and Estes
emphasize four factors that have a major influence on motivational goals:
(a) help people develop self-and team-confidence in work skills; (b) be alert
and remove perceived organizational barriers to goal achievement; (c)
create a positive emotional environment for individuals and teams at work;
and (d) suggest reasons and values for performance goals. Clark and
Estes (2002) also note,
The objective of adopting a more positive motivational climate
is to increase individual and team confidence, interpersonal
and organizational trust, collaborative spirit, optimism, positive
emotions, and values about work. The benefit of achieving a
more motivated organization is in increased persistence at
work tasks and a higher quality of mental effort invested in
work goals (p. 100).

Professional learning communities in community colleges require people
who make active choices in learning, and applying effort in producing
desired outcome for student learning, and people who are pursuing these
goals relentlessly. In order for people work interdependently with a sense
of common connectedness, it requires trust.

255
Tschannen-Moran elaborates on trust as having five facets:
benevolence, honesty, openness, reliability, and competence (Tschannen-
Moran, 2007). The author notes, “The absence of trust impedes
effectiveness and progress. If trust breaks down among any constituency,
it can spread like a cancer by eroding academic performance and ultimately
undermining the tenure of the instructional leader (p. 99).” The trust among
professional learning community members binds them together. They rely
on each other to be honest and open to solve problems together. They
trust each other to be competent at what they do and rely on each other’s
benevolence while serving one another to develop the entire staff
collectively. Along with trust, the energy must focus on staff development.
DuFour and Eaker point out the content of staff development
programs in a professional learning community includes the following: (1)
Staff development content is based on research; (2) Staff development
content focuses on both generic and discipline-specific teaching skills; and
(3) Staff development content expands the repertoire of teachers to meet
the needs of students who learn in different ways (DuFour & Eaker, 1998).
This type of staff development in professional learning communities will
raise faculty efficacy.
During this type of staff development among adults, Tate encourages
using 20 professional learning strategies that could engage the adult
learners. These strategies can be used as a tool to increase collective
efficacy to foster a positive climate within the professional learning

256
community. These 20 learning strategies include Gardner’s multiple
intelligences along with learning modalities (Tate, 2004): (1) brainstorming
and discussion; (2) drawing and artwork; (3) field trips; (4) games; (5)
graphic organizers; (6) humor and celebration; (7) manipulatives and
models; (8) metaphors, analogies, and similes; (9) mnemonic devices; (10)
movement; (11) music, rhythm, rhyme, and rap; (12) project – and problem
– based instruction; (13) reciprocal teaching, cooperative learning, and peer
coaching; (14) role-plays, drama, pantomimes, and charades; (15)
storytelling; (16) technology; (17) visualization; (18) visuals; (19) work study
and action research; and (20) writing and reflection. The comparison of
professional learning strategies to learning theory is shown in appendix L.
(3) The Need for Staff Development to Raise Faculty Efficacy
Professional development to raise faculty’s efficacy demands for the
mastery of knowledge and skills, reflection and dialogue, time, and
evaluation. The importance of the process of staff development in a
professional learning community includes four components: (1) The
process of staff development provides the coaching critical to mastery of
new skills; (2) The process of staff development results in reflection and
dialogue; (3) The process of staff development is sustained over a
considerable period of time; and (4) The process of staff development is
evaluated at several different levels (DuFour & Eaker, 1998).
Teaching is complex. To teach effectively, not only the teacher has
to have deep content understanding, but also needs to aware of when to

257
use what instructional strategy of having pedagogy knowledge and skills. In
addition, the teacher has to ensure that new concepts are taught explicitly
with structured guided practice to break an abstract concept into a chunk
that students can understand. This requires the need for direct instruction:
orientation, presentation, structured guided practice, guided practice, and
independent practice (Joyce, Weil, & Calhoun, 2004).
As the teacher navigates by imparting the factual and procedural
knowledge of mathematics by assisting students to remember and
understand, students seem to likely to retain the knowledge when the
lesson is taught with an objective of assisting students to develop
interrelationships and patterns of the concept by analyzing and evaluating
the differences and similarities of concepts. This is the conceptual
understanding of knowledge dimension and helping students to be aware of
their own cognition, which is thinking about thinking, by analyzing their
errors of problem solving and developing strategies on what needs to be
learned requires a deep level of teacher motivation because this takes time
and tremendous effort on the teacher.
Staff development to raise faculty’s efficacy can be done through
Bandura’s four building blocks of self-efficacy: mastery experience through
modeling, vicarious experience through peer observations to create
dialogue, social persuasion through collaboration to promote collective
efficacy, and emotional arousal though raising the moral of teachers by
making data driven decision making that is doable and attainable. This will

258
require a guideline of professional development. The editors, DuFour,
Eaker, and DuFour of the book, On Common Ground which is about the
power of professional learning communities, agree on these strategies: (1)
embrace learning rather than teaching as their school’s mission; (2) work
collaboratively to help all students learn; (3) use formative assessments and
a focus on results to foster continuous improvement; and (4) assume
individual responsibility to take steps to create such schools (Barth et al.,
2005).
These four strategies for professional staff development can be
integrated in the community college context by embracing learning
pedagogical knowledge and skills, work collaboratively as a division; use
ongoing assessments to establish teaching and learning goals that is based
on data, and take steps to be accountable for student learning. To raise the
motivation of teacher efficacy, the professional development can be
learning teaching strategies from each colleague through modeling and
observation.
Bandura believes that by providing modeling, one can transmit skills,
attitudes, values, and emotional proclivities (Evans, 1989). He calls this
process as the acquisition function – the teaching function of modeling.
Modeling can also reduce or strengthen inhibitions over preexisting
behavior. If people observe a model’s action resulting in punishing
consequences, this discourages them from using that pattern of behavior.
However, if they observe that modeling results in positive consequences,

259
this encourages them to adopt similar behavior (Evans, 1989). Success
typically raises self-efficacy; failure lowers it (Pajarez, 2000).
The second source is the vicarious experiences of the effects
produced by the actions of others by social models, such as seeing people
similar to oneself manage task demands successfully. Seeing people
similar to oneself succeed by sustained effort raises observers’ beliefs that
they, too, possess the capabilities master comparable activities to succeed
(Bandura, 1994). Bandura emphasizes that the greater the assumed
similarity, the more persuasive are the models’ successes and failures. If
people see the models as very different from themselves, their perceived
self-efficacy is not influenced much by the models’ behavior and the results
it produces.
The third source is social persuasion. Individuals also create and
develop self-efficacy beliefs as a result of the social messages,
persuasions, and dispersuasions they receive from others (Pajares, 2000).
Social persuasion is a way of strengthening people’s beliefs that they have
what it takes to succeed. People who are persuaded verbally that they
possess the capabilities to master given activities are likely to mobilize
greater effort and sustain it than if they harbor self-doubts and dwell on
personal deficiencies when problems arise (Bandura, 1994). Bandura adds
that it is more difficult to instill high beliefs of personal efficacy by social
persuasion alone than to undermine it. Unrealistic boosts in efficacy are
quickly disconfirmed by disappointing results of one’s efforts. But people

