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Examining the faculty implementation of intermediate algebra for statistics: An evaluation study

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Content Running head: IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STA TISTICS 1

Examining the Faculty Implementation of Intermediate Algebra for Statistics:
An Evaluation Study
By Carlos G. Montoya

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

May 2018

Copyright 2018 Carlos G. Montoya
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 2
DEDICATION
To my daughter, Savannah, since your birth you have always been my reason. You were
supportive and understanding in more ways than you know. I love you.
To Binh, for always being supportive and understanding of the time and dedication
needed to research and write. Thank you!
To my family, for their love and support. Thank you.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 3
ACKNOWLEDGEMENTS
Thank you, Dr. Melora Sundt, my dissertation chair, without your guidance and
encouragement I would still be searching for a topic. You provided a sense calm and made me
comfortable with an unfamiliar process where I learned about myself and what I can accomplish.
To the rest of my dissertation committee, Dr. Darline Robles and Dr. Angela Laila Hasan,
I am so thankful for your support and guidance in tackling a topic so important yet different from
my professional experience.
Finally, this dissertation could not have been possible without the support and dedication
of the organization, its staff, and most importantly its faculty. Thank you for your support.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 4
TABLE OF CONTENTS
Dedication ....................................................................................................................................... 2
Acknowledgements ......................................................................................................................... 3
Table of Contents ............................................................................................................................ 4
List of Tables ................................................................................................................................... 8
List of Figures ............................................................................................................................... 10
Abstract ......................................................................................................................................... 11
Chapter One: Introduction ............................................................................................................ 12
Introduction of the Problem of Practice ..................................................................................... 12
Organizational Context and Mission .......................................................................................... 13
Organizational Goal .................................................................................................................... 13
Related Literature ....................................................................................................................... 14
College Preparedness ............................................................................................................... 15
Student Placement .................................................................................................................... 16
Institutional Resources and Support ........................................................................................ 17
Importance of the Study ............................................................................................................. 19
Description of Stakeholder Groups ............................................................................................ 20
Organizational Mission and Stakeholder Performance Goals .................................................... 21
Stakeholder Group for the Study ................................................................................................ 22
Purpose of the Project and Questions ......................................................................................... 23
Conceptual and Methodological Framework ............................................................................. 24
Definitions .................................................................................................................................. 24
Organization of the Project ......................................................................................................... 25
Chapter Two: Review of the Literature ......................................................................................... 26
Developmental Math Instruction ................................................................................................ 26
Factors Influencing Developmental Math Curriculum ............................................................ 26
Curriculum alignment. ............................................................................................................. 27
Acceleration. .......................................................................................................................... 28
Statistics pathways. ................................................................................................................ 29
Factors Influencing Math Instruction Delivery ........................................................................ 30
Effective math instruction. ..................................................................................................... 30
Faculty preparation. ............................................................................................................... 32
Professional Development. .................................................................................................... 33
The Clark and Estes (2008) Gap Analytic Conceptual Framework ........................................... 34
Stakeholder Knowledge, Motivation and Organizational Influences ......................................... 35
Knowledge and Skills .............................................................................................................. 35
Assumed factual knowledge influences. ................................................................................ 36
Assumed conceptual knowledge influences. ......................................................................... 37
Assumed procedural knowledge influences. ......................................................................... 38
Motivation ................................................................................................................................ 43
Expectancy value theory. ....................................................................................................... 44
Assumed expectancy value influences. ................................................................................. 45
Self-efficacy theory. ............................................................................................................... 46
Assumed self-efficacy influences. ......................................................................................... 47
Attribution theory. .................................................................................................................. 48
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 5
Assumed attributional influences. ......................................................................................... 49
Organizational Influences ........................................................................................................ 51
Assumed cultural model influences. ...................................................................................... 53
Assumed cultural setting influences. ..................................................................................... 54
Conclusion .................................................................................................................................. 57
Chapter Three: Methodology ........................................................................................................ 62
Purpose of the Project and Research Questions ......................................................................... 62
Conceptual Framework .............................................................................................................. 63
Methodological Framework ....................................................................................................... 67
Assessment of Performance Influences ...................................................................................... 68
Knowledge Assessment ............................................................................................................ 69
Motivation Assessment ............................................................................................................ 73
Organization/Culture/Context Assessment .............................................................................. 74
Participating Stakeholders and Sample Selection ...................................................................... 76
Data Collection ........................................................................................................................... 77
Interviews ................................................................................................................................. 77
Sampling. ............................................................................................................................... 77
Interview recruitment and rationale. ...................................................................................... 78
Interview instrumentation and fielding. ................................................................................. 79
Observations ............................................................................................................................. 80
Sampling. ............................................................................................................................... 80
Observation recruitment and rationale. .................................................................................. 80
Observation instrumentation and fielding. ............................................................................ 81
Document Analysis .................................................................................................................. 82
Data Analysis .............................................................................................................................. 83
Interviews ................................................................................................................................. 83
Observations ............................................................................................................................. 83
Credibility and Trustworthiness ................................................................................................. 84
Role of Investigator .................................................................................................................... 85
Ethics .......................................................................................................................................... 85
Chapter Four: Findings ................................................................................................................. 87
Introduction ................................................................................................................................ 87
Definition of Gap Validation ...................................................................................................... 88
Participating Stakeholders .......................................................................................................... 88
Findings for Knowledge Influences ........................................................................................... 89
Assumed factual knowledge influences ................................................................................... 90
Faculty need to know the goal. .............................................................................................. 90
Assumed conceptual knowledge influences ............................................................................. 92
Faculty need to know the content of course curricula. .......................................................... 92
Assumed procedural knowledge influences ............................................................................. 94
Faculty need to know how to adapt their instruction. ............................................................ 94
Faculty need to know how to teach math effectively. ............................................................ 97
Faculty need to know how to align instructional activities to performance. ....................... 100
Findings for Motivation Influences .......................................................................................... 104
Assumed expectancy value influences ................................................................................... 104
Faculty need to value implementing intermediate algebra for statistics. ............................. 104
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 6
Faculty need to value improving student success. ............................................................... 105
Assumed self-efficacy influences .......................................................................................... 106
Faculty need to believe they are capable of effectively delivering instruction. .................. 106
Assumed attributional influences ........................................................................................... 107
Faculty need to believe that student outcomes can be attributed to their instruction. ......... 107
Findings for Organization Influences ....................................................................................... 108
Assumed cultural model influences ....................................................................................... 108
There is a culture that supports implementing new courses to improve student success. ... 108
There is a culture that believes underprepared students can complete math coursework. .. 110
Assumed cultural setting influences........................................................................................ 111
The organization supports a standard approach to improve math remediation. ................... 111
The organization provides resources to support academic and professional standards. ...... 113
Conclusion ................................................................................................................................ 116
Chapter Five: Solutions, Implementation and Evaluation Plan .................................................. 117
Recommendations for Practice to Address KMO Influences ................................................... 117
Knowledge Recommendations .............................................................................................. 117
Motivation Recommendations ............................................................................................... 118
Organization Recommendations ............................................................................................ 118
Introduction. ......................................................................................................................... 118
Cultural Model. .................................................................................................................... 120
Cultural Setting. ................................................................................................................... 120
Integrated Implementation and Evaluation Plan ...................................................................... 121
Implementation and Evaluation Framework .......................................................................... 121
Level 4: Results and Leading Indicators ................................................................................ 122
Level 3: Behavior ................................................................................................................... 123
Critical behaviors. ................................................................................................................ 123
Required drivers. .................................................................................................................. 124
Organizational support. ........................................................................................................ 126
Level 2: Learning ................................................................................................................... 126
Learning goals. .................................................................................................................... 126
Program. ............................................................................................................................... 127
Components of learning. ...................................................................................................... 128
Level 1: Reaction ................................................................................................................... 129
Evaluation Tools ..................................................................................................................... 130
Immediately following the program implementation. ......................................................... 130
Delayed for a period after the program implementation. .................................................... 130
Data Analysis and Reporting .................................................................................................. 131
Summary ................................................................................................................................ 132
Strengths and Weaknesses of Approach ................................................................................... 133
Limitations and Delimitations .................................................................................................. 134
Recommendation for Further Inquiry ....................................................................................... 135
Conclusion ................................................................................................................................ 137
References ................................................................................................................................... 140
Appendix A: Request for Interview Participation ....................................................................... 151
Appendix B: Stakeholder Interview Protocol ............................................................................. 153
Appendix C: Stakeholder Observation Protocol ......................................................................... 157
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 7
Appendix D: Information/Facts Sheet for Exempt Non-Medical Research ............................... 162
Appendix E: Sample Post-Training Survey Items Measuring Kirkpatrick Levels 1 and 2 ........ 164
Appendix F: Sample Delayed Blended Evaluation Survey Kirkpatrick Levels 1, 2, 3, and 4 ... 166

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 8
LIST OF TABLES
Table 1. Organizational Mission, Global Goal and Stakeholder Performance Goals 21
Table 2. Assumed Knowledge Influences, Type, and Research Literature 41
Table 3. Assumed Motivation Influences, Theory, and Research Literature 50
Table 4. Assumed Organizational Influences, Type, and Research Literature 55
Table 5. Summary of Assumed Influences on Math Faculty Ability to Implement 57
Intermediate Algebra for Statistics Course
Table 6. Sources of Assumed Knowledge, Motivation, and Organizational Influences 68
Table 7. Assumed Knowledge Influences and Proposed Assessment 70
Table 8. Assumed Motivation Influences and Proposed Assessment 73
Table 9. Assumed Organizational Influences and Proposed Assessment 74
Table 10. Summary of Participant Gender and Faculty Status 89
Table 11. Respondent Years of Teaching Experience 89
Table 12. Prevalence of the Instructor Codes PQ - Posing non-clicker question to 96
students and CQ - Asking a clicker question
Table 13. Prevalence of the Instructor Code FUp - Follow-up/feedback on clicker 97
question or activity
Table 14. Prevalence of the Instructor Code MG - Moving through class guiding 97
ongoing student work during active learning task
Table 15. Prevalence of the Instructor Codes Lec - Lecturing and RtW - Real-time 102
writing on board, doc. projector, etc.
Table 16. Prevalence of the Student Codes L - Listening to instructor/taking notes, 102
etc. and Ind - Individual thinking/problem solving.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 9
Table 17. Prevalence of the Student Codes WG - Working in groups on 103
worksheet activity and SP - Presentation by student(s)
Table 18. Respondent Perception of Student Pass Rate Percentage 110
Table 19. Validated Influencers Table 115
Table 20. Summary of Organization Influences and Recommendations 119
Table 21. Outcomes, Metrics, and Methods for External and Internal Outcomes 122
Table 22. Critical Behaviors, Metrics, Methods, and Timing for Math Faculty 124
Table 23. Required Drivers to Support Math Faculty’s Critical Behaviors 125
Table 24. Components of Learning for the Program 128
Table 25. Components to Measure Reactions to the Program 129
Table 26. Possible Key Performance Indicators for Internal Reporting and 131
Accountability

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 10
LIST OF FIGURES
Figure 1. Previous Math Remediation Sequence at Community College Z 16
Figure 2. Current Math Remediation Sequence at Community College Z 23
Figure 3. Interactive conceptual framework. 65
Figure 4. Gap analysis process. Adapted from Clark and Estes (2008) 68
Figure 5. Example KPI Dashboard 132

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 11
ABSTRACT
This dissertation study examined the factors that influence the ability of math faculty at a local
community college to implement a new intermediate algebra for statistics course designed to
improve the math remediation pathway. A gap analysis framework was used to identify the
knowledge, motivation and organizational influences found in the literature. The methodology
used in this study included literature reviews, interviews, classroom observations, and document
analysis. The data collected were used to determine if a gap for each influence was validated, not
validated, or unable to validate based on the findings. According to the findings, two validated
gaps tied to the organizational culture were found. Findings indicate that parts of the
organizational culture do not believe that underprepared students can complete math coursework.
It was also found that the organization does not support a standard approach to improve math
remediation. The findings were used to develop recommendations specific to the validated gaps
found at the college. Recommendations include that the college create a place where faculty can
refer to references and resources on student success data, effective pedagogy, and instructional
tools. It was also recommended that the college facilitate faculty discussions to share and review
approaches to improving student outcomes in math remediation to ensure curriculum alignment
and increase faculty buy-in on student success. Additionally, a training framework was used to
develop an implementation and evaluation plan to train additional faculty or used as a model for
other institutions attempting to adopt a similar math remediation intervention.

Keywords: Math, Acceleration, Statistics, Teaching, Community College, Faculty

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 12
CHAPTER ONE: INTRODUCTION
Introduction of the Problem of Practice
Nationally, over 60% of first time college students entering college require some form of
basic skills remediation (California Community Colleges Student Success Task Force, 2012). In
California, the community college system, considered the gateway to higher education, provides
the bulk of all remediation for higher education students. In this system, which serves more than
2.3 million students (California Community Colleges Chancellor’s Office, 2015a), more than
70% of students entering the system are under-prepared for college-level course work (Biswas,
2007; California Community Colleges Student Success Task Force, 2012).
The traditional intervention for under-prepared students is to enroll them in a sequence of
remedial, or developmental, courses. However, rather than being an effective intervention,
developmental education has become an additional barrier for students pursuing their educational
goals (Bailey, Jeong, & Cho, 2010; Bonham & Boylan, 2011; Okimoto & Heck, 2015). Of those
students placed into directly into developmental math courses, only 31% successfully completed
a degree, certificate, and/or transfer outcome compared to approximately 69% of those students
prepared for college-level coursework (California Community Colleges Chancellor’s Office,
2015a). The purpose of this study was to examine the knowledge, motivation, and organizational
resources influencing the ability of developmental math faculty at a local community college to
implement an intervention designed to designed to shorten the basic skills math pathway and
improve student success.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 13
Organizational Context and Mission
The research site for this case study was assigned a pseudonym to maintain
confidentiality. The pseudonym for the site is Community College Z
1
. Community College Z is a
community college located in Southern California that provides workforce training, transfer
education, and basic skills education. The mission of Community College Z is to provide
students with essential academic skills by offering accessible and enriching education that
prepares students to reach their educational goals (Community College Z website). As one of the
113 community colleges in California, Community College Z currently enrolls over 31,000
students at the institution (California Community Colleges Chancellor’s Office, 2015a).
Community College Z currently employs over 1,100 employees across 10 administrative
divisions: business services, economic development, foundation, external relations, facilities,
human resources, institutional development, off-site operations, instruction, and student services
(Community College Z website). The racial and ethnic makeup of the faculty and staff is as
follows: 62.96% are White Non-Hispanic, 20.99% are Hispanic, 8.73% are Asian, 2.56% are
African-American, 1.15% are American Indian/Alaskan Native, 0.09% are Pacific Islander, and
3.53% are other (California Community Colleges Chancellor’s Office, 2015b). The primary role
of faculty and staff is to help each student achieve their educational goals and fulfill their
potential.
Organizational Goal
Community College Z’s goal is that by June 2019, 100% of students will meet math
transfer eligibility requirements. The math department established this goal during the most
recent program review process along with the introduction of an intervention designed to shorten

1
All names, organizations, and locations have been assigned pseudonyms.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 14
the basic skills math pathway and improve course success rates. Accomplishing this task falls
primarily on the ability of math faculty to effectively deliver math instruction to those students
placed into remediation. In addition, the College Planning Team incorporated this goal during the
development of the college strategic plan (Community College Z Strategic Plan, 2015). The
completion of the math transfer eligibility requirement is also one of the student achievement
indicators selected to align with the statewide Institutional Effectiveness Initiative to improve
student achievement. The achievement of Community College Z’s goal will be measured and
reported through the annual student success scorecard (California Community Colleges
Chancellor’s Office, 2015a), the institutional effectiveness indicators portal, and the Chancellor’s
Office basic skills tracker.
Related Literature
Nationally, college completion has been a focus for education and policy leaders (Bragg
& Durham, 2012; Harbour & Smith, 2015). In the literature, the focus of the completion agenda
is to improve the economy by increasing the education level of the workforce (Harbour & Smith,
2015). The strategy to improve the education level of the workforce is supported by data
indicating that higher levels of educational attainment coincide with higher levels of wage
earnings and lower rates of unemployment (United States Department of Labor, 2015). The
relationship between educational attainment and wage earning is important to note as the value
of graduating from high school has diminished as it no longer secures a high wage job (Karp,
2015). Given the education levels and skills needed in the workforce, the repercussions from
failing to improve completion rates will be a great strain on the nation’s current economy and its
ability to adapt to changing conditions (Carnevale, Smith, & Strohl, 2013). By the year 2020, the
percentage of jobs in the U.S. that will require some form of postsecondary education will grow
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 15
to 65% (Carnevale et al., 2013). Current estimates indicate that there will be 1.9 million job
openings in California by 2020 that will require some form of postsecondary education that is
less than a four-year degree (Carnevale et al., 2013).
In California, community colleges are at the forefront of the completion agenda and play
an important role in preparing students with the basic skills to pursue their educational pathway,
transfer to a four-year institution, and/or the skills necessary to enter the workforce (California
Community Colleges Chancellor’s Office, 2015a). However, the overall completion rate for all
students within the community college system in California is less than 50%, which falls below
the 62% completion goal set by the California Community Colleges Board of Governors
(California Community Colleges Chancellor’s Office, 2014). The gap between the desired
educational attainment level and current outcomes demonstrates a problem. A review of the
literature reveals several factors affecting community college completion rates nationally such
as: students’ college preparedness, student placement, and the availability of institutional
resources (Belfield, Crosta, & Jenkins, 2014; Bound, Lovenheim, & Turner, 2010; Calcagno,
Crosta, Bailey, & Jenkins, 2007).
College Preparedness
In the literature, college preparedness refers the level of preparation of incoming college
students and is one of the factors that can affect completion rates (Bound et al., 2010; Davidson,
2015). Research indicates that while access to college has improved, the proportion of college
completion has declined between the class of 1972 and the class of 1992 (Bound et al., 2010).
According to Bound et al. (2010), 90 percent of the decline in college completion rates
community college students can be attributed to declining levels of college preparation. In
addition, a third of the declines in the completion rate can be attributed to math preparation
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 16
(Bound et al., 2010). Research conducted by Davidson (2015), further indicates that degree
completion and transfer rates had the highest negative correlation with being academically
underprepared. Since underprepared students face additional challenges, their rates of success are
lower than their counterparts that enter college academically prepared (Davidson, 2015).
Therefore, a critical factor to student success is the level of academic preparation of incoming
students that can be assessed in part by placement scores in math and English.
Student Placement
The current system of student placement in remediation courses is another factor
affecting community college completion rates (Belfield et al., 2014; Calcagno et al., 2007;
Phillips & Horowitz, 2013). Student placement tests are used to determine the remedial courses a
student must take to develop the skills necessary for success in college (Goldrick-Rab, 2010).
The current challenge is that remediation courses can delay students on their path toward
completion, through remediation sequences that are long and do not lead to a college degree or
certificate (Belfield et al., 2014). In existing student placement systems, students are being
placed in remediation courses that are part of long developmental course sequences that average
3.6 courses in math and 2.7 courses in English (Bailey, Jeong, & Cho, 2010). These long
pathways of remediation have been referred to in the literature as inefficient when compared to
pathways of those students entering college academically prepared (Belfield et al., 2014). Figure
1 below illustrates the previous math remediation sequence at Community College Z, which is
typical for community colleges with four levels of courses below transfer.

Figure 1. Previous Math Remediation Sequence at Community College Z
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 17
As students enter college and are assessed as being underprepared, they often struggle in
remediation courses, eventually lowering an institution’s completion rate (Valdez & Marshall,
2013). Of those students entering college during the 2008 Fall semester and enrolling in a math
remediation course four levels below a transfer-level course, only 4 percent successfully
completed a transferable math course (California Community Colleges Chancellor’s Office,
2017). Large scale data tools can highlight the progression of students through the current
process of multi-course remediation (Hern & Snell, 2014). For example, data have demonstrated
that placement in remedial level courses can affect the success of first time community college
students. In 2008-09 only 39.2% of students enrolled in either a remedial math or English level
course successfully completed a degree, certificate, and/or transfer outcome by 2013-14
(California Community Colleges Chancellor’s Office, 2015a). Failing to complete the remedial
math course sequence therefore carries consequences for students (Belfield et al., 2014), the
workforce (Carnevale et al., 2013), and the economy (Harbour & Smith, 2015).
Additionally, previous research has documented how the costs associated with college
completion increases for students placed into remediation courses as their pathway is extended
with additional courses (Belfield et al., 2014). The process of placing students into
developmental education sequences can therefore negatively impact the efficiency and
effectiveness of higher education. As a process, student placement for students assessed as
academically unprepared for college level courses reduces the overall rates of student success
and has implications for both the student and the institution’s resources.
Institutional Resources and Support
The additional time needed to assist students placed into traditional developmental
education course sequences can lead to increases in institutional resources and support services.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 18
The long developmental course sequences that are found in existing remediation pathways create
multiple opportunities for students to exit their education and resources that include support
systems are needed to help students persistent through these exit opportunities (Bailey et al.,
2010). In the literature, institutional resources include several items such as administration,
faculty, support services, and institutional funding (Belfield et al., 2014; Bound et al., 2010).
In their study, Linderman and Kolenovic (2013) provide evidence that supports using a
combination of institutional resources to increase the support and services available to students
in order to improve the completion rates. Since students enter college from a variety of
backgrounds, they may not have prior access to financial, academic, and/or family resources
(Linderman & Kolenovic, 2013). According to research by Belfield et al. (2014), institutional
resources are an important factor in college completion rates, but gains in completion rates likely
result in increased expenditures. Students in developmental course sequences in particular may
require resources such as additional contact with faculty and student services (Linderman &
Kolenovic, 2013). According to Linderman and Kolenovic (2013), the ongoing challenge is that
allocating additional services increases the cost and resources per student. Additionally, the cost
per student can fluctuate based on the level of remediation that a student enters the
developmental sequence (Belfield et al., 2014). However, it is noted that while the cost per
student may increase with additional resources, the cost per graduate may be less when
compared to other student groups (Linderman & Kolenovic, 2013). Therefore, implementing
reforms designed to improve college completion rates need to account for the economic
considerations increased expenditures to improve student success may or may not be sustainable
over time.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 19
At the institutional level, there is a much larger system influencing the success of those
students needing additional preparation for college-level coursework, particularly in math. There
are multiple reasons for the lower rates of success for underprepared students when compared
with students that enter directly into transfer level math courses. One reason proposed in the
literature is the notion that there is a curricular misalignment between high school and college
and also between the assessment tools and the math skills required for success in college level
courses (Hern & Snell, 2014). A second reason for lower student success rates is related to the
increase level of persistence required of students as they move through long remediation
sequences with multiple exit points (Bailey et al., 2010). Additionally, a contributing factor
towards the success or failure of students in math remediation is the effectiveness of the
instruction and the preparation level of faculty to deliver the course content (Edwards, Sandoval,
& McNamara, 2015; Kozeracki, 2005). Since faculty are a recognized component to either the
success or failure of students within math remediation courses, the way in which faculty frame
and approach the problem of low success rates can influence the outcome (Bensimon, 2005).
Importance of the Study
This study is important for a variety of reasons. The community colleges in particular
play an important role in preparing students with basic skills, including math, to pursue their
chosen educational path such as transferring to a four-year institution and/or the skills necessary
to enter the workforce. In California alone, community colleges serve more than 2.3 million
students (California Community Colleges Chancellor’s Office, 2015a), with more than 70% of
those students under-prepared for college level course work (California Community Colleges
Student Success Task Force, 2012). Students who are placed in remediation courses prior to
engaging in college level coursework complete at lower rates and are at greater risk of leaving
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 20
the system (Hern & Snell, 2014). In California community colleges, the completion rate is 31%
for students placed into developmental math courses (California Community Colleges
Chancellor’s Office, 2015a). In the literature, it is argued that the current system of remediation
hinders students’ ability to successfully complete their education goals (Hern & Snell, 2014).
Therefore, developing a better understanding of how faculty can improve the progression of
students through course sequences of developmental math can lead to improved educational
outcomes (Fong, Melguizo, & Prather, 2015).
Description of Stakeholder Groups
At Community College Z, the stakeholders include administrators, faculty, student
support staff, and students. Administrator stakeholders at the college include executive, senior,
and middle level educational administrators at the college. These administrators are responsible
for the planning, operation, and management of the resources used to implement the programs
necessary to support students. The chancellor of the college is the person at the top of the
organizational structure, which extends down to the department chair, that is the management
level closest to the faculty stakeholders.
Faculty stakeholders at Community College Z include 181 full-time faculty and 546
adjunct faculty. The total faculty stakeholders within the math department include 19 full-time
faculty and 73 adjunct faculty. The number of math faculty stakeholders that teach courses
related to the developmental math sequence including the statistics transfer course are 66 faculty
stakeholders: 13 full-time faculty and 53 adjunct faculty.
There are over 31,000 students that attend the college annually (California Community
Colleges Chancellor’s Office, 2015a). Hispanics comprise the largest student group at 42% of all
students. White students account for 38.5% of the student population, African Americans account
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 21
for 5.5% of the student population and Asians represent 5.3% of the student population. The
most common education goal for students is to achieve an associate degree for transfer to a four-
year institution (Community College Z Fact Book, 2015). However, 89% of first time students
place below transfer-level math.
Organizational Mission and Stakeholder Performance Goals
Table 1.
Organizational Mission, Global Goal and Stakeholder Performance Goals
Organizational Mission
The mission of Community College Z is to provide students with essential academic skills by
offering accessible and enriching education that prepares students to reach their educational goals
Organizational Performance Goal
By June 2019, 100% of Community College Z students will meet math transfer eligibility
requirements.
Math Faculty Administrators Students
Stakeholder goal: By Fall
2017, faculty will
implement 100% of the
content of the intermediate
algebra for statistics
course using 100%
appropriate pedagogy.
By Fall 2017, college
administration will create a plan to
increase the number of
intermediate algebra for statistics
math sections to 30 course
sections.
By Fall 2017, all students
placing in developmental math
will successfully complete a
math course with a passing
grade within 36 units.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 22

Stakeholder Group for the Study
While the joint efforts of all stakeholders contribute to the achievement of the overall
organizational goal of 100% of students meeting math transfer eligibility requirements, it is
important to evaluate where Community College Z is in relation to their performance goal.
Therefore, the stakeholders of focus for this study will be the Community College Z math
faculty. The stakeholders’ goal, is that that by the Fall of 2017 math faculty will be able to
implement 100% of the content for the intermediate algebra for statistics course using 100%
appropriate pedagogy. Failure to accomplish this goal will lead to lower rates of student success
in the pre-transfer math class. Lower rates of student success will lead to lower transfer rates and
increase the resources funding required to support existing students, which adversely impacts the
organization’s ability to provide support services and interventions to incoming students and the
organization’s overall goal of 100% of students meeting math transfer eligibility requirements.
Figure 2 below illustrates the new math remediation sequence at Community College Z, with
three levels of courses below transfer and the new intermediate algebra for statistics course
replacing two courses in the prior sequence.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 23