260
who have been persuaded that they lack capabilities tend to avoid
challenging activities that cultivate potentialities and give up quickly in the
face of difficulties.
The fourth source is emotional arousal. Positive mood enhances
perceived self-efficacy, despondent mood diminishes it. This way of
modifying self-beliefs of efficacy is to reduce people’s stress reactions and
alter their negative emotional proclivities and interpretations of their physical
states. Working together as a department as a team might be challenging
at first, yet as they focus their energy on monitoring progress on student
performance data will cause them to become learning leaders who exercise
control over students’ learning through their personal and collective
efficacy. This goal of becoming learning leaders can accompany a variety
of physiological states such as anxiety, stress, arousal, fatigue, and mood
states provide us with information about self-efficacy beliefs (Pajares,
2000). The motivational effects are rooted in goal setting and outcome
expectations (Zimmerman, 2002). The emotional arousal contributes
positively among three building blocks of self-efficacy: modeling, vicarious
experiences, and social persuasion.
(4) The Need for Data Based Decision Making to Produce Results
Deepening teachers’ content knowledge with pedagogical knowledge
and skills will require a systematic focus on professional development that
is led by faculty and administrative instructional leadership. This focus on
professional development must be accompanied with analysis of student

261
performance data. Data based decision making will contribute positively to
the improvement of student learning and faculty evaluation of effective
instructional delivery.
To close the achievement gap using data, Johnson points out these
stages of the change process: (1) building the leadership and data teams;
(2) killing the myth/building dissatisfaction; (3) creating a culture of inquiry:
assessing where you are, why you are there, and what needs to be done,
(4) creating a vision and plan for your school, and (5) monitoring progress
(Johnson, 2002). The importance of monitoring is underscored by Douglas
Reeves, “If educators and leaders are to achieve their goals of excellence
and equity, then the key are monitoring, evaluation, values, beliefs, and
implementation – not one more stack of beautifully bound documents
(Reeves, 2006).” In addition to this, Reeves urges that a comprehensive
accountability system can help professional development efforts achieve
their potential through monitoring not only the delivery of professional
development but also its application. A comprehensive accountability
system links professional development to application and effectiveness –
the things that matter for students (Reeves, 2000). Reeves points out,
Although many excellent efforts have been made to articulate
standards for staff development, there are three criteria at the
heart of the matter. These criteria are integrity – the
relationship of our values to our learning; efficacy – the pursuit
of those practices that make a positive difference for students;
and diligence - the application of what we have learned
(Reeves, 2000, p. 61).

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Recommendations for Community College Administrators

The overall recommendations are simple. To make significant
improvement in student learning, this demands for efficacious community
college administrators to impact teaching and learning. The administrators
influence student learning positively through teachers and creating
opportunities for teachers to grow professionally. Therefore, a professional
leaning community (PLC) needs to become a part of the culture of the
college. This requires commitment and motivation from the community
college administrators’ leadership. This calls for highly efficacious
community college administrators.
Recommendations within Community Colleges
The recommendations are two-fold: (1) within community colleges
and (2) beyond community colleges. First of all, within the community
college in order to improve student learning, the following action steps are
to be taken by the community college administrators: (1) provide corrective
feedback to teachers about their teaching by evaluating them; (2) meet with
individual teachers to establish target goals for student learning; (3) present
student performance data to the mathematics department to establish
common goals on determining effective teaching strategies; (4) encourage
and provide financial resources for faculty to visit each other’s classrooms
to observe teaching; (5) create opportunities for the faculty to debrief on
what they observe and collaborate on seeking effective instructional
approaches; (6) seek assistance outside of the community college by

263
bringing in experts in teaching; (7) provide systematic professional
development opportunities regularly with teacher compensation; and (7)
continue the professional learning community, so peer coaching becomes
an integral part of the school culture.
Recommendations Beyond Community Colleges
Beyond the community college, another set of action steps to take to
increase student performance are as following: (1) Community college
administrators need to be proactive in communicating with higher
educational and K-12 leaders. This can be done by establishing a line of
vertical articulation that informs students about what they need to know to
prepare for the college experience. (2) Community college administrators
need to create opportunities for faculty to have a vertical articulation with K-
12 teachers about effective teaching and mathematics curriculum. (3)
Community college administrators need to make the community college a
place where it becomes a center for brining K-12 and higher education
learners to experience community events. (4) Community college
administrators need to work with media, local commerce, and businesses to
build alliances for training the future workforce in order to meet the
challenges of knowledge economy. Finally, (5) community college leaders
need to become instructional leaders. In order for the faculty to work
collaboratively, it is going to require instructional administrative support.
Schlechty (2002) states, “What is needed is system change specifically
targeted to support the improvement of classroom practice (p. 54).”

264
Anderson (1997) urges, “We need to commit to work together to
systematically apply what we know succeeds for large numbers of children
in diverse communities (p. 48).” To meet the needs of the teaching gap of
community college mathematics faculty, the leaders of the college need to
create a learning environment where the faculty members learn about how
students learn and how they could improve teaching by providing content
specific professional development that uses student performance data.
This data is going to be the focus that initiates content specific professional
development.
The deficiency of student knowledge and skills demands an
instructional leadership that closes the teaching gap. School leaders shape
school conditions and teaching practices through their beliefs, and beliefs
are subtle but powerful forces used to effect change (Young & King, 2002,
as cited in Marzano et al. 2005). Marzano and his colleagues (2005)
examined the 69 studies in their meta-analysis looking for specific
behaviors related to principal instructional leadership. They identified 21
categories of behaviors that they refer to as “responsibilities.” Although the
meta-analysis focuses on the K-12 context, the responsibilities of a dean of
curriculum and instruction, president, or vice president might benefit from
the 21 responsibilities of the instructional leader: affirmation, change agent,
contingent rewards, communication, culture, discipline, flexibility, focus,
ideas/beliefs, input, intellectual stimulation, involvement in curriculum,
instruction, and assessment, knowledge of curriculum, instruction, and

265
assessment, monitoring/evaluating, optimizer, order, outreach,
relationships, resources, situational awareness, and visibility. The detailed
description of 21 responsibilities is listed in Appendix K.
The reason for college administrators to become instructional
leaders is, so that they can assist faculty to implement effective teaching.
The instructional practice that is relevant in the life of students and the
changes that are taking place in the social, political, economical, and
cultural arena demand that the faculty and instructional leaders reflect on
the instructional practice within the context of the changes that are
occurring in the global economy. The faculty and college administrators
cannot afford to remain isolated from the current market of the world
economy. They must transform themselves to be highly efficacious with
the effective pedagogical leadership skills that prepare the 21
st
century
American citizen.
This requires a paradigm shift in instructional leadership practice that
ensures that all students understand content knowledge with the best
instruction in order to have students retain the information whether they are
English language learners or English only students. The instructional
leadership practice should be a priority that must be concrete and visible for
all staff, so that they collectively focus on the goal of student learning. This
will require much support from the community college administrative
leadership. It will take everyone’s efficacy to raise students’ efficacy in
learning. Facing the challenges of a brutal knowledge economy, it is going

266
to take tenacious and persistent instructional leaders who are deeply
committed to positive results in student achievement as they collectively
choose to learn, apply mental effort in raising student performance with
effective instructional strategies, and do it persistently.
America needs instructional leaders who are willing to commit
themselves by rolling up their sleeves to help students to become people of
great knowledge and with the capacity to think critically. This nation is in
crisis due to lack of people knowledge. We can no longer accept the
current mediocre status as an acceptable expectation. In order for this
nation to grow to its optimum level with all of its available resources, it
needs to empower students with knowledge and skills.
To accomplish this, it is necessary that instructional leaders create
urgency by declaring a radical change on the inadequacy of students’ basic
skills understanding. Let it be so. This is a revolution that must be
actualized within each instructional leader’s heart that comes from the
leader’s realization that teachers are the ones who make this happen. This
radical change is a war against inadequacy on basic skills that involves
declaration by each teacher who makes a resolution, “I will teach for
mastery understanding, so all students can become problem solvers in 21
st

century with good character and citizenship.”
The instructional leader must realize that this radical change begins
with the teacher’s motivation of wanting to teach effectively while making
active choices in designing effective instruction to engage students in

267
learning with research-based instructional strategies with the force of
managing the classroom with care in building relationships with students.
This radical change is an art form that must be infused with evidence-based
student performance data to provide appropriate feedback to the students
within the learning communities between the teacher and students and
among students. The instructional leader needs to be aware that this
radical change demands corrective feedback on teacher performance from
the educational leadership with meaningful evidence-based feedback
between the administration and teachers and among teachers. This radical
change involves battles that must be fought in the trenches of teaching all
students in each classroom by the instructional leadership.
This radical change is a quiet yet very loud reform that requires
every teacher in America to lead with their authentic educational leadership
in teaching knowledge and skills and efficacious leadership. This is a
reform that causes crawling caterpillars to grow to become butterflies. Each
student must experience the metamorphosis of knowledge acquisition by
going through the transformations of lower to higher cognitive and
knowledge dimensions in order for them to fly. Teachers equip these
caterpillar students to acquire skills to fly to ensure that students have
mastered these knowledge and skills to be at the automaticity level.
Effective instruction takes place in the heart of a great teacher who
cares about student learning. The teacher prepares the learning
environmental cocoon with classroom rules and expectations with care by

268
building relationships. The teacher carefully finds out each student’s
capabilities of learning because their levels vary in a wide range. The
teacher scaffolds the learning to ensure student understanding of the
lesson with academic language and making connections with their
background. The teacher lets them know how important they are and their
learning is; therefore, with a great deal of motivation and urgency, the
teacher expects everyone to make choices to learn, apply mental effort to
learn, and learn persistently. The teacher models what they need to know,
shows them how, asks questions to make sure their understanding, and
provides opportunities to practice, so students can solve problems
individually and with others. To promote student engagement to have the
information to be fully submerged into their long-term memory, the teacher
provides opportunities to practice with research-based strategies by tapping
into their emotional intelligence through interactive activities. The teacher
enhances their learning by infusing factual, conceptual, procedural, and
metacognitive knowledge by engaging them cognitively with the cognitive
process. The students are engaged and ready to fly by demonstrating their
competence of newly acquired knowledge and skills. In order for the
teacher to do this, the teacher needs the support from the administrative
instructional leadership.
Effective community colleges require highly efficacious teachers and
instructional leaders who are courageous and motivated realizing that
effective instruction and teacher efficacy are highly correlated because

269
effective instruction and teacher efficacy are reciprocal. Effective
instruction is the outcome of the input of effective pedagogy. Effective
instruction targets for student mastery of concepts by cognitively engaging
students with various types of knowledge dimension, direct instruction, and
research-based strategies to increase students’ intellectual development
through content with the gravity force of the teacher’s classroom
management in a caring learning environment. Effective teaching raises
teacher efficacy while effective leadership efficacy creates pathways for
effective teaching to take place. These instructional leaders know the
importance of effective instruction of its critical element that teachers’
pedagogical knowledge and skills are crucial.
Teachers and instructional leaders must equip students in the
cocoon of Pre K to 16 education in America. This takes much care
because we are dealing with people with real emotions, feelings, difficulties
of learning, diverse socioeconomic status, varying degree of supportive
learning environment, rising violence and eroding ethics that are modeled
through media and leaders, and ineffective teaching. Administrators can
support the teachers by mobilizing resources for effective instruction;
however, the battle must be fought within each teacher’s classroom to win
the goal of student achievement. It takes every teacher to raise the flag of
learning declaration with the motto, “Every student will learn and graduate
with excellent knowledge and skills.” America needs teachers with
courage. Palmer puts it like this,

270
Good teachers posses a capacity for connectedness. They
are able to weave a complex web of connections among
themselves, their subjects, and their students so that students
can learn to weave a world for themselves. The methods
used by these weavers vary widely: lectures, Socratic
dialogues, laboratory experiments, collaborative problem
solving, creative chaos. The connections made by good
teachers are held not in their methods but in their hearts-
meaning heart in its ancient sense, as the place where
intellect and emotion and spirit and will converge in the human
self (Palmer, 1998, p.11).

Palmer states that good teaching cannot be reduced to technique; good
teaching comes from the identity and integrity of the teacher. Yet, I want to
add that in order for good teachers to become great teachers, they not only
have to posses identity and integrity, but also the pedagogical knowledge
and skills, motivation, and organizational support.

271

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299

Appendix A: Community College Demographic Survey

Thank you for taking this survey. Your honest feedback will be greatly
appreciated.