Figure 2. Current Math Remediation Sequence at Community College Z
Purpose of the Project and Questions
The purpose of this project was to evaluate the degree to which the math faculty are
meeting their goal of 100% implementation of the content for the intermediate algebra for
statistics course using 100% appropriate pedagogy. This goal is in support of the organizational
goal of 100% of students meeting the math transfer eligibility requirements. The analysis focused
on knowledge, motivation and organizational influences related to faculty achieving the program
goal. While a complete evaluation project would focus on all stakeholders, for practical purposes
the stakeholder of focus in this analysis were the faculty within the math department of
Community College Z that teach the intermediate algebra for statistics course.
As such, the questions that guided this study are the following:
1. What are the knowledge, motivation and organizational influences affecting the ability of
math faculty to implement 100% of the content for the intermediate algebra for statistics
course using 100% appropriate pedagogy?
2. What are the recommendations for organizational practice in the areas of knowledge,
motivation, and organizational resources?
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 24
Conceptual and Methodological Framework
Clark and Estes (2008) gap analysis, a systematic, analytical method that helps to clarify
organizational goals and identify the knowledge, motivation and organizational influences, was
adapted to an evaluation model and implemented as the conceptual framework. The
methodological framework is a qualitative case study with descriptive statistics. Assumed
knowledge, motivation and organizational influences on faculty that impact Community College
Z’s organizational goal achievement were generated based on personal knowledge and related
literature. These influences were assessed by using interviews, observations, document analysis,
and a literature review. Research-based solutions were recommended and evaluated in a
comprehensive manner.
Definitions
The following key terms are used throughout this study and their definitions are
presented here clarify their meaning for the purposes of this study:
Acceleration: “the reorganization of instruction and curricula in ways that facilitate the
completion of educational requirements in an expedited manner” (Edgecombe, 2011, p. 4).
Gatekeeper course: “the first college-level course the student must take after remediation”
(Bailey et al., 2010, p. 258).
Developmental, Remedial, Basic Skills: terms often used interchangeably to refer to coursework
designed to prepare students for transfer-level coursework (Melguizo, Kosiewicz, Prather, &
Bos, 2014, p. 717)
Developmental sequence: the process of “student preparation for college-level” coursework that
starts with assessment and ends with the completion of the highest remediation course of a
particular discipline (Bailey et al., 2010, p. 256).
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 25
Placement: a method for assessing a “student’s preparedness for college-level work” (Ngo &
Kwon, 2014, p. 444)
Progression: “attempting and passing each level” of the remedial course sequence (Fong et al.,
2015, p. 719).
Student Pathway: “the sequence of courses and enrollments that leads to a credential” (Belfield
et al., 2014, p. 331)
Transfer-level: “courses that count toward a bachelor’s degree” (Melguizo et al., 2014, p. 717),
used interchangeably with the term college-level.
Organization of the Project
Five chapters are used to organize this study. This chapter provided the reader with the
key concepts and terminology commonly found in a discussion about college completion of
students placed into development math. The organization’s mission, goals and stakeholders as
well as the initial concepts of gap analysis were introduced. Chapter Two provides a review of
current literature surrounding the scope of the study. Topics of curriculum, statistics pathways,
instructional delivery, and faculty preparation in developmental math instruction are addressed.
Chapter Three details the assumed influences for this study as well as methodology when it
comes to the choice of participants, data collection and analysis. In Chapter Four, the data and
findings are assessed and analyzed. Chapter Five provides recommendation for practice, based
on data and literature as well as recommendations for an implementation and evaluation plan.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 26
CHAPTER TWO: REVIEW OF THE LITERATURE
This literature review examined the factors influencing the implementation of the
intermediate algebra for statistics course at Community College Z. This review is divided into
two major sections and begins with an overview of literature on the influencing factors
contributing to current level of college completion for students placed into development math.
This section also includes an in-depth discussion on current research in curriculum, statistics
pathways, instructional delivery, and faculty preparation in developmental math instruction.
Following the general research literature, the review turns to the conceptual gap analysis
framework presented by Clark and Estes (2008), which is a systematic analytical method that
helps to understand organizational goal achievement by specifically addressing the knowledge,
motivation, and organizational influences on the ability of faculty to implement the intermediate
algebra for statistics course at Community College Z.
Developmental Math Instruction
Factors Influencing Developmental Math Curriculum
Reviewing the current literature on developmental math and how it influences completion
rates reveals two sets of influences that can be divided into curriculum and pedagogy or
instructional delivery, which will be discussed later. The first set of factors that can be grouped
around the developmental math curriculum include curriculum alignment, acceleration, and
statistics pathways (Davidson, 2015; Edgecombe, 2011; Hern, 2012; Valdez & Marshall, 2013).
Curriculum alignment in the literature highlights the importance of aligning the exit requirements
at the high school level with college level entrance requirements to ensure that students leave
high school prepared for college-level coursework (Valdez & Marshall, 2013). The second factor
identified in the literature is acceleration, which refers to strategies that are focused on
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 27
addressing the long developmental course sequences that increases the time spent by
underprepared students in remediation (Davidson, 2015). The third main factor in developmental
math curriculum is the use of statistic pathways, which challenges the fundamental assumption
that students pursuing a humanities major require the same math knowledge as those students
pursuing stem majors (Hern, 2012). Collectively, the factors presented influence what curriculum
should be used to help students succeed through the development math course sequence.
Curriculum alignment. Previous research has documented the importance of identifying
both the content and the methods of teaching when developing curriculum (Ball, Sleep, Boerst,
& Bass, 2009). Additionally, within developmental math curriculum, an influencing factor is the
alignment between exit and entrance points either between courses in a sequence or educational
segments. Researchers have proposed that revisions to existing math sequences and pathways
can improve student success and increase college completions (Hern & Snell, 2014). In the
literature, two issues presented point to curriculum alignment as an area in need of further
investigation. The first issue includes existing practices where math sequences and pathways
assess and promote math skills such as algebra, regardless of the skills a student needs,
particularly if they pursue non-math intensive majors (Hern & Snell, 2014).
In addition, the literature on curriculum alignment identifies the issue of gaps between
exit and entrance points in the educational pathway of students (Valdez & Marshall, 2013). The
argument put forth by Hern and Snell (2014), highlights the extent that the current system of
remediation, assessment, and placement can hinder student success as was previously discussed.
However, Valdez and Marshall (2013) clarify the argument by addressing the context in which
the curriculum misalignment occurs, particularly between the high school and college
educational segments. For example, as students in high school work toward completing common
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 28
core standards, a gap begins to form if the colleges assess incoming high school students along a
different set of math skills. According to Valdez and Marshall (2013), addressing the macro inter-
segmental misalignment will require revisiting curriculum at the micro level. At the micro level,
the goal will be to ensure that assignments are developed to align with the entrance requirement
of the next step in the pathway such as the next course, assessment test, or college entrance
requirements (Valdez & Marshall, 2013). Current research on application of a vertical approach
to curricular alignment has provided evidence that the method helps students transition between
segments thereby reducing remediation and increasing student success (Hern & Snell, 2014;
Valdez & Marshall, 2013). The focus of recent research on curricular alignment has been on
pathways through either acceleration or redesigning the entire pathway.
Acceleration. A collaborative approach to aligning the curricular expectation between
education segments attempts to address the issues with existing developmental sequences that
provide multiple exit opportunities for students. To solve this issue, many researchers have
proposed various methods of accelerating a student’s path through remediation (Cafarella, 2016;
Davidson, 2015; Edgecombe, 2011; Hern, 2012; Hern & Snell, 2014). Specifically, acceleration
accomplishes two goals, reducing the time to complete developmental sequences (Cafarella,
2016; Davidson, 2015; Edgecombe, 2011) and reducing the number of opportunities for students
to leave their education prematurely (Hern & Snell, 2014). Previous studies proposed that the use
of acceleration models to assist students in completing their remediation requirements help to
improve completion rates (Cafarella, 2016; Davidson, 2015; Edgecombe, 2011), which are
correlated with academic momentum (Davidson, 2015). Over the past four decades, acceleration
has spread across institutions of higher education can be found at over 250 institutions nationally
(Wlodkowski, 2003). However, the application of acceleration in much of the literature is
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 29
inconsistent, often adapted to address the specific set of circumstances at a local institution
(Cafarella, 2016; Edgecombe, 2011; Hern, 2012; Hern & Snell, 2014). In the literature,
acceleration initiatives have incorporated a redesign of the course sequence, adjusted support
services then scaffold course content (Hern & Snell, 2014), while other efforts have focused on
offering compressed schedules (Cafarella, 2016). Collectively, each method of acceleration
attempts to overcome the inherent challenge of multiple exit points created by the length of
traditional course sequences and programs (Wlodkowski, 2003). Moving forward, the
application of acceleration methods that focuses on the redesign of developmental course
sequences has led to the implementation of accelerated pathways.
Statistics pathways. The implementation of accelerated pathways moves beyond
acceleration and takes into consideration course and program expectations upon completion. An
example of a pathway is the implementation of a statistics pathway that addresses several of the
concerns previously discussed within the current system of math remediation such as multiple
exit points, long course sequences, and content relevance (Edwards et al., 2015; Hern, 2012;
Hodara & Jaggars, 2014). As discussed, existing math remediation is built around a course
progression suitable for stem majors that disregards the skills in statistics needed by those
students pursuing majors in humanities (Hern, 2012). The existing disconnect between statistics
and the content of remediation sequences can hinder student progression (Edwards et al., 2015;
Fong et al., 2015). In the literature, recent focus has been on the creation of clear pathways that
connect the skills required during remediation to improve student success as measured by
completion and transfer rates (Fong et al., 2015; Hodara & Jaggars, 2014). In the field of math
remediation, the statistics pathway serves as the vehicle for improving a student’s progression
through the developmental sequence of courses (Edwards et al., 2015). However, the creation of
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 30
a statistics pathway requires several changes beyond reducing the timeline. Ball et al. (2009)
stated that both content and teaching methods are important to curriculum development.
Additionally, Edwards et al. (2015) argued that for a revised statistics pathway, changes to
lessons materials, support services, and faculty development are needed in addition to changing
content goals and pedagogy. Implementing adjustments to the curricular pathways of math
remediation to foster a new statistics pathway addresses one component of a larger issue, another
component is role of the faculty in delivering the redesigned pathway effectively.
Factors Influencing Math Instruction Delivery
In addition to the role of curriculum, previous research has documented the role of
instructional delivery on efforts to improve math remediation. The literature on instructional
delivery for math remediation identified influential factors that included effective math
instruction and faculty preparation (Alexander, Karvonen, Ulrich, Davis, & Wade, 2012; Ball et
al., 2009; Edwards et al., 2015; Kozeracki, 2005). Current research on effective math instruction
has focused on the content and pedagogical knowledge that faculty need to be effective
(Alexander et al., 2012; Ball et al., 2009; Edwards et al., 2015). The second factor identified in
the literature is the level of preparation faculty received in order to teach math remediation
(Kozeracki, 2005). Additionally, faculty preparation is influenced by the type and amount of
resources that are available to faculty (Alexander et al., 2012; Edwards et al., 2015). The
combination of these factors demonstrates that for instructional delivery to be effective, the
faculty is an important resource.
Effective math instruction. Previous research has documented that teaching math
incorporates planning, deconstruction of mathematical concepts, leading discussions, and
determining how best to represent problems to students (Ball et al., 2009). Current research on
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 31
the delivery of math remediation indicates that a critical influence on effective math instruction
is faculty knowledge of course content and pedagogy (Alexander et al., 2012; Edwards et al.,
2015). According to Edwards et al. (2015), traditional methods of math instruction are focused
on factual and procedural knowledge, whereas the pedagogy associated with pathways focuses
on developing a conceptual understanding of the course content. Previous research has
documented the two instructional orientations, which have been labeled as knowledge
transmission and learning facilitation (Kember & Gow, 1994).
In the literature, knowledge transmission is where faculty transfer their knowledge to
students by presenting facts, lectures, and other media (Bailey, Jaggars, & Jenkins, 2015;
Kember & Gow, 1994). In contrast, learning facilitation changes the role of faculty to be more
interactive since they serve as a facilitator, guiding students in the development of skills such as
critical thinking and problem solving as they learn the concepts underlying the course content
(Bailey et al., 2015; Kember & Gow, 1994). Additionally, Cohen, Raudenbush, and Ball (2003)
support the notion that instruction can be viewed as an interaction that occurs between teacher,
student, content, and environment. Therefore, the ideas presented by Edwards et al. (2015) such
as mathematical discourse, productive struggle, student engagement, and sense-making each
contribute toward an understanding of what constitutes effective instruction in math.
In their book, Bailey et al. (2015) build on earlier research on different teaching
orientations and propose that the current emphasis of procedures in middle- and high-school
mathematical instruction instead of engaging students in learning mathematical concepts is one
example of how students are led to develop an academic foundation that leaves them unprepared
for college-level coursework. However, Alexander et al. (2012) propose that at the community
college level, teaching effectiveness not only includes content knowledge and pedagogy, but also
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 32
the skills to address the various types of learners that enroll at the institution. Content
knowledge, pedagogy, and student learning are three areas that can be unpacked in order
understand the specific components of effective math instruction. First, content knowledge has
been described as including both procedural and conceptual knowledge of the course content
(Alexander et al., 2012; Edwards et al., 2015). In Hill and Ball (2004), the idea of content
knowledge was further unpacked to reflect a “specialized knowledge of content” that included
the ability of effective math instructors to explain the rationale behind a mathematical procedure
and its meaning (p. 332). The importance of knowing how to breakdown and explain a
mathematical procedure is demonstrated as faculty work to align pedagogy with the ability of
their students to learn the content (Ball et al., 2009).
Knowing the pedagogical tasks available is only part of the equation, it is also important
to understand when to use them. According to Cohen et al. (2003), “effective teachers planned
carefully, used appropriate materials, made the goals clear to students, maintained a brisk pace,
checked student work regularly, and taught material again if students had trouble” (p. 121). In
addition, effective teachers viewed students as having the ability to learn and in turn the role of
teachers is to help those students by using available resources (Cohen et al., 2003). Effective
math instruction requires an understanding of both the content and the practices required to
facilitate learning that engages a conceptual understanding within a variety of learners. However,
at community colleges effective math instruction is challenging for a variety reasons, one of
which is the lack of faculty preparation.
Faculty preparation. In the literature, it has been documented that the amount of
preparation faculty has received can influence the level of student achievement (Edwards et al.,
2015; Kozeracki, 2005). As previously discussed, teaching math requires faculty to possess
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 33
knowledge of both course content and pedagogy (Alexander et al., 2012; Edwards et al., 2015).
In addition, effective math instruction requires skills that are associated with being able to
deconstruct mathematical concepts so that students can learn those concepts (Ball et al., 2009).
However, it has been documented that a gap often exists between the knowledge that faculty
gained as part of their educational program and the skills identified for effective teaching
(Kozeracki, 2005).
Current research indicates that math faculty are particularly at risk of having limited
education coursework focused on effective instructional practices and instead are primarily
exposed to lecture or teacher centered practices (Edwards et al., 2015). The ongoing challenge
with faculty preparation is that solutions often draw on current institutional resources for support
such as administration, faculty, support services, and institutional funding (Belfield et al., 2014;
Bound et al., 2010). The complexity of teaching within a community college is in part a
reflection of the diverse set of learners and the respective competencies needed to facilitate
learning.
Professional Development. As previously mentioned, community college faculty
possess the content knowledge in a subject area, but often lack formal preparation in the skills
needed to teach (Alexander et al., 2012). Given the potential gap in faculty preparation,
researchers have turned to the role that professional development can play in improving effective
teaching for current and new faculty (Alexander et al., 2012; Ball et al., 2009). In the literature,
the personal growth that is derived from activities that lead to knowledge acquisition is referred
to as professional development (Aguinis & Kraiger, 2008). According to Matos et al. (2009), the
lack of faculty preparation is reflective of the, “change in our understanding of what constitutes
learning” (p. 167). Previously, when mathematics faculty participated in professional
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 34
development, the approach was based on a training model of professional development where
faculty engaged in learning mathematical content (Matos et al., 2009). This is in contrast with
recent calls for practice-based models of professional development that focus on classroom
practices of mathematics instruction (Matos et al., 2009). Alexander et al. (2012) argues that
currently at the college level there is often a lack of professional development opportunities for
faculty around pedagogy. Although, according to Edwards et al. (2015) professional development
that is focused on developing the knowledge of skills for teaching math is critical to improving
student outcomes. Specifically, professional development programs should utilize professional
learning, job-embedded activities, contextual learning activities, and be centered on classroom
practice (Edwards et al., 2015). Professional development designed to improve the skillset of
faculty to deliver course curriculum span a wide range of competencies and highlights the
complexity of teaching mathematics within a community college.
The Clark and Estes (2008) Gap Analytic Conceptual Framework
The Clark and Estes (2008) gap analysis conceptual framework is a systematic approach
to improving performance. The Clark and Estes (2008) gap analysis conceptual framework was
used in this study to address the research questions and examine the knowledge/skill, motivation,
and organizational barriers influencing the achievement of the organizational goal. The gap
analysis process starts with defining key long-term organizational goals and then identifying
shorter-term performance goals (Clark & Estes, 2008). The process continues with determining
the gaps between current levels of performance and the stated goals. In addition, the process calls
for the identification of possible causes and influences for those gaps prior to developing and
implementing solutions. Once the solutions have been implemented the results are evaluated for
further refinement.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 35
The gap analysis conceptual framework is centered around three main components (a)
knowledge and skills, (b) motivational factors, and (c) organizational factors (Clark & Estes,
2008). Clark and Estes (2008) argue that these three components align with the three “causes of
performance gaps” and work together as “interacting systems” to achieve performance goals (p.
43). The knowledge and skills component of the framework refers to whether the people within
the organizational possess the ability to achieve the performances goals. The motivational
component of the framework addresses the importance of an employee choosing to achieve the
goal. The third component, organizational factors, acknowledges that processes or resources may
not be aligned with achieving the goals. By combining each component into a process, Clark and
Estes (2008) identify a process that works to provide a more complete solution to performance
improvement.
Stakeholder Knowledge, Motivation and Organizational Influences
Knowledge and Skills
Improving college completion has been a focus of education and policy leaders nationally
(Bragg & Durham, 2012; Harbour & Smith, 2015). At Community College Z, the strategy begins
with assisting students in achieving math transfer eligibility earlier in their college career.
Accomplishing this task falls primarily on the ability of math faculty to effectively deliver math
instruction to those students placed into remediation. Clark and Estes (2008) suggest that
effectively performing a task is related to the knowledge and skills that people have acquired.
According to the cognitive view of learning, learning or knowledge acquisition is a process that
begins with a change in the learner’s environment that changes the learner’s knowledge, which
then changes the learner’s behavior (Mayer, 2011). A key factor in the effectiveness of learning
can be traced to the instructional design of the learning opportunity, since information processing
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 36
theory acknowledges that for information to enter long-term memory, instruction must work
within the limitations of working memory (Kirschner, Kirschner, & Paas, 2009; Schraw &
McCrudden, 2013). This literature review focuses on the knowledge and skills necessary for
math faculty at Community College Z to achieve the stakeholder goal of implementing 100% of
the content for the intermediate algebra for statistics course using 100% appropriate pedagogy.
In a revision to Bloom’s Taxonomy, Krathwohl (2002) identifies four categories of
knowledge types: factual knowledge, conceptual knowledge, procedural knowledge, and
metacognitive knowledge. Since knowledge is a component of learning, understanding the
differences between these knowledge types helps to identify which type is most relevant for a
particular context (Mayer, 2011). Factual knowledge refers to the basic elements needed to solve
problems while conceptual knowledge refers to how those basic elements are interrelated and
can work together within larger constructs (Krathwohl, 2002). The third knowledge type
proposed by Krathwohl (2002) is procedural knowledge, which revolves around the knowledge
of how to do something. The fourth knowledge type is metacognitive knowledge, which is the
knowledge and awareness of cognition (Krathwohl, 2002) and has also been described as
knowing the when and why of proceeding with a task (Rueda, 2011). The knowledge influences
identified as part of this study are classified into factual, conceptual, and procedural knowledge
dimensions. The application of the metacognitive knowledge type provides a foundation for
understanding how faculty can assess their own effectiveness in achieving the stakeholder goal.
Assumed factual knowledge influences.
Faculty need to know the goal. According to the literature, the knowledge and skills of
the people within an organization tasked to achieve a particular goal is an important component
to addressing existing issues (Clark & Estes, 2008). To implement the intermediate algebra for
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 37
statistics course, math faculty will need to have knowledge of the goal of improving math
transfer eligibility of students. According to Rueda (2011), the knowledge of the goal needed by
math faculty can be classified as a form of factual knowledge, which includes facts “basic to
specific disciplines, contexts, or domains” (p. 28). In the implementation of the intermediate
algebra for statistics course, the factual knowledge needed includes the role of the course to
improve the success of those students placed into math remediation. The current system of math
remediation, assessment, and placement has been documented as hindering student success
(Hern & Snell, 2014). Revisions to existing math sequences and pathways like the intermediate
algebra for statistics course, can serve as a method to improve student success (Hern & Snell,
2014).
Assumed conceptual knowledge influences.
Faculty need to know the content of course curricula. For the math faculty to achieve
the stakeholder goal, they will need to know the mathematical content of the new intermediate
algebra for statistics course curriculum. According to the course outline of record
2
the
intermediate algebra for statistics course will contain the following mathematical concepts:
formulas and algebraic expressions; linear equations and inequalities in one and two variables;
analyzing and producing data; simple statistics and graphs; functions; and probability. The
knowledge type that corresponds with this knowledge influence is conceptual knowledge.
Conceptual knowledge focuses on the ability to connect different components, such as discrete
course content, into an organized model or schema (Krathwohl, 2002; Rueda, 2011). In the
literature, effective teaching is an important component to student success and effectiveness is
composed of a number of factors including pedagogy and the specific knowledge of the course