1. Do you teach full time or part time? □ full time □ part time
2. What is your gender? □ male □ female
3. What is your age? □ 25-30 □ 31-35 □ 36-40 □ 41-45 □ 46-50 □
51-55
□ 56-60 □ 61-65 □ 66 or Older
4. What is your ethnicity?
□ Latina/o □ Caucasian □ Black □ Asian □ Pacific Islander □
Other:_______
5. How long have you been teaching ?
□ less than 1 year □ 1-5 years □ 6-10 years □ 11-15 years □ 16-20
years
□ 21- 25 years □ 26 or more years
6. What grade level have you taught from Kindergarten through grade 12?
 □ grades K- 3 □ grades 4 -6 □ grades 7- 8 □ grades 9-12
none
7. What is your highest degree?
□ Bachelor’s degree in Mathematics □ Bachelor’s degree in other
major:______
□ Master’s degree in Mathematics □ Master’s degree in other
major:_______
□ Doctorate degree: □ Ed. D or /and □ Ph. D
8. How many courses do you usually teach per semester?
□ 1 course □ 2 courses □ 3 courses □ 4 courses □ 5 courses  □ 6 or
more courses
9. What type of math course do you teach (Check applicable boxes)?
□ College Algebra □ Elementary Algebra □ Intermediate Algebra □ College
Geometry
□ Calculus I, II, or III □Differential Equations □ Precalculus □Statistics
□Trigonometry
□ Non-degree credit courses: Arithmetic, Pre-algebra, Fractions, Intro
Decimals, others

300
10. How often did you meet as a department to collaborate last year?
□ Once a week □ Every two weeks □ Once a month  □ Once every
semester
□ Once a year □ Not at all □ Other:________

11. What teaching methods do you use (Check applicable boxes)?
□ Lecture □ Modeling □ Problem solving □ Manipulatives □ Technology
□ Interactive activities □ Identifying similarities and differences
 □ Summarizing and note taking □ Reinforcing effort and providing recognition
□ Homework and practice □ Using non-linguistic representations
□ Cooperative learning □ Setting objectives and providing feedback
□ Generating and testing hypotheses □ Cues, questions, and advance
organizers
□
Other:____________________________________________________________

Thank you very much for your feedback. Please continue with the second page.

301

Appendix B: The Revised Survey of Teachers’ Sense of Efficacy
Scale (Tschannen-Moran & Woolfolk Hoy, 2001) revised
by Oghwa Ladner, 2007

Teachers’ Beliefs
Directions: This questionnaire is
designed to help us gain a better
understanding of the kinds of things that
create difficulties for teachers in their
school activities. Please indicate your
opinion about each of the statements
below. Your answers are confidential.
How much can you do?
N = Nothing
VL = Very Little
SI= Some Influence
QAB= Quite a bit
AGL= A great deal

N VL SI QAB AGL

1. How much can you do to get through
to the most difficult students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
2. How much can you do to help your
students think critically?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
3. How much can you do to control
disruptive behavior in the classroom?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
4. How much can you do to motivate
students who show low interest in
learning Math?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
5. To what extent can you make your
expectations clear about student
behavior?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
6. How much can you do to get students
to believe they can do well in learning
Math?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
7. How well can you respond to difficult
questions from your students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
8. How well can you establish routines to
keep activities running smoothly?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
9. How much can you do to help your
students value learning?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
10. How much can you gauge student
comprehension of what you have taught?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
11. To what extent can you craft good
questions for your students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
12. How much can you do to foster
student creativity?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
13. How much can you do to get
students to follow classroom rules?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
14. How much can you do to improve
the understanding of a student who is
(1) (2) (3) (4) (5) (6) (7) (8) (9)

302
failing?
15. How much can you do to calm a
student who is disruptive or noisy?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
16. How well can you establish a
classroom management system with
each group of students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
17. How much can you do to adjust your
lessons to the proper level for individual
students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
18. How much can you use a variety of
assessment strategies?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
19. How well can you keep a few
problem students from running an entire
lesson?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
20. To what extent can you provide an
alternative explanation or example when
students are confused?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
21. How well can you respond to defiant
students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
22. How much can you assist families in
helping their children do well in school?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
23. How well can you implement
alternative strategies in your classroom?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
24. How well can you provide
appropriate challenges for very capable
students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)

303

Appendix C: Community College Mathematics Faculty Self-Efficacy
Survey (CCMFSES) by Oghwa Ladner

Directions: On the left side, please indicate
how much you believe in your ability to
perform the task.
Key:
1= Very Well (VW)
2= Moderately Well (MW)
3= Somewhat Well (SWW)
4= Slightly Well (SW)
5= Not Well at All (NWA)
Directions: On the right side, please
indicate how satisfied you are with your
ability to perform the task.
Key:
1= Very Effective (VE)
2= Moderately Effective (ME)
3= Somewhat Effective (SWE)
4= Slightly Effective (SE)
5= Never Effective (NE)

How much do you believe in your ability? How effective is your instruction?

VW MW SWW SW NWA VE ME SWE SE NE
1 2 3 4 5
1. How well can I help the most
difficult student to understand problem
solving?
1 2 3 4 5
1 2 3 4 5
2. How well can I engage my students
in the learning activities through
modeling the problem solving process?
1 2 3 4 5
1 2 3 4 5
3. How well can I create a learning
climate for reasoning?
1 2 3 4 5
1 2 3 4 5
4. How well can I connect teaching
Math with other disciplines?
1 2 3 4 5
1 2 3 4 5
5. How well can I communicate with
my students to help them learn Math?
1 2 3 4 5
1 2 3 4 5
6. How well can I use technology in
teaching Math?
1 2 3 4 5
1 2 3 4 5
7. How well can I promote
mathematical power in teaching Math?
1 2 3 4 5
1 2 3 4 5
8. How well can I link multiple
representations in teaching Math?
1 2 3 4 5
1 2 3 4 5
9. How well can I teach with
technology to engage my students in
learning?
1 2 3 4 5
1 2 3 4 5
10. How well can I use active and
interactive activities to ensure all
students resolve difficulties while
learning Math?

1 2 3 4 5
1 2 3 4 5
11. How well can I make connections
by scaffolding lessons and by building
background knowledge to teach the
current concept?

1 2 3 4 5
1 2 3 4 5
12. How well can I use multiple
strategies to adapt my teaching
practices to respond to my students’
learning needs?

1 2 3 4 5
1 2 3 4 5
13. How well can I assist my students
to experience Math?
1 2 3 4 5
1 2 3 4 5
14. How well can I create a learning
environment for students to experience
Math?

1 2 3 4 5

304
1 2 3 4 5
15. How well can I teach number
sense?

1 2 3 4 5
1 2 3 4 5
16. How well can I teach symbolism
and algebra?

1 2 3 4 5
1 2 3 4 5
17. How well can I teach geometry
and measurement?

1 2 3 4 5
1 2 3 4 5
18. How well can I teach function
sense?

1 2 3 4 5
1 2 3 4 5
19. How well can I teach continuous
and discrete models?

1 2 3 4 5

1 2 3 4 5
20. How well can I teach data
analysis, statistics, and probability?

1 2 3 4 5

1 2 3 4 5
21. How well do I teach by identifying
similarities and differences?

1 2 3 4 5
1 2 3 4 5 22. How well do I teach by
summarizing and note taking?

1 2 3 4 5
1 2 3 4 5 23. How well do I teach while
reinforcing effort and providing
recognition?

1 2 3 4 5
1 2 3 4 5 24. How well do I teach by providing
homework and practice?

1 2 3 4 5
1 2 3 4 5 25. How well do I teach by using non-
linguistic representations?

1 2 3 4 5
1 2 3 4 5 26. How well do I teach by using
cooperative learning activities?

1 2 3 4 5
1 2 3 4 5 27. How well do I teach by setting
objectives and providing feedback?

1 2 3 4 5
1 2 3 4 5 28. How well do I teach by generating
and testing hypotheses?

1 2 3 4 5
1 2 3 4 5 29. How well do I teach by using
questions, cues, and advance
organizers?

1 2 3 4 5

Thank you so much for completing this survey. Your contribution to this study has
been greatly appreciated.

305

Appendix D: Self-efficacy Survey (Tschannen Moran & Woolfolk
Hoy, 2001)

Teachers’ Sense of Efficacy Scale1 (long form)
Teacher Beliefs How much can you do?
Directions: This questionnaire is designed to help us gain a better
understanding of the
kinds of things that create difficulties for teachers in their school activities.
Please indicate
your opinion about each of the statements below. Your answers are
confidential.

Nothing Very Little some Influence Quite a Bit A Great Deal
(1) (2) (3) (4) (5) (6) (7) (8) (9)

1. How much can you do to get through to the most difficult students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
2. How much can you do to help your students think critically?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
3. How much can you do to control disruptive behavior in the classroom?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
4. How much can you do to motivate students who show low interest in
school work?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
5. To what extent can you make your expectations clear about student
behavior?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
6. How much can you do to get students to believe they can do well in
school work?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
7. How well can you respond to difficult questions from your students ?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
8. How well can you establish routines to keep activities running smoothly?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
9. How much can you do to help your students value learning?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
10. How much can you gauge student comprehension of what you have
taught?
(1) (2) (3) (4) (5) (6) (7) (8) (9)

11. To what extent can you craft good questions for your students?

306
(1) (2) (3) (4) (5) (6) (7) (8) (9)
12. How much can you do to foster student creativity?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
13. How much can you do to get children to follow classroom rules?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
14. How much can you do to improve the understanding of a student who is
failing?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
15. How much can you do to calm a student who is disruptive or noisy?

(1) (2) (3) (4) (5) (6) (7) (8) (9)
16. How well can you establish a classroom management system with each
group of students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)

17. How much can you do to adjust your lessons to the proper level for
individual students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
18. How much can you use a variety of assessment strategies?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
19. How well can you keep a few problem students form ruining an entire
lesson?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
20. To what extent can you provide an alternative explanation or example
when students are confused?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
21. How well can you respond to defiant students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
22. How much can you assist families in helping their children do well in
school?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
23. How well can you implement alternative strategies in your classroom?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
24. How well can you provide appropriate challenges for very capable
students?
(1) (2) (3) (4) (5) (6) (7) (8) (9)

307

Appendix E: May I Have Your Permission to Use Your Survey?

23 Sept. ‘07
Good morning Dr. Tschannen-Moran,

I am Oghwa Ladner, an Ed. D. student at University of Southern California. I am writing
this letter to ask permission to use your survey: Teachers’ Sense of Efficacy Scale (long
form, 2001). My research is to explore the relationship between self-efficacy of community
college mathematics faculty and effective instructional practice.

The research question I will be addressing is as follows: What Is the Relationship between
Self-efficacy of Community College Mathematics Faculty and Effective instructional
practice? I will use a mixed method of quantitative study and qualitative study. The
quantitative study will include the existing 24 item survey (Tschannen-Moran & Woolfolk
Hoy, 2001) to measure self efficacy as it pertains to student engagement, instructional
strategies, and classroom management.

There will be three item modifications to be context specific for the community college
setting. It includes three items: 4, 6, and 13. For the items 4 and 6, the phrase “school
work” will be changed to “learning math.” For the item 13, the word “children” will be
changed to “students” to target community college students. Therefore, these three
questions will look like this: How much can you do to motivate students who show low
interest in learning Math? How much can you do to get students to believe they can do
well learning Math? How much can you do to get students to follow classroom rules?

After collecting the survey data, it will be analyzed by using the SPSS software with the
demographic information. For the qualitative study, with the collected data, six
mathematics faculty will be selected for classroom observations and interviews.

Studying the relationship between mathematics faculty’s self-efficacy and instructional
practice will benefit educators, researchers, parents, and policymakers by increasing
awareness in how faculty’s belief system might impact their instructional practices. The
limitation of the study could include the limited number of faculty members as participants;
however, it is my hope that this study will fill the gap in the research on how faculty’s self-
efficacy might be related to their teaching practices.

Thank you for your support in my learning process by giving me permission to use your
survey.

Sincerely,

Oghwa Ladner
email: oladner@usc.edu

308

Appendix F: Permission from Dr. Tschannen-Moran to Use the Survey,
Teacher Sense of Efficacy Scale

Oghwa,

You have my permission to use the Teacher Sense of Efficacy Scale in your study and to
make the modifications that you have proposed. It sounds like an interesting study.

I have a doctoral student who is conducting a similar study examining middle school math
teachers self-efficacy for teaching students with disabilities and instructional strategies. I
wonder how you are defining effective instructional strategies as those may be quite
contextually based depending on the concepts being taught and the skills and aptitude of
the students. All instructional strategies are not equally effective in all situations. Will you
include any measure of student growth in achievement--e.g., pre and post?

I also wonder if you might gather more interesting demographic information than just
gender, race, and age, etc. --factors a=that may not be expected to be especially pertinent
to self-efficacy beliefs, except perhaps for the availability of models for vicarious
experiences and some potential differences in verbal persuasion. You might also want to
ask about their own mastery experiences with mathematics concepts and their own self-
efficacy for mathematical reasoning, for example. I think that you might be able to enhance
the utility of your study by attempting to capture some information about the sources of
self-efficacy as well as their outcomes.