2
Community College Z course outline of record for intermediate algebra for statistics
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 38
content (Alexander et al., 2012). Therefore, the ability of the math faculty to effectively deliver
the course will be connected to their knowledge of the course content.
Assumed procedural knowledge influences.
Faculty need to know how to adapt their instruction. As math faculty work toward
implementing the intermediate algebra for statistics course, they will need to know how to adapt
their instruction to meet the needs of developmental math students. The knowledge of how to do
something, such as adapting instruction to students, is a form of procedural knowledge
(Krathwohl, 2002; Rueda, 2011). Research conducted by Hill, Ball, and Schilling (2008), suggest
that math faculty can possess knowledge of the mathematical thinking of students, which
includes how they learn certain concepts or why they make certain mistakes and errors.
Possessing knowledge of how students think about math and why those students make certain
errors can lead math faculty to adjust in their preparation for teaching the course material as they
adapt to their students (Hill & Ball, 2004; Hill et al., 2008). In Cohen et al. (2003), it was
presented how effective teachers used various skills in planning and goal setting to guide
students through course content while checking in and even teaching the material again if
students struggled. As part of the course pedagogy of intermediate algebra for statistics, students
are allowed to struggle through material with the expectation that students will develop a level of
persistence
3
to become a critical thinker. Additionally, research has documented that knowledge,
training, and experience are key factors in the ability of faculty to serve the needs of students
(Kozeracki, 2005).
Faculty need to know how to teach math effectively. To implement the new course,
intermediate algebra for statistics, math faculty will need to know how to deliver effective

3
Community College Z course syllabus for intermediate algebra for statistics.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 39
mathematics instruction to improve student outcomes. The knowledge type that corresponds with
this knowledge influence is procedural knowledge. Procedural knowledge focuses on the
knowledge of how to do something, such as teaching effectively (Krathwohl, 2002; Rueda,
2011). In the literature, the two instructional orientations have been identified are knowledge
transmission and learning facilitation (Bailey et al., 2015; Kember & Gow, 1994). Both
orientations see the role of teaching differently and therefore promote different skills for
teaching.
As previously mentioned, knowledge transmission focuses on the transfer of knowledge
through the presentation of facts, lectures, and other media (Bailey et al., 2015; Kember & Gow,
1994). Whereas learning facilitation promotes skills in facilitation as the instructor guides
students in learning the concepts of the course (Bailey et al., 2015; Kember & Gow, 1994).
Further, work by Ball et al. (2009) would suggest support for learning facilitation as they noted
that effective math instruction requires math faculty have the skills to deconstruct mathematical
concepts to align activities so that students can learn needed concepts. Additionally, the planning
associated with matching the right materials and pace to mathematics concept is part of the skills
attributed to effective math teachers (Cohen et al., 2003).
In the literature it is recognized that there is often a gap between the knowledge faculty
gained in their graduate programs and the skills needed to teach effectively (Kozeracki, 2005).
Research indicates that faculty are often hired to meet minimum accreditation standards, which
provides potential faculty with content knowledge but not effective skills in teaching (Alexander
et al., 2012). Math faculty in particular are more likely to not have any coursework in education,
which limits their exposure to learning effective instructional practices (Edwards et al., 2015).
Previous studies indicate that knowledge of effective teaching is a critical knowledge influence
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 40
to improving student outcomes (Alexander et al., 2012; Edwards et al., 2015; Kozeracki, 2005).
Specifically, current research indicates that when implementing a statistic pathway in math, a key
component to improving student outcomes is professional development that focuses on the
knowledge and practices of teaching math (Edwards et al., 2015).
A meta-analysis on the impact of teaching on student achievement found that certain
teacher preparation, education, and professional development programs can improve student
achievement (Kyriakides, Christoforou, & Charalambous, 2013). Measuring improvement
through professional development training in effective teaching starts with collecting student
success data and instituting a professional development program that utilizes professional
learning, job-embedded learning, contextual learning activities, and learning of classroom
practice (Edwards et al., 2015). Clark and Estes (2008) provide further support for knowledge
and skill enhancement, while also elaborating on the importance of matching specific forms of
knowledge solutions to types of knowledge needed. As the math faculty work toward achieving
the stakeholder goal, knowing and possessing the skills to deliver effective instruction within the
domains of mathematics and statistics is an important component for success.
Faculty need to know how to align instructional activities to performance. Another
factor influencing the implementation of the intermediate algebra for statistics is that math
faculty will need to know how to align learning activities to course performance objectives. In a
review by Hern and Snell (2014), evidence was found to support the notion that changes in the
classroom such as redesigned course curriculum with revised activities can improve student
outcomes. Further evidence has suggested that improving curriculum alignment that incorporates
course assignments that are developed to better align with course objectives also demonstrate
improved student success (Valdez & Marshall, 2013). Existing literature also supports the role
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 41
that knowledge of learning theory and instructional delivery has effectively connected course
content to the course performance objectives (Illowsky, 2008). A review of the course syllabus
4

for the intermediate algebra for statistics course identifies that the content will be delivered
though in-class based discovery activities and assignments utilizing a combination of reading,
writing, and presentations to achieve the course objectives.
Table 2 shows the five assumed knowledge influences related to the implementation of
the intermediate algebra for statistics course. In addition, the table also shows the type of
knowledge and the related research literature for each assumed knowledge influence.
Table 2.
Assumed Knowledge Influences, Type, and Research Literature

Assumed Influences Research Literature
Knowledge

Factual Faculty need to know the
goal.
(Clark and Estes, 2008; Hern
and Snell, 2014; Illowsky,
2008; Mayer, 2011; Rueda,
2011; Valdez & Marshall,
2013)
Conceptual Faculty need to know the
content of course curricula.
(Alexander, Karvonen,
Ulrich, Davis, & Wade,
2012; Ball, Sleep, Boerst, &
Bass, 2009; Hill & Ball,

4
Community College Z course syllabus for intermediate algebra for statistics.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 42
2004; Clark and Estes, 2008;
Edwards, Sandoval, &
McNamara, 2015;
Kozeracki, 2005;
Krathwohl, 2002; Rueda,
2011)
Procedural Faculty need to know how to
adapt their instruction.
(Alexander, Karvonen,
Ulrich, Davis, & Wade,
2012; Cohen, Raudenbush,
& Ball, 2003; Edwards,
Sandoval, & McNamara,
2015; Kozeracki, 2005;
Krathwohl, 2002;
Kyriakides, Christoforou, &
Charalambous, 2013; Rueda,
2011)

Faculty need to know how to
teach math effectively.
(Alexander, Karvonen,
Ulrich, Davis, & Wade,
2012; Ball, Sleep, Boerst, &
Bass, 2009; Clark and Estes,
2008; Edwards, Sandoval, &
McNamara, 2015; Hill, Ball,
& Schilling, 2008;
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 43
Kozeracki, 2005;
Krathwohl, 2002;
Kyriakides, Christoforou, &
Charalambous, 2013; Rueda,
2011)
Faculty need to know how to
align instructional activities
to performance.
(Hern and Snell, 2014;
Illowsky, 2008; Mayer,
2011; Valdez & Marshall,
2013)

Motivation
The purpose of this analysis of the motivational literature was to determine the
motivation influences of math faculty as they work to achieve the stakeholder goal of
implementing 100% of the content for the intermediate algebra for statistics course using 100%
appropriate pedagogy. Since motivation can be a complex process to understand, developing an
understanding of the motivational influences can prove invaluable during self-reflection, which
has been recognized as an important step in making improvements in student outcomes
(Alexander et al., 2012). In the literature, motivation is concerned with the underlying factors
that contribute to an individual engaging in behavior that works toward specific tasks or interests
(Pintrich, 2003). Clark and Estes (2008) further identify three motivation processes that can be
used as indicators of motivation, these processes are active choice, persistence, and mental effort.
Additionally, Eccles (2009) suggests that the two fundamental questions that describe the
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 44
underlying factors of motivation revolve around an individual’s expectancy and the value of a
task.
From these foundational elements of motivation, further issues surrounding an
individual’s interests and self-efficacy, which is the degree of belief in accomplishing tasks, take
shape (Bandura, 2000; Pajares, 2009; Pintrich, 2003; Schraw & Lehman, 2009). Another
dimension of motivation concerning beliefs are the reasons an individual attributes their success
or failure in completing a task and whether they believe they had some control in affecting the
outcome (Rueda, 2011; Weiner, 2005). Collectively, the conceptual elements that form a basis for
understanding motivation can be used to connect an individual’s decision to engage to the effort
and outcomes from that engagement (Eccles, 2009; Mayer, 2011).
Expectancy value theory. In expectancy value theory, motivation is tied to an
individual’s belief in accomplishing the task and their interest in engaging in the task (Eccles,
2009). The literature supports the underlying principle in expectancy value theory, which is that
those with the expectation for successful task achievement demonstrate greater levels of task
achievement (Pintrich, 2003). Eccles (2009) states that interest is an important component in
choosing to engage in a task. Within the framework of expectancy value theory, motivational
interest can be deconstructed to the following four components: intrinsic interest, utility value,
attainment value, and cost (Eccles, 2009; Pintrich, 2003). In the literature, intrinsic interest refers
to the personal interest in a task, utility value refers to the perceptions of the usefulness of
accomplishing a task, attainment value identifies the level of importance associated with a task,
and cost refers the perceived cost of engaging in the task (Pintrich, 2003). In addition, the four
components of expectancy value theory are interrelated and help to define an individual’s own
identity that then works to influence future levels of motivation (Eccles, 2009). As math faculty
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 45
look to achieve the stakeholder goal of implementing a new course that would improve student
success, the level of motivation of faculty to engage in efforts to improve can be tied to their
expectation and perceived value of accomplishing the task.
Assumed expectancy value influences.
Faculty need to value implementing intermediate algebra for statistics. In order to
achieve the stakeholder goal, math faculty need to value implementing the intermediate algebra
for statistics course for developmental math students, which corresponds to the expectancy value
theory. Eccles (2009) proposed that utility value is derived from the future benefit of
accomplishing a task. In addition, there is evidence to support that higher values that are placed
on a task are associated with higher levels of motivation (Pintrich, 2003). Previous research by
Cafarella (2016) on faculty experience with acceleration math found that faculty driven
initiatives of acceleration appeared to have higher morale and were better integrated. Currently,
the assumption underlying the implementation of the intermediate algebra for statistics course is
that the course will lead to better student achievement. The assumption is validated by current
research, which indicates that acceleration initiatives that are designed to shorten the time or
course sequence in developmental math can improve student success (Cafarella, 2016).
Therefore, the motivation of math faculty to engage in achieving the stakeholder goal will in part
be derived from the value associated with improving student success.
Faculty need to value improving student success. To achieve the stakeholder goal, math
faculty need to value improving student success. Current research indicates that at the
institutional level, success can be tied to prepared and motivated faculty (Hardré, 2012). The
literature indicates that faculty play an important role in key performance areas of an institution,
particularly in teaching, therefore their existing level of preparation and ongoing motivation to
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 46
engage in further professional development are contributing factors to both student and
institutional success (Wallin, 2003). In the literature, improved student success metrics from
acceleration methodology can be attributed to student comfort level with computers, skill level,
learning style, and the instructor’s comfort level with teaching acceleration courses (Cafarella,
2016). Research into the role of faculty motivation indicates that the level of motivation is an
important component in efforts to reform existing instructional practices (Hardré, 2012; Wallin,
2003) and in professional development participation levels (Wallin, 2003). In addition,
understanding the role that motivation plays in the creation of the environment to support faculty
development is important to improving the effectiveness of faculty (Wallin, 2003).
Self-efficacy theory. In social cognitive theory, self-efficacy is a major contributor to
motivation (Bandura, 2005; Pajares, 2009). Further, the standards that are adopted by individuals
to inform personal self-awareness and self-regulation are developed in part from personal levels
of efficacy (Bandura, 2005). In the literature, self-efficacy is defined as the personal judgements
that people hold with regards to their capabilities for learning/organizing and performance
(Bandura, 2005; Pajares, 2009). Therefore, the beliefs that people possess regarding their ability
to accomplish a task will inform their motivation to act or persist since beliefs determine in part
the incentives associated with success (Pajares, 2009). As reported by Pintrich (2003),
individuals with higher expectations are found to have achieved higher levels of success. This is
further supported by current research that indicates within an academic environment, learning
and performance can be affected by the self-efficacy of students (Denler, Wolters, & Benzon,
2014). While self-efficacy beliefs can inform levels of motivation, it is important to note that
motivation and the various components are often specific to the context or environment that is
being observed (Rueda, 2011). Previous research on the of self-efficacy has documented that
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 47
under a situation where self-efficacy has been raised individuals focus on opportunities, which is
in contrast to situations where self-efficacy has been lowered and the focus shifts toward
problems (Bandura, 2005). Despite this limitation, Rueda (2011) argues that developing an
understanding of motivation provides tools for examining and addressing problems within an
educational context. For example, the literature on training and development identified self-
efficacy as one of the trainee characteristics that is correlated to the transfer of learning
(Grossman & Salas, 2011).
Assumed self-efficacy influences.
Faculty need to believe they are capable of effectively delivering instruction. In addition
to valuing the stakeholder goal, the math faculty need to believe that they are capable of
effectively delivering instruction in intermediate algebra for statistics. However, in research by
Lowenthal, Wray, Bates, Switzer, and Stevens (2012) and Kozeracki (2005), it is argued that
generally faculty are not prepared during their graduate education to deliver effective instruction
and instead are taught to be scholars. The experience that community college math faculty
possess is often limited to lecture and discussion that is centered on the faculty (Edwards et al.,
2015). In addition, Cafarella (2016) notes that the faculty comfort level with delivering
instruction in alternative formats remains an ongoing concern. Further, research has documented
that the environmental context can influence the expectations that faculty have set for the success
of their students (Ellerbe, 2015). Previous research has documented that better student outcomes
and performance in developmental education are linked to programs with professional
development in effective instructional practices (Illowsky, 2008).
To achieve the education goals established, faculty need to believe that they have the
capability to plan and execute the tasks needed to assist their students in succeeding (Skaalvik &
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 48
Skaalvik, 2010). In the literature, faculty self-efficacy is noted as being important in determining
motivation (Bandura, 2005; Pajares, 2009) and is shown to be positively correlated with student
success (Swackhamer, Koellner, Basile, & Kimbrough, 2009). Current research has shown that
students completing their developmental math sequence achieve outcomes similar to college-
prepared students (Bahr, 2010). Recently, Edwards et al. (2015) noted that improving student
outcomes in math can be tied to professional development that is targeted at faculty knowledge,
skills, practices, and beliefs. In Swackhamer et al. (2009), it was found that the level of efficacy
in science and math teachers could be raised by increasing their content knowledge. However, a
limitation within self-efficacy research is that there have been few studies that have attempted to
understand the role of self-efficacy within the context of community college faculty (Hardré,
2012). Despite this limitation, the field of motivation research has demonstrated the importance
of self-efficacy (Bandura, 2005; Eccles, 2009; Pajares, 2009; Pintrich, 2003) that can inform the
current application of implementing the new intermediate algebra for statistics course.
Attribution theory. In attribution theory, the important variable to determining
motivation are beliefs regarding the reasons for success or failure including the level of control
an individual has in influencing the outcome (Rueda, 2011; Weiner, 2005). According to Weiner
(2005), the three main dimensions to the beliefs identified in attribution theory are locus,
stability, and controllability. In the literature locus is used to describe whether the attribution is
located either internal or external to an individual (Rueda, 2011; Weiner, 2005). The second
dimension known as stability, is used to describe the cause of an event according to whether the
cause is stable or unstable across either a period of time or various situations (Anderman &
Anderman, 2009). In the literature, a student’s aptitude for a particular subject is often used as an
example of stability (Rueda, 2011; Weiner, 2005). Controllability refers to the perceived level of
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 49
control an individual has over a cause to influence the outcome (Rueda, 2011). In the literature,
the causal beliefs or attributions are important to both motivation and eventual outcomes
(Pintrich, 2003). Research has indicated that students with attributions such as a higher degree of
control over their own learning are associated with higher levels of achievement as compared to
those that believe they have little control (Pintrich, 2003).
Assumed attributional influences.
Faculty need to believe that student outcomes can be attributed to their instruction. To
achieve the stakeholder goal, the math faculty need to believe that some of the student success or
failure can be attributed to their instruction. In attribution theory, individuals attribute outcomes
to various causal beliefs and the combination of each of the three dimensions of attributions
affect future behavior (Rueda, 2011). Faculty can influence the attributions of students along the
three dimensions of locus, stability, and control (Anderman & Anderman, 2009). In the
literature, the ideas that contribute toward effective instruction in math include mathematical
discourse, productive struggle, student engagement, and sense-making (Edwards et al., 2015).
Additionally, in the teaching orientation known as learning facilitation, faculty serve as a
facilitator guiding students in an interactive process (Bailey et al., 2015; Kember & Gow, 1994).
Previous research define the interaction in instruction as occurring between teacher, student,
content, and environment (Cohen et al., 2003). According to Cohen et al. (2003), effective
teachers review the work of students and repeat material if needed. Through the interaction of
instruction, faculty communicate information to students that is used to inform their attributions
through feedback on activities and repeating material or instructional lessons to students
(Anderman & Anderman, 2009).
Table 3 identifies the assumed motivational influences for math faculty along with the
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 50
motivation theory and related research literature. The first two motivational influences address
the expectancy value of the stakeholder goal for math faculty. While the third motivational
influence addresses the self-efficacy of the math faculty to deliver instruction in the intermediate
algebra for statistics course. The fourth motivational influence addresses the degree to which
math faculty attribute the success or failure of their students to their instruction.
Table 3.
Assumed Motivation Influences, Theory, and Research Literature

Assumed Influences Research Literature
Motivation

Expectancy value Faculty need to value
implementing intermediate
algebra for statistics.
(Cafarella, 2016; Eccles, 2009;
Hardré, 2012; Pintrich, 2003;
Wallin, 2003)