I will include an article by my co-author Anita Woolfolk Hoy and I that was recently
published in Teaching and Teacher Education about the antecedents of self-efficacy.

All the best,

Megan Tschannen-Moran

College of William and Mary
The School of Education
PO Box 8795
Williamsburg, VA 23187-8795
Telephone: 757-221-2187
http://mxtsch.people.wm.edu

-----Original Message-----
From: Oghwa Ladner [mailto:oladner@usc.edu]
Sent: Sunday, September 23, 2007 12:15 PM
To: MeganTM@aol.com
Subject: May I have permission to use your survey please, Dr.
Tschannen-Moran?

309

Appendix G: IRB Recruitment Letter
21 Oct. 2007

To: Human Subject Review Committee at _______________ Community College
From: Oghwa Ladner, an Ed. D. student at University of Southern California

Dear IRB Committee at __________________ Community College,
I am Oghwa Ladner, a graduate student at University of Southern California. I am writing
this letter to ask your permission to conduct research at your community college. My
research is to explore the relationship between self-efficacy of community college
mathematics faculty and effective instructional practices.

The research question I will be addressing is as follows: What Is the Relationship between
Self-efficacy of Community College Mathematics Faculty and Effective Instructional
Practices? Current researchers have been challenged to go beyond socioeconomic status
in the search for school-level characteristics that make a difference in student achievement
(Hoy, Tarter, & Woolfolk Hoy, 2006). Highly self-efficacious teachers tend to invest more
effort and persist longer than those low in self-efficacy (Schwarzer & Schmitz, 2000).
When setbacks occur, these efficacious teachers recover more quickly and maintain
commitment to their goals by selecting challenging settings and exploring their
environment. These researchers found that teachers high in self-efficacy were found to
sacrifice more leisure time for their students than their less self-efficacious counterparts
(Schwarzer & Schmitz, 2000). Teachers’ sense of efficacy has made a strong positive link
to student performance (Tschannen-Moran & Hoy, 2001) and provided to be significantly
related to teachers’ success (Armor et el, 1976).

This study will use a mixed method of quantitative study and qualitative study. The
quantitative study will include using the existing 24 item survey (Tschannen-Morran &
Woolfolk Hoy, 2001) to measure student engagement, instructional strategies, and
classroom management on a Likert scale of one being nothing to nine being a great deal.
After collection of the survey data, it will be analyzed by using the SPSS software with the
demographic information. For the qualitative study, if participants volunteer to be
interviewed or observed, three to six mathematics faculty will be selected for classroom
observations and interviews.

Studying the relationship between the mathematics faculty and instructional practices may
benefit educators, researchers, parents, and policymakers in assisting faculty in exploring
instructional strategies by increasing awareness in how faculty’s belief system might
impact their instructional practices. The limitation of the study could include the limited
number of faculty members as participants; however, it is my hope that this study will fill
the gap in the research on how faculty’s self-efficacy might be related to their teaching
practices.

Thank you for your support in my learning process.

Sincerely,

Oghwa Ladner

310

Appendix H: Informed Consent Form to Conduct Research

University of Southern California
INFORMATION SHEET FOR NON-MEDICAL RESEARCH

Completion and return of the questionnaire or response to the
survey questions will constitute consent to participate in this
research project.

Title of the study: What Is the Relationship between Community College
Mathematics Faculty and Effective Instructional Practice?

You are asked to participate in a research study conducted by Oghwa
Ladner, an Ed. D. student from the Rossier School of Education at the
University of Southern California. The results of this study will be
contributed to a dissertation. You were selected as a possible participant in
this study because you teach Mathematics at a community college. A total
of 90 subjects will be selected from many community colleges. Your
participation is voluntary. Please take as much time as you need to read
this information sheet. You may also decide to discuss it with your family or
friends. You will be given a copy of this information sheet for non-medical
research.

PURPOSE OF THE STUDY
I am asking you to take part in a research study because I am trying to
learn more about community college faculty and instruction. I will study the
relationship between community college teachers’ perceived ability and
effective instructional practice. This study includes a mixed method of
research: quantitative and qualitative studies. The quantitative study is to
measure teachers’ belief system of their ability through student
engagement, instructional strategies, and classroom management. Also,
items on the surveys include the standards on American Mathematics
Association on Two Year Colleges (AMATYC) and research based
strategies.

PROCEDURES
You will be asked to take three anonymous and voluntary surveys: 1.
demographic survey, 2. self-efficacy survey, and 3. survey with AMATYC
(1995) and research based instructional strategies (Marzano, Pickering, &
Pollock, 2001). The first survey asks about each faculty’s demographic
information: full time or part time status, gender, age, ethnicity, years of

311
teaching, K-12 experience, educational background, number of courses
taught, types of math courses taught, opportunities for collaboration, and
teaching methods. The second one is a revised self-efficacy survey
(Tschannen-Moran & Woolfolk Hoy, 2001) about student engagement,
instructional strategies, and classroom management. The third survey
includes the AMATYC’s standards: intellectual development, content, and
pedagogy. Each survey should take about 5 to 10 minutes to complete.
The total time required to complete the surveys is about 15 to 30 minutes.
The survey can be taken at a place convenient to you.

You will not be photographed nor videotaped. When completing the three
surveys, you will be asked whether you would like to participate in an
interview or be observed during instruction. If you agree to be interviewed
or observed, please check the appropriate box (es) that are on a separate
sheet of paper: Interview or Observation Permission form. During the
interview, you may be audio-taped. As a participant, your contact
information will be kept confidential, you will be coded by a number, such as
interview participant one from ABC community college.

POTENTIAL RISKS AND DISCOMFORTS
There are no anticipated risks to your participation. Some discomfort may
be experienced due to the time it takes to complete the questionnaires.

POTENTIAL BENEFITS TO SUBJECTS AND/OR TO SOCIETY
You may not directly benefit from this research study. However, the
potential benefit of this study could help other researchers to learn about
the relationship between self-efficacy of community college Mathematics
faculty and effective instructional practice. Also, this study will assist other
researchers to learn about the art of effective teaching. Other benefits
could include long term improvement in student achievement and
graduation rate.

PAYMENT/COMPENSATION FOR PARTICIPATION
You will not receive any payment for your participation in this research
study.

CONFIDENTIALITY
Any information that is obtained in connection with this study and that can
be identified with you will remain confidential. The information collected
about you will be coded using a number, for example, participant 1, etc.
The coded information which has your identifiable information for an
interview or an observation will be kept separately from the rest of your
data.

312
Only this researcher will have access to the data. The data will be stored in
the investigator’s office in a locked file cabinet/password protected
computer. The collected data with numerically coded data of participants
will be released to the dissertation committee to share its findings. The
personal information, research data, and related records will be coded and
stored.