Faculty need to value
improving student success.
(Cafarella, 2016; Eccles, 2009;
Hardré, 2012; Pintrich, 2003;
Wallin, 2003)
Self-efficacy Faculty need to believe they
are capable of effectively
delivering instruction.
(Bandura, 2005; Pajares, 2009;
Skaalvik & Skaalvik, 2010;
Swackhamer, Koellner, Basile,
& Kimbrough, 2009)
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 51
Attribution Faculty need to believe that
student outcomes can be
attributed to their instruction.
(Anderman & Anderman,
2009; Bensimon, 2005;
Cafarella, 2016; Eccles, 2009;
Hardré, 2012; Mayer, 2011;
Pintrich, 2003; Wallin, 2003;
Rueda, 2011)

Organizational Influences
The purpose of this analysis of the organizational literature was to determine the
organizational influences on math faculty as they work to achieve the stakeholder goal of
implementing the intermediate algebra for statistics course. Clark and Estes (2008) identified
work processes, material resources, and value streams as three organizational factors that can be
a source of organizational performance gaps. Since organizations are composed of complex and
interacting systems, each with their own culture, developing an understanding of the influencing
factors or barriers affecting the conditions of an organization is important to improving
organizational performance (Clark & Estes, 2008; Rueda, 2011). The complexity in
understanding the conditions of an organization in part stems from the notion that organizational
culture is: (a) not visible, (b) automated, and (c) consists of values that are relative (Rueda,
2011). Further, organizational culture can form and manifest differently across environments,
groups, and individuals within the same organization (Clark & Estes, 2008). In the literature
culture is defined as, “a pattern of shared basic assumptions learned by a group as it solved its
problems of external adaptation and internal integration…to be taught to new members” (Schein,
2010, p. 18). Collectively, the conceptual elements that form the definition of culture can be used
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 52
to connect the process of learning of an individual to their social interactions with others as
highlighted by sociocultural theory, which views learning as being social in nature (Scott &
Palincsar, 2013). With the introduction of the cultural model and cultural setting concepts,
Gallimore and Goldenberg (2001) propose that shared mental models and the settings where
culture exists are distinct despite being interconnected.
Additionally, organizational culture can serve as an invisible yet interactive layer that sits
between existing processes and resources and all attempts to improve organizational performance
(Clark & Estes, 2008). As math faculty at Community College Z look to achieve the stakeholder
goal of implementing a new course that would improve student outcomes in math remediation it
is important to evaluate the organizational influences on current efforts. To better understand the
stakeholder goal, the literature reviewed here organizes the organizational influences into two
organizational types (Gallimore & Goldenberg, 2001; Rueda, 2011). To address the stakeholder
goal, four organizational influences have been identified. The first organizational influence is
that there is a culture in the math department that supports the implementation of intermediate
algebra for statistics, which is a cultural model. The second organizational influence is a general
belief that underprepared students can learn the skills to complete math coursework, which is
also a cultural model. The third organizational influence is that the college supports and
incentivizes a standard approach to improve math remediation, which reflects the cultural setting.
The fourth organizational influence is that the college provides resources to support math faculty
in maintaining academic standards and professional expertise, which also reflects the cultural
setting.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 53
Assumed cultural model influences.
There is a culture that supports implementing new courses to improve student success.
The intermediate algebra for statistics course at Community College Z is a new course that will
require math faculty to participate in learning new skills to implement the new curriculum.
Previous research indicates that resistance is an expected part of organizational change efforts
(Agócs, 1997). In the literature, faculty resistance to the implementation of a redesigned math
curriculum was noted as part of the findings at another community college (Ellerbe, 2015).
Cafarella (2016) found similar faculty experiences at a community college implementing a
computer-based math acceleration course. In both studies, change was driven by administration
and faculty resisted based on their experience in the classroom (Cafarella, 2016; Ellerbe, 2015).
However, previous research has also found that initiatives of math acceleration that were driven
by faculty appeared to have higher morale and were better integrated (Cafarella, 2016). At
Community College Z, the process to propose curriculum changes or new courses is driven by
the faculty, departments, and academic senate which may limit the circumstances for faculty to
resist.
There is a culture that believes underprepared students can complete math coursework.
In a current study that analyzed declines in college completion rates it was found that 90% of the
decline could be attributed to declines in college preparation (Bound et al., 2010). More than
70% of California community college students enter the system under-prepared for college level
course work (California Community Colleges Student Success Task Force, 2012). In California
community colleges, the completion rate is 31% for students placed directly into developmental
math courses (California Community Colleges Chancellor’s Office, 2015). As students enter
college, many struggle through remediation courses thereby increasing the risk of not completing
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 54
a degree (Bailey et al., 2010; Valdez & Marshall, 2013). Research on the faculty perspective is
mixed regarding students’ skill and fit to participate in acceleration interventions (Cafarella,
2016). However, as previously discussed the existing system of math remediation is built around
a course sequence for stem majors that disregards the skills in statistics needed by those students
pursuing majors in the humanities (Hern, 2012). The existing disconnect between statistics and
the content of remediation sequences can hinder student progression (Edwards et al., 2015; Fong
et al., 2015). This has led to recent efforts to create clear pathways that connect the skills
required during remediation to improve student success as measured by completion and transfer
rates (Fong et al., 2015; Hodara & Jaggars, 2014).
Assumed cultural setting influences.
The organization supports a standard approach to improve math remediation. While
this study focused on the implementation of the intermediate algebra for statistics course, there is
no universally accepted approach to improving math remediation. In the literature, other
approaches to improving student outcomes in math remediation include: curriculum alignment,
acceleration, and statistics pathways (Davidson & Petrosko, 2015; Hern, 2012; Hern & Snell,
2014; Valdez & Marshall, 2013). Curriculum alignment is an approach that looks to align the exit
and entrance requirements between courses or education segments (Valdez & Marshall, 2013).
Acceleration is a strategy that looks to reduce the time spent in the developmental course
sequence (Davidson & Petrosko, 2015). Statistics pathways attempt to decouple the statistics
curriculum from the traditional developmental math sequence, thereby reducing the sequence of
remediation (Hern, 2012). However, since there is no standard approach to improving math
remediation, community colleges are free to implement intervention at their own pace and even
combine interventions, as is the case at Community College Z. According to Clark and Estes
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 55
(2008), organizational performance gaps can stem from processes, resources, and value streams.
Implementing interventions therefore has the potential to result in performance issues affecting
the cultural setting of the college.
The organization provides resources to support academic and professional standards.
At Community College Z, the math faculty have developed a new course to improve student
outcomes in math remediation by providing an alternative to the existing developmental math
course sequence. Research indicates a gap often exists between the knowledge faculty gained in
their graduate programs and the skills needed for effective teaching (Kozeracki, 2005). Current
research also indicates that a key component to improving student outcomes with the
implementation of a statistic pathway is professional development that focuses on the knowledge
and practices of teaching math (Edwards et al., 2015). However, programs designed to improve
remediation outcomes have high costs and require public resources (Bailey et al., 2010).
Additionally, the literature highlights the existing challenges with culture and infrastructure at
community colleges that do not support professional development (Edwards et al., 2015). In the
literature, professional development is often cut with budgets and when funded is a “randomly
grouped collection of activities” not necessarily tied to improving faculty instructional methods
(Murray, 2001, p. 497). Nevertheless, professional development that is focused on developing
the knowledge and skills for teaching math is critical to improving student outcomes (Edwards et
al., 2015).
Table 4 shows the four organizational influences related to the implementation of the
intermediate algebra for statistics course. In addition, each influence is identified as a cultural
model or setting.
Table 4.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 56
Assumed Organizational Influences, Type, and Research Literature

Assumed Influences Research Literature
Organization

Cultural models There is a culture that supports
implementing new courses to
improve student success.
(Cafarella, 2016; Clark &
Estes, 2008; Ellerbe, 2015;
Murray, 2001; Schein, 2004)

There is a culture that believes
underprepared students can
complete math coursework.
(Bailey, Jeong, & Cho, 2010;
Valdez & Marshall, 2013)
Cultural settings The organization supports a
standard approach to improve
math remediation.
(Cohen, Raudenbush, & Ball,
2003; Davidson & Petrosko,
2015; Hern, 2012; Hern &
Snell, 2014; Valdez &
Marshall, 2013)

The organization provides
resources to support academic
and professional standards.
(Bolman & Deal, 2008; Burke,
2005; Clark & Estes, 2008;
Cohen, Raudenbush, & Ball,
2003; Edwards, Sandoval, &
McNamara, 2015; Firestone &
Shipps, 2005; Hentschhke &
Wohlstetter, 2004; Stecher,
Barney, & Kirby, 2004:
Kozeracki, 2005)
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 57

Conclusion
In the literature, math remediation at community colleges is a complex issue that is
affected by programs and policies often external to a math department. Chapter 2 of this
dissertation has attempted to review the general literature and outline the influencing factors
affecting developmental math education. Factors influencing the ability of faculty to implement
the intermediate algebra for statistics course at Community College Z such as instructional
delivery, statistics pathways, faculty preparation, professional development practices, and
institutional resources have been identified in the literature. Specifically, the factors identified in
the research as possible knowledge, motivation, and organizational influences are presented
according to the conceptual gap analysis framework detailed by Clark and Estes (2008). In
Chapter 3, the conceptual gap analysis framework was used to evaluate the knowledge,
motivation, and organizational influences identified in this chapter (Clark & Estes, 2008).
Table 5.
Summary of Assumed Influences on Math Faculty Ability to Implement Intermediate Algebra for
Statistics Course

Assumed Influences Research Literature
Knowledge

Factual Faculty need to know the
goal.
(Clark and Estes, 2008;
Hern and Snell, 2014;
Illowsky, 2008; Mayer,
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 58
2011; Rueda, 2011; Valdez
& Marshall, 2013)
Conceptual Faculty need to know the
content of course curricula.
(Alexander, Karvonen,
Ulrich, Davis, & Wade,
2012; Ball, Sleep, Boerst, &
Bass, 2009; Hill & Ball,
2004; Clark and Estes, 2008;
Edwards, Sandoval, &
McNamara, 2015;
Kozeracki, 2005;
Krathwohl, 2002; Rueda,
2011)
Procedural Faculty need to know how
to adapt their instruction.
(Alexander, Karvonen,
Ulrich, Davis, & Wade,
2012; Cohen, Raudenbush,
& Ball, 2003; Edwards,
Sandoval, & McNamara,
2015; Kozeracki, 2005;
Krathwohl, 2002;
Kyriakides, Christoforou, &
Charalambous, 2013; Rueda,
2011)
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 59

Faculty need to know how
to teach math effectively.
(Alexander, Karvonen,
Ulrich, Davis, & Wade,
2012; Ball, Sleep, Boerst, &
Bass, 2009; Clark and Estes,
2008; Edwards, Sandoval, &
McNamara, 2015; Hill, Ball,
& Schilling, 2008;
Kozeracki, 2005;
Krathwohl, 2002;
Kyriakides, Christoforou, &
Charalambous, 2013; Rueda,
2011)
Faculty need to know how
to align instructional
activities to performance.
(Hern and Snell, 2014;
Illowsky, 2008; Mayer,
2011; Valdez & Marshall,
2013)
Motivation

Expectancy value Faculty need to value
implementing intermediate
algebra for statistics.
(Cafarella, 2016; Eccles,
2009; Hardré, 2012;
Pintrich, 2003; Wallin,
2003)

Faculty need to value
improving student success.
(Cafarella, 2016; Eccles,
2009; Hardré, 2012;
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 60
Pintrich, 2003; Wallin,
2003)
Self-efficacy Faculty need to believe they
are capable of effectively
delivering instruction.
(Bandura, 2005; Pajares,
2009; Skaalvik & Skaalvik,
2010; Swackhamer,
Koellner, Basile, &
Kimbrough, 2009)
Attribution Faculty need to believe that
student outcomes can be
attributed to their
instruction.
(Anderman & Anderman,
2009; Bensimon, 2005;
Cafarella, 2016; Eccles,
2009; Hardré, 2012; Mayer,
2011; Pintrich, 2003; Wallin,
2003; Rueda, 2011)
Organization

Cultural models There is a culture that
supports implementing new
courses to improve student
success.
(Cafarella, 2016; Clark &
Estes, 2008; Ellerbe, 2015;
Murray, 2001; Schein, 2004)

There is a culture that
believes underprepared
students can complete math
coursework.
(Bailey, Jeong, & Cho,
2010; Valdez & Marshall,
2013)
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 61
Cultural settings The organization supports a
standard approach to
improve math remediation.
(Cohen, Raudenbush, &
Ball, 2003; Davidson &
Petrosko, 2015; Hern, 2012;
Hern & Snell, 2014; Valdez
& Marshall, 2013)

The organization provides
resources to support
academic and professional
standards.
(Bolman & Deal, 2008;
Burke, 2005; Clark & Estes,
2008; Cohen, Raudenbush,
& Ball, 2003; Edwards,
Sandoval, & McNamara,
2015; Firestone & Shipps,
2005; Hentschhke &
Wohlstetter, 2004; Stecher,
Barney, & Kirby, 2004:
Kozeracki, 2005)