After the study has been completed, the data will be stored for three years.
Then, the data will be destroyed in May 2011 by using a shredding
machine.

When the results of the research are published or discussed at
conferences, no information will be included that would reveal your identity.
Your identity will be protected or disguised by using a number, such as
participant 1 from ABC community college.

PARTICIPATION AND WITHDRAWAL
You can choose whether to be in this study or not. If you volunteer to be in
this study, you may withdraw at any time without any kind of consequences.
You may also refuse to answer any questions you do not want to answer
and still remain in the study. The investigator may withdraw you from this
research if circumstances arise which warrant doing so.

ALTERNATIVES TO PARTICIPATION
Your alternative is to not participate.

RIGHTS OF RESEARCH SUBJECTS
You may withdraw your consent at any time and discontinue participation
without penalty. You are not waiving any legal claims, rights or remedies
because of your participation in this research study. If you have any
questions about your rights as a study subject or you would like to speak
with someone independent of the research team to obtain answers to
questions about the research, or in the event the research staff can not be
reached, please contact the University Park IRB, Office of the Vice Provost
for Research Advancement, Stonier Hall, Room 224a, Los Angeles, CA
90089-1146, (213) 821-5272 or upirb@usc.edu

IDENTIFICATION OF INVESTIGATORS
If you have any questions or concerns about the research, please feel free
to contact the principle investigator: Oghwa Ladner, an Ed. D. candidate, at
Rossier School of Education. The email address is as follows:
oladner@usc.edu. Your participation in this research will be greatly
appreciated.

313

Appendix I: Interview Questions

Revised Interview Questions after Piloting the Interview Questions

Interviewee: __________________________ Date: Class:

Interviewer: Oghwa Ladner

1. What motivated you to become a community college faculty?

2. What do you most like about teaching community college students?
3. What do you least like about teaching community college students?
4. What does effective instruction mean to you?
5. What professional development have you attended?
6. How familiar are you with AMATYC (American Mathematics Association for
Two Year Colleges) strands and standards?
7. There are eight sub-standards for intellectual development:
1. Problem solving
2. Modeling
3. Reasoning
4. Connecting with other disciplines
5. Communicating
6. Using technology
7. Developing mathematical power
8. Linking multiple representations.

7.1. Which one would you feel is the most important? Why?

7.2. Which one would you feel is the least important? Why?

7.3. What can the community college leadership do to assist you to
effectively implement the intellectual development standard?

8. Here are Content sub-standard(s):
1. Number sense
2. Symbolism and algebra
3. Geometry and measurement
4. Function sense
5. Continuous and discrete models
6. Data analysis, Statistics, and Probability

314
8.1. Which standard are you most prepared to teach?

8.2. Which standard are you least prepared to teach?

8.3. How can you better prepare yourself to teach the least prepared
standard?

9. There are five standards for pedagogy:

1. Teaching with technology
2. Active and interactive learning
3. Making connections
4. Using multiple strategies
5. Experiencing mathematics.

9.1. What pedagogy standard do you feel most comfortable using in your
classroom?

9.2. Which pedagogy standard do you least feel comfortable using in your
classroom?

9.3. What can the community college leadership do to help increase your
ability in teaching?

10. There are nine Marzano’s research-based instructional strategies:
1. Identifying similarities and differences
2. Summarizing and note taking
3. Reinforcing effort and providing recognition
4. Homework and practice
5. Nonlinguistic representation
6. Cooperative learning
7. Setting objectives and providing feedback
8. Generating and testing hypotheses
9. Questions, cues, and advance organizers
10.1 Which strategy do you most frequently use in your classroom?
10.2 Which strategy do you least frequently use in your classroom?
11. Do you find your belief system makes a difference in teaching?
12. Do you find that there is a relationship between a faculty’s belief system and
his or her instructional practice?

13. Do you consider yourself a highly efficacious teacher?

315
14. If you have an opportunity to attend professional development dealing with
these strands, intellectual development, content, and pedagogy, which one would
you attend? Why?

15. If you have one wish as a teacher, what would that be?
16. What would you like the community college leadership to do to assist the
Mathematics faculty?

17. What should future researchers research about Mathematics faculty and
student achievement?

Thank you very much for your time and effort.

316

Appendix J: Interview or Observation Permission Form

May I interview or observe your classroom teaching, please?
If you agree, please check the appropriate box.

□ I agree to be interviewed and be observed during instruction.

□ I agree to be interviewed only.

□ I agree to be observed during instruction only.

How may I contact you? Contact information please…

Email: __________________________________
Phone:_______________________

Name (Optional):____________________________

Your willingness to participate in this study will make a huge difference in
research of teaching practice and student achievement. Thank you very
much for volunteering your time and effort. I truly appreciate it.

317

Appendix K: Twenty-one Responsibilities Listed in Order of
Correlation for Student Academic Achievement
(Marzano et al, 2005)

Correlation
with
Achievement
Responsibility Definition
___ is the extent…
Characteristics
.33 Situational
Awareness
Leader’s awareness of the
details and the
undercurrents regarding the
functioning of the school
and their use of this
information to address
current and potential
problems.
• Accurately predicting what could go
wrong from day to day
• Being aware of informal groups and
relationships among the staff
• Being aware of issues in the school
that have not surfaced but could
create discord
.28 Flexibility
The Leader adapts their
leadership behavior to the
needs of the current
situation and is comfortable
with dissent.
• Adapting leadership style to the
Needs of specific situations
• Being directive or nondirective as
the situation warrants
• Encouraging people to express
diverse and contrary opinions
• Being comfortable with making
major changes in how things are
done

.27 Discipline
Protecting teachers from
issues and influences that
would detract from their
instructional time or focus.
• Protecting instructional time from
interruptions
• Protecting teachers from internal
and external distractions.
.27 Outreach
The leader is an advocate
and a spokesperson for the
school to all stakeholders
• Ensuring that the school complies
with
all district and state mandates
• Being an advocate of the school with
parents
• Being an advocate of the school with
the central office
• Being an advocate of the school with
the community at large
.27 Monitoring and
Evaluating
The most powerful single
modification that enhances
achievement is feedback
(Hattie, 1992). Feedback
does not occur
automatically. It is a
function of design. Creating
a system that provides
feedback is at the core of
the responsibility of
monitoring/evaluating.
• Continually monitoring the
effectiveness of the school’s
curricular, instructional, and
assessment practices
• Being continually aware of the
impact of the school’s practices on
student achievement
.25 Culture
The effective leader builds a
culture that positively
influences teachers, who, in
turn, positively influence
students.
• Promoting cohesion among staff
• Promoting a sense of well-being
among staff
• Developing an understanding of
purpose among staff
• Developing a shared vision of what
the school could be like
.25 Order
Groups need structures that
provide them with the
leadership, time, resources,
and incentives to engage in
• Establishing routines for the smooth
running of the school that staff
understand and follow
• Providing and reinforcing clear