Running head: IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STA TISTICS 62
CHAPTER THREE: METHODOLOGY
Purpose of the Project and Research Questions
The purpose of this study was to evaluate the extent that the math faculty at Community
College Z were meeting the goal of implementing 100% of the content for the intermediate
algebra for statistics course using 100% appropriate pedagogy. The goal supported the
organizational goal of 100% of students meeting the math transfer eligibility requirements. As
previously mentioned in Chapter 1, 70% of California community college students entering the
system are under-prepared for college level course work (California Community Colleges
Student Success Task Force, 2012). Additionally, the completion rate of the remedial math
sequence in the California community college system is 31% for students placed into
developmental math courses (California Community Colleges Chancellor’s Office, 2015a).
While a complete evaluation project would focus on all stakeholders, for practical
purposes the stakeholder in this analysis were the full-time faculty within the math department
that teach the intermediate algebra for statistics course. The gap analysis framework by Clark and
Estes (2008) was chosen to be the primary framework for this study. The analysis focused on
knowledge, motivation and organizational influences related to faculty achieving the program
goal. The resultant findings from this study could be used by the college leadership and faculty to
develop critical implementation strategies for future interventions.
The research questions that guided this investigation are:
1. What are the knowledge, motivation and organizational influences affecting the ability of
math faculty to implement 100% of the content for the intermediate algebra for statistics
course using 100% appropriate pedagogy?
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 63
2. What are the recommendations for organizational practice in the areas of knowledge,
motivation, and organizational resources?
Conceptual Framework
The purpose of the conceptual framework is to present a model of the concepts that
informed the theory that was used to study the research questions (Maxwell, 2013). In addition,
the conceptual framework served as the structure for guiding the development of the research
design (Merriam & Tisdell, 2016). By demonstrating the relationships that exist between the
different conceptual elements that influence the phenomena being studied (Maxwell, 2013), the
conceptual framework served as a tool for informing how each component of the framework
should be measured and analyzed (Merriam & Tisdell, 2016). In this study, each of the potential
influencers included in the conceptual framework were initially introduced and presented
independently of each other. However, it is recognized that the potential influencers included in
this study are not isolated. An evaluation of the assumed influences affecting Community
College Z math faculty in achieving its goal to implement 100% of the content for the
intermediate algebra for statistics course using 100% appropriate pedagogy highlighted how each
of the assumed influences interact through the proposed conceptual model below.
To address the research questions, this study utilized the conceptual framework presented
in Figure 3 to examine the knowledge/skill, motivation, and organizational influences affecting
the achievement of the stakeholder goal. Additionally, the conceptual framework highlighted the
relationship between the organization influences at the college and the math faculty. In Figure 3
the organizational influences are depicted as surrounding the math faculty as they work to
achieve the stakeholder goal of implementing the intermediate algebra for statistics course. By
depicting the college as the organization that surrounds the math faculty, the conceptual
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 64
framework acknowledges that organizations are composed of complex and interacting systems,
each with their own culture (Clark & Estes, 2008; Rueda, 2011). Specifically, the cultural model
and cultural setting concepts found at the college level highlight the distinct yet interconnected
shared mental models and the settings of the organizational culture (Gallimore & Goldenberg,
2001).
At the center of the conceptual model are the math faculty stakeholders who are located
within the college. Additionally, the framework in Figure 3 incorporates the conceptual and
procedural knowledge and skills that influence curriculum and instruction within the sphere of
the math faculty. According to Krathwohl (2002) conceptual knowledge refers to how the basic
elements needed to solve problems are interrelated and can work together within larger
constructs while procedural knowledge focuses on the how to do something. The stakeholder
sphere also includes key motivation concepts such as utility value, self-efficacy, and attributions
as they relate to the implementation and delivery of math instruction. In the literature, motivation
is concerned with the underlying factors that contribute to an individual engaging in behavior
that works toward specific tasks or interests (Pintrich, 2003). In the conceptual framework, the
specific task or interest is achievement of the stakeholder goal, which is the direction that the
organization is moving toward.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 65

Figure 3. Interactive conceptual framework.
The conceptual framework presented acknowledges the interaction between the each of
the influencing concepts identified. In the literature, organizational culture is referred to as the
interactive layer that sits between existing processes and resources and all attempts to improve
organizational performance (Clark & Estes, 2008). To achieve the organizational goal, the four
organizational influences identified in the conceptual framework work together to create the
cultural models and settings that the math faculty operate within. The first cultural model
influencing the organization is a culture that supports implementing new courses to improve
student success. In the literature, resistance is an expected part of organizational change efforts
(Agócs, 1997). However, faculty driven initiatives of math acceleration appeared to have higher
morale and were better integrated (Cafarella, 2016). The second cultural model influencing the
organizational culture is a general belief that underprepared students can complete math
coursework. The research describes a common scenario that students entering college struggle
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 66
through remediation, lowering the rate of degree completion (Bailey et al., 2010; Valdez &
Marshall, 2013). However, the current system of math remediation is built around a course
sequence for stem majors that disregards the skills needed by those students pursuing majors in
the humanities (Hern, 2012). At Community College Z, both cultural models interact and are
further influenced by the standard approach to improve math remediation and the resources
provided to support professional and academic standards, which reflect the cultural setting at the
institution.
As math faculty work toward accomplishing the stakeholder goal, they do so within the
culture that is defined by both the cultural models and settings that exist. The first motivational
influence identified in the conceptual framework addresses the utility value of the stakeholder
goal for math faculty. The second motivational influence addresses the self-efficacy of the math
faculty to deliver instruction in the intermediate algebra for statistics course. The third
motivational influence addresses the attributions of the math faculty for their student outcomes.
In the literature, utility value refers to the perceived usefulness of a task, while value identifies
the level of importance associated with a task (Pintrich, 2003). The two utility value components
of conceptual framework interact to define an individual’s own identity that then works to
influence future levels of motivation (Eccles, 2009). Faculty self-efficacy, which is also
important in determining motivation (Bandura, 2005; Pajares, 2009), is shown to be positively
correlated with student success (Swackhamer et al., 2009). In attribution theory, the beliefs
regarding the reasons for success or failure including the level of control an individual has in
influencing the outcome is important (Rueda, 2011; Weiner, 2005). In the conceptual framework,
the motivational influences of value, self-efficacy, and attributions interact with the beliefs and
resources found within the organization to either strengthen or hinder organizational success of
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 67
the college and the math faculty. In the literature, key factors in the ability of faculty to serve the
needs of students include knowledge, training, and experience (Kozeracki, 2005). In the
conceptual framework, the factual, conceptual, and procedural knowledge and skills of the math
faculty work together with the motivation influences to interact with the conceptual elements
found within the college to meet the stakeholder goal.
Methodological Framework
The methodological framework utilized by this study was the Clark and Estes (2008) gap
analysis model, which is a systematic, analytical process used to clarify organizational goals and
identify the knowledge, motivation and organizational influences. Clark and Estes (2008)
describe the gap analysis model as a process consisting of six steps. Those steps include: (a)
identify key business goals; (b) identify individual performance goals; (c) determine
performance gaps; (d) analyze gaps to determine causes; (e) identify knowledge/skill,
motivation, and organizational process and material solutions and implement; and (f) evaluate
results, tune system and revise goals (p. 22). While the original focus of the gap analysis process
was to improve performance within a business context, Rueda (2011) has extended the work of
Clark and Estes (2008) and applied the gap analysis model to specifically address educational
problems. Figure 4 below illustrates the Gap Analysis Process.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 68

Figure 4. Gap analysis process. Adapted from Clark and Estes (2008)

Assessment of Performance Influences
In Chapter 2, five Knowledge, four Motivation, and four Organizational influences were
identified from either the learning, motivation, and organizational theory literature or the
research literature.
Table 6.
Sources of Assumed Knowledge, Motivation, and Organizational Influences
Assumed Influences on Faculty Ability to Implement Course Content
Source Knowledge Motivation Organization
Learning,
Motivation, and
Faculty need to know
the goal.
Faculty need to value
improving student
success.
There is a culture that
supports implementing
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 69
Organizational
Theory
new courses to improve
student success.
Faculty need to know
the content of course
curricula.
Faculty need to believe
they are capable of
effectively delivering
instruction.
The organization
provides resources to
support academic and
professional standards.
Faculty need to know
how to align
instructional activities
to performance.
Faculty need to believe
that student outcomes
can be attributed to
their instruction.

Research
Literature
Faculty need to know
how to adapt their
instruction.
Faculty need to value
implementing
intermediate algebra
for statistics.
There is a culture that
believes underprepared
students can complete
math coursework.
Faculty need to know
how to teach math
effectively.
The organization
supports a standard
approach to improve
math remediation.

Knowledge Assessment
Table 7 describes the five assumed knowledge influences related to ability of math
faculty to achieve the stakeholder goal of implementing the intermediate algebra for statistics
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 70
course. The table includes a description of how these assumed influences were assessed through
the use of in-person interviews and document analysis.
Table 7.
Assumed Knowledge Influences and Proposed Assessment

Assumed Influence Method of Assessment
Knowledge

Factual Faculty need to know the
goal.
Interview Questions:
Tell me about the math department.
Probe: Can you describe any goals?
Probe: To what extent do you collaborate?
Is there any team teaching? How are faculty
evaluated? What kind of criteria are used?
Is workload evenly shared or distributed?
Can you describe the purpose of the
intermediate algebra for statistics course?

Document Analysis:
Review written planning documents related
to the math department and the syllabus for
all four courses of developmental math,
including the intermediate algebra for
statistics course.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 71
Conceptual Faculty need to know the
content of course curricula.
Interview Questions:
Tell me about the curriculum of the
intermediate algebra for statistics course?
Observation:
Observe faculty led course discussions that
explain the course curriculum identified in
the syllabus and lesson plan to students.
Document Analysis:
Review the syllabus and course outlines for
all four courses of developmental math,
including the intermediate algebra for
statistics course and activity worksheets for
the intermediate algebra for statistics
course.
Procedural Faculty need to know how
to adapt their instruction.
Interview Questions:
Can you describe how the students in a class
may influence how you teach the course
material?
Observation:
Observe practices and interactions that
illustrate faculty is adapting their
instructional practices to help students
understand the course material.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 72

Faculty need to know how
to teach math effectively.
Interview Questions:
Describe how you work with students in
developmental math courses to help them
learn the material?
Observation:
Observe the structure of lesson activities
and how faculty sequence material to help
students understand the course material.
Faculty need to know how
to align instructional
activities to performance.
Interview Questions:
Can you describe how the instructional
activities help you reach the student
learning objectives of the course?
Observation:
Observe the range and type of instructional
activities faculty use to practices use to help
students understand the course material.
Document Analysis:
Review the training documents for the
intermediate algebra for statistics course
and math faculty.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 73
Motivation Assessment
Table 8 describes the four assumed motivational influences related to math faculty’s
ability to implement the intermediate algebra for statistics course. The table includes a
description of how these assumed influences were assessed through the use of in-person
interviews.
Table 8.
Assumed Motivation Influences and Proposed Assessment

Assumed Influence Method of Assessment
Motivation

Expectancy value Faculty need to value
implementing
intermediate algebra
for statistics.
Interview Questions:
Tell me about why you teach the intermediate
algebra for statistics course?

Faculty need to value
improving student
success.
Interview Questions:
What do you do to help your students be
successful in courses you teach?
Probe: Tell me about why you choose to take
those steps?
Self-efficacy Faculty need to
believe they are
capable of effectively
delivering instruction.
Interview Questions:
How confident do you feel about your ability
to deliver instruction for the intermediate
algebra for statistics course?
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 74
What percentage of students do you think will
be able to pass the course you are teaching?
Probe: What accounts for that pass rate?
Attribution Faculty need to
believe that student
outcomes can be
attributed to their
instruction.
Interview Questions:
What do you believe are the factors that lead to
better student outcomes?
Probe: What impact, if any, do instructional
materials, teaching methods, or experience
have?

Organization/Culture/Context Assessment
Table 9 describes the four assumed organizational influences related to math faculty’s
ability to implement the intermediate algebra for statistics course. The table includes a
description of how these assumed influences were assessed through the use of in-person
interviews and document analysis.
Table 9. Assumed Organizational Influences and Proposed Assessment

Assumed Influences Method of Assessment
Organization

Cultural models There is a culture that
supports implementing
new courses to improve
student success.
Interview Questions:
How supportive is the college toward
developing new courses to improve student
success?
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 75
Probe: Can you share an example?
Document Analysis:
Review written policies related to the math
department.

There is a culture that
believes underprepared
students can complete
math coursework.
Interview Questions:
What is the general feeling in the department
about students in the developmental math
course, and the likelihood that they will be
successful?
Probe: Could they all learn this material or are
there some who will never get it?
Probe: Who is responsible for their success?
Cultural settings The organization
supports a standard
approach to improve
math remediation.
Interview Questions:
Tell me about the college’s approach to math
remediation?
Document Analysis:
Review any existing research briefs and
training documents for the intermediate
algebra for statistics course and any relevant
written policies and planning documents
related to the math department.

The organization
provides resources to
Interview Questions:
What kind of resources are available to
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 76
support academic and
professional standards.
support you in maintaining academic and/or
professional standards?
Probe: What has been helpful, what's missing,
if anything?
Can you describe any training that is available
to faculty?
Probe: Are there any rewards for
participation? How often do you participate?
Why or why or why not?
When you are successful with your students,
to what extent is that noticed by the
department or college?
Document Analysis:
Review any training documents for the
intermediate algebra for statistics course and
any relevant written policies and planning
documents related to the math department.

Participating Stakeholders and Sample Selection
The stakeholder group of focus in this study consisted of math faculty at Community
College Z that were currently teaching the intermediate algebra for statistics course or taught the
course during a previous term. The math faculty are the individuals tasked with implementing the
intermediate algebra for statistics course consistently across multiple course sections and were
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 77
the purposefully selected sample population based on the following data collection and sample
criteria.
Data Collection
This study utilized a qualitative methods approach to examine the assumed knowledge,
motivation, and organization factors influencing the stakeholder’s goal. This qualitative study
included telephone stakeholder interviews, course observations, and an analysis of relevant
documents. The site and the participant population were selected based on a purposeful selection
process that allowed for the deliberate selection of participants based on the criteria that would
best identify those most likely to provide data to inform the research questions (Creswell, 2014;
Maxwell, 2013; Merriam & Tisdell, 2016). The sample of study participants was selected from
the population of 66 developmental math faculty at Community College Z.
In this study, the telephone stakeholder interviews served to document in-depth
information on each of the assumed influences. The interview protocol is attached as Appendix
B. The course observations supplemented the data collected through the interviews and provided
information on the events, interactions, and classroom environment. The observation protocol is
attached as Appendix C. In addition, the study included an analysis of relevant documents such
as the syllabus, selected lesson plans or course pacing documents, and prior reports to assess
existing curricula, policies, and procedures related to the research questions.
Interviews
Sampling.
Criterion 1. Participant must be current full-time or adjunct math faculty of Community
College Z.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 78
Criterion 2. Participant must have taught the intermediate algebra for statistics course
during the current semester or previously completed semester.
Interview recruitment and rationale. This qualitative study utilized in-depth semi-
structured interviews as the primary data collection method. The sample of potential interview
participants was selected using a purposeful sampling strategy based on the identified criteria.
The first criterion was that participants must be current full-time or adjunct math faculty at
Community College Z. The second criterion was that participants must have taught intermediate
algebra for statistics during the current semester or previously completed semester. The use of
the purposive sampling ensured that selected participants shared specific characteristics to
inform the study (Johnson & Christensen, 2014). According to Merriam and Tisdell (2016),
purposeful sampling is the appropriate sampling strategy when the goal to learn as much from a
sample as possible. Based on these criteria, seven participants agreed to participate and
scheduled an interview.
Given the criteria, participants were recruited using the following steps. Step 1 in the
recruitment process included working with the math department to identify all math faculty at the
institution that taught the intermediate algebra for statistics course and create an email
distribution list. Step 2 included working with the institutional gatekeeper to send an email cover
letter to the email distribution list requesting participation in a semi-structured interview with a
link to an online calendar for participants to schedule an interview. A copy of the email cover
letter requesting participation is included as Appendix A. Step 3 was a follow-up email a week
later to the distribution list thanking those participants that had signed up and requesting
additional participants. Step 4 in the process was to confirm the interview appointment and
provide participants with an information sheet regarding the details of the study and their
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 79
participation. As part of the recruitment strategy, no incentives were provided to solicit
participation.
Interview instrumentation and fielding. The first method of data collection consisted of
seven, one-time, semi-structured faculty interviews. The interviews were conducted over the
phone and recorded for later transcription. According to Merriam and Tisdell (2016), the semi-
structured interview format provides a general set of questions that are designed to be used
flexibly to guide the interview while allowing the researcher to further explore the information
shared by respondents on the assumed knowledge, motivation, and organizational influencing
factors. The interview protocol consisted of 20 questions designed to address each of the
knowledge, motivation, and organizational influences identified through the literature cited in
Chapter 2 and the conceptual framework identified in Chapter 3. In the literature, good interview
questions are designed to provide rich and descriptive data, and this is partially accomplished
through open-ended questions (Krueger & Casey, 2009; Merriam & Tisdell, 2016; Patton, 2002).
The interview questions were designed to provide data on each of the assumed influences first
identified in Chapter 2 to answer each research question from multiple angles.
Each interview session was scheduled for 60 minutes; all interviews lasted between 60
and 120 minutes. Scheduling was conducted through the email requesting participants and a link
to an online calendaring tool as discussed in the recruitment strategy. No incentives were
provided for participation. Once scheduled, each interview was conducted over the phone. Each
interview was recorded and transcribed with the original recording destroyed after transcription
to maintain confidentiality. Recording and transcribing each interview also provided for
accurately capturing rich descriptions of the information contained within the views of the
faculty being interviewed (Creswell, 2014). The interview protocol is included in Appendix B.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 80
Observations
Sampling.
Criterion 1. Participant must have participated in the interview described above.
Criterion 2. Participant must currently teach the intermediate algebra for statistics course.
Criterion 3. Participant must have provided permission during the interview to allow the
researcher to observe a course session.
Observation recruitment and rationale. The second method of data collection
consisted of classroom observations. According to Creswell (2014), observations provide an
opportunity to collect data on the “behaviors and activities of individuals” while those
individuals are engaged in a natural setting (p. 190). The sample of potential participants for a
follow-up course observation was selected based on the identified criteria. The first criterion was
that participants must have participated in the interview described above. The second criterion
was that participants needed to be currently teaching intermediate algebra for statistics. During
the Fall 2017 semester there were 13 faculty teaching 16 course sections. The third criterion was
that participants must have provided permission during the interview to allow the researcher to
observe a course session. Based on these criteria, six of the interview participants agreed to a
follow-up course observation, which provided the researcher with an opportunity to reach a point
of saturation with data collection.
Given the criteria used to identify the most meaningful participants, the recruitment
process consisted of the following steps. Step 1 was to work with the institution gatekeeper to
send a cover letter to the email distribution list requesting participation in a semi-structured
interview along with an information sheet that identified the possibility of providing permission
to observe a course session. A copy of the email cover letter is included as Appendix A.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 81
Step 2 occurred at the end the interviews when interview participants were asked
permission to observe a session of his/her intermediate algebra for statistics course. During this
step, the researcher obtained permission from six interview participants to observe a course
session. Step 3 included working with the institutional gatekeeper to establish the on-campus
logistics for conducting the course observations. Step 4 in the recruitment process included
scheduling six course observations directly with participants through an email exchange.
Observation instrumentation and fielding. The second method of data collection
consisted of six observations of the intermediate algebra for statistics course. According to
Maxwell (2013), observation provides a direct opportunity to capture a record of behaviors and
experiences in the natural setting as opposed to interviews, which is better suited for gathering
participant’s perspective. The observation protocol was created to address each of the
knowledge, motivation, and organizational influences identified through the literature cited in
Chapter 2 and the conceptual framework identified in Chapter 3. The observation protocol was
designed to record a description of the physical setting, specific course activities, and faculty and
student actions during the observation period. To accomplish this task, the observation protocol
was adapted from the Classroom Observation Protocol for Undergraduate STEM (COPUS)
developed by Smith, Jones, Gilbert, and Wieman (2013), to help facilitate the collection to
observational data. The observation protocol is included in Appendix C.
Each observation was scheduled for an entire course session, which during the Fall 2017
semester was scheduled for 145 or 180 mins per course. Observations were scheduled as
discussed in the recruitment strategy. During the observation, data were collected by the
researcher as an observer-as-participant, which allowed the researcher to gain greater access to
people and information (Merriam & Tisdell, 2016). In addition, conducting the observation as an
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 82
observer-as-participant allowed the participants to be aware that they were participants in a
research study (Johnson & Christensen, 2014). No observation was recorded, but field notes
were taken as part of the observation protocol.
Document Analysis
The third source of data collection included documents and artifacts. According to
Merriam and Tisdell (2016), documents serve as a main source of data that can help a researcher
understand the context of a research phenomenon. Since documents often exist prior to data
collection, they can serve as a way for a researcher to quickly learn the language of the study
area (Creswell, 2014). As discussed in Chapter 2 and as part of the conceptual framework, there
are specific assumed influences that can be investigated through a combination of existing
documents. In the literature, teaching mathematics requires knowledge of course content in
addition to the practices for delivery (Ball et al., 2009). The following documents were collected:
the syllabus for all four courses of developmental math, including the intermediate algebra for
statistics course; all lesson plans or course pacing documents for the intermediate algebra for
statistics course; any existing research briefs on the intermediate algebra for statistics course; any
relevant training documents for the intermediate algebra for statistics course and math faculty;
and any relevant written policies and planning documents related to the math department.
Access to each document was provided by Community College Z through the publicly
available website for examination throughout the study. The syllabus and course outline for all
four courses of developmental math were examined to evaluate the structure of the original
developmental math sequence and the alternative provided by the intermediate algebra for
statistics course. The lesson plans for the intermediate algebra for statistics course provided the
specific curricula, proposed progression, and context for the data that were collected during the
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 83
interviews. An examination of existing research briefs on the intermediate algebra for statistics
course focused on gathering data on the level of student success attained through the course.
Faculty training documents for the intermediate algebra for statistics course were examined to
identify what was being included as part of the training and how training was being conducted,
which informed the level or type of resources being allocated to training. Additionally, written
policies and planning documents related to the math department provided information on the
organizational processes that exist as well as any stated goals that have been established.
Data Analysis
A systematic qualitative data analysis was facilitated through the use of interviews,
observations, and documents detailed in the previous sections. The following sections describe
the analytic methods employed for both the telephone interviews and in-person course
observations.
Interviews
For interviews, data analysis began after data collection. Analytical memos were used to
document initial reflections of the data. After the interviews were completed, each interview was
transcribed and coded. The first phase of analysis included organizing the data collected into the
thirteen knowledge, motivation, and organizational influencers outlined earlier in this chapter.
The second phase of analysis examined the extent to which the data thus sorted supported the
validation of each of the thirteen assumed influences.
Observations
For observations, the analysis included a calculation of frequencies for each observation
code in accordance with the observation protocol adapted from the Classroom Observation
Protocol for Undergraduate STEM (COPUS) that was developed by Smith et al. (2013). In the
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 84
second phase of the analysis, observation data were used to triangulate the data collected during
the interviews to support the evaluation of the thirteen assumed influences identified in this
chapter.
Credibility and Trustworthiness
According to Merriam and Tisdell (2016), qualitative research is designed with the intent
of connecting research findings with reality. To ensure that the research and the associated
findings maintain credibility, this study employed multiple strategies to address potential threats
to validity. The first strategy employed was ensuring confidentiality and communicating the
specific actions with all research participants to encourage study participants to share their
thoughts and perspectives. In addition, the data collection process employed member checks,
which involved reviewing initial qualitative interpretation and findings with key participants to
determine if the findings were accurate (Creswell, 2014; Maxwell, 2013; Merriam & Tisdell,
2016). In this study, two forms of member checks were conducted. The first form of member
checks was focused on response validation and was conducted during the interviews where the
researcher rephrased the interview participant’s responses to verify participant statements. The
second type of member checks included emailing the first round of interview participants a copy
of their interview transcripts for review to verify the methods of recording and transcription as
well as the initial qualitative interpretation and findings from the interviews. The third strategy
was the use of rich, thick descriptions to describe the setting, the data collected, and to present
the findings. By using rich, thick descriptions, the researcher contextualized the data collected so
that the reader is provided with enough detail to understand the setting and determine what is
occurring (Creswell, 2014; Maxwell, 2013; Merriam & Tisdell, 2016). Additionally, this study
included a level of peer review as members of the dissertation committee have reviewed and
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 85
commented on the research to ensure that the researcher maintained professional standards of
credibility.
Role of Investigator
My role was as an independent qualitative student researcher to collect data that
contributed to the knowledge needed to understand the research questions put forth in this study
(Merriam & Tisdell, 2016). I had no direct personal relationship with the institution.
Additionally, the area of study was in a discipline outside of my professional areas of
responsibility. Professionally, I work for a state organization with limited oversight authority
over the organization, but I did not have any professional interaction with any potential
participants.
Ethics
To maintain the credibility of the research, it is important to ensure that decisions
regarding methods and data collection are ethical and adhere to rigorous research standards
(Merriam & Tisdell, 2016). As part of my effort to ensure the safety of the participants, the study
and data collection protocols were submitted to the University of Southern California
Institutional Review Board (IRB) and adhere to their rules and guidelines regarding the
protection of the rights and welfare of the participants in this study. In addition, the study and
data collection protocols were also submitted to research site’s Institutional Review Board (IRB).
In conducting this research study, all participants were provided with information sheets prior to
their participation. It is necessary to provide participants with “sufficient information” so that
they can make an informed decision regarding their participation (Glesne, 2011, p. 163). The
information sheet provided clearly informed participants that their participation was voluntary
and that they could withdraw from the study at any point without any penalty. In addition, the
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 86
information sheet informed participants that their discussions and related data would be kept
confidential (Krueger & Casey, 2009; Merriam & Tisdell, 2016). Prior to conducting the
interviews, permission to record the interviews was verbally obtained, and transcripts of the
interviews were deidentified to ensure the confidentially of research participants and the original
audio recordings were deleted. The deidentified data was stored securely during the duration of
the study to prevent a breach in confidentiality.
According to Rubin and Rubin (2012), the ethical obligation of a researcher is to ensure
that no harm is done to study participants. As part of the information sheet provided, I reminded
the participants that compensation or other forms of incentives would not be provided for their
participation. By not incorporating an incentive as part of the solicitation for participating in the
study, the risk of coercing participants was minimized. After each interview, I thanked each
participant for their participation in the study.
Running head: IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STA TISTICS 87
CHAPTER FOUR: FINDINGS
Introduction
The purpose of this study was to evaluate the knowledge, motivation and organizational
influences affecting the ability of math faculty to implement the intermediate algebra for
statistics course. The intermediate algebra for statistics course was an intervention designed to
shorten the pathway of developmental math and improve student success rates. As mentioned in
Chapter 3, the completion rate for the developmental math sequence in the California community
college system is 31% for students placed into developmental math courses (California
Community Colleges Chancellor’s Office, 2015a). Therefore, understanding the factors
influencing the ability of faculty to implement the intermediate algebra for statistics course can
improve the progression of students through developmental math sequences and can lead to
improved student outcomes (Fong et al., 2015).
Qualitative data were collected to determine the presence or absence of each of the
assumed influences identified in Chapter 3. The sources of qualitative data included telephone
interviews, observations, and document analysis. The first phase of qualitative data collection
consisted of