318
instructional work (Supovitz,
2002)
structures, rules, and procedures for
staff
• Providing and reinforcing clear
structures, rules, and procedures for
students
.25 Resources
The extent to which the
leader provides teachers
with materials and
professional development
necessary for the successful
execution of their duties.
• Ensuring that teachers have the
necessary materials and equipment
• Ensuring that teachers have the
necessary staff development
opportunities to directly enhance
their teaching
.25 Knowledge of
Curriculum,
Instruction,
and Assessment
The leader is aware of best
practices in curriculum,
instruction, and assessment
Possessing extensive knowledge
about effective…
• instructional practices
• curricular practices
• assessment practices
• classroom practices to provide
conceptual guidance regarding
effective classroom practices
.25 Input
The extent to which the
school leader involves
teachers in the design and
implementation of important
decisions and policies.
• Providing opportunities for staff to be
involved in developing school
policies
• Providing opportunities for staff on
all important decisions
• Using leadership teams in decision
Making
.25 Change Agent
The leader’s disposition to
challenge the status quo.
• Consciously challenging the status
quo
• Being willing to lead change
Initiatives with uncertain outcomes
• Systematically considering new and
better ways of doing things
• Consistently attempting to operate at
the edge versus the center of the
school’s competence
.24 Focus
The leader establishes clear
goals and keeps those
goals in the forefront of the
school’s attention
• Establishing concrete goals for
curriculum, instruction, and
assessment
practices within the school
• Establishing concrete goals for the
general functioning of the school
• Establishing high, concrete goals,
and expectations that all students
will meet them
• Continually keeping attention on
established goals
.24 Contingent
Rewards
The school leader
recognizes and rewards
individual accomplishments
• Using hard work and results as the
basis for rewards and recognition
• Using performance versus seniority
as a primary criterion for rewards
and recognition
.24 Intellectual
Stimulation
The school leader ensures
that faculty and staff are
aware of the most current
theories and practices
regarding effective
schooling and makes
discussions of those
theories and practices a
regular aspect of the
school’s culture.
• Continually exposing staff to cutting-
edge research and theory on
effective
schooling
• Keeping informed about current
research and theory on effective
schooling
• Fostering systematic discussion
regarding current research and
theory on effective schooling
.23 Communication
The school leader
establishes strong lines of
communication with and
between teachers and
students.
• Developing effective means for
teachers to communicate with one
another
• Being easily accessible to teachers
• Maintaining open and effective lines
of communication with staff

319
.22 Ideals/Beliefs
• The leader shape school
conditions and teaching
practices is through their
beliefs (Young & King,
2002)
• Beliefs are connected to
intimacy. Beliefs come from
polices or standards or
practices (De Press, 1989)
• Well-articulated ideals and
beliefs are at the core of
effective leadership (Bennis,
2003)

• Possessing well-defined beliefs
About schools teaching, and
learning
• Sharing beliefs about school,
teaching, and learning with the staff.
• Demonstrating behaviors that are
consistent with beliefs
.20 Involvement in
Curriculum
Instruction and
Assessment
The leader is directly
involved in the design and
implementation of
curriculum, instruction, and
assessment activities at the
classroom level.
Being directly involved in helping
teachers…
• design curricular activities
• address assessment issues
• address instructional issues
.20 Visibility
The extent to which the
school leader has contact
and interacts with teachers,
students, and parents.
• Making systematic and frequent
visits to classrooms
• Having frequent contact with
students
• Being highly visible to students,
teachers, and parents
.19 Affirmation
To which the leader
recognizes and celebrates
school accomplishment –
and acknowledges failures.
•Systemically and fairly recognizing
and celebrating the
accomplishments of students,
teachers, and the school as a whole
.18 Relationships
The extent to which the
school leader demonstrates
an awareness of the
personal lives of teachers
and staff.
• Being informed about significant
personal issues within the lives of
staff members
• Being aware of personal need of
teachers
• Acknowledging significant events in
the lives of staff members
• Maintaining personal relationships
with teachers

320

Appendix L: Comparison of Professional Learning Strategies to
Learning Theory (Tate, 2004, p. XV)

Professional
Learning Strategies (Tate)
Multiple Intelligences
(Gardner)
Learning
Modality
1. Brainstorming and discussion Verbal-linguistic Auditory
2. Drawing and artwork Spatial Kinesthetic-
tactile
3. Field trips Naturalist Kinesthetic-
tactile
4. Games Interpersonal Kinesthetic-
tactile
5. Graphic organizers Logical-mathematical
spatial
Visual-tactile
6. Humor and celebration Verbal-linguistic Auditory
7. Manipulatives and models Logical-mathematical Tactile
8. Metaphors, analogies, and similes Spatial Visual-auditory
9. Mnemonic devices Musical-rhythmic Visual-auditory
10. Movement Bodily-kinesthetic Kinesthetic
11. Music, rhythm, rhyme, and rap Musical-rhythmic Auditory
12. Project-and problem-based instruction Logical-mathematical Visual-tactile
13. Reciprocal teaching, cooperative learning, and
peer coaching
Verbal-linguistic Auditory
14. Role-plays, drama, pantomimes, and charades Bodily-kinesthetic Kinesthetic
15. Storytelling Verbal-linguistic Auditory
16. Technology Spatial Visual-tactile
17. Visualization Spatial Visual
18. Visuals Spatial Visual
19. Work study and action research Interpersonal Kinesthetic
20. Writing and reflection Intrapersonal Visual-tactile

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Asset Metadata

Creator Ladner, Oghwa (author)

Core Title What is the relationship between self-efficacy of community college mathematics faculty and effective instructional practice?

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 05/06/2010

Defense Date 03/17/2008

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag community college mathematics faculty,dire,effective instructional practice,efficacious teachers,gap analysis,knowledge dimension,mixed method study,OAI-PMH Harvest,professional development,self-efficacy

Language English

Advisor Hocevar, Dennis (committee chair), Gothold, Stuart E. (committee member), Stowe, Kathy Huisong (committee member)

Creator Email oladner@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1216

Unique identifier UC165124

Identifier etd-Ladner-20080506 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-77850 (legacy record id),usctheses-m1216 (legacy record id)

Legacy Identifier etd-Ladner-20080506.pdf

Dmrecord 77850

Document Type Dissertation

Rights Ladner, Oghwa

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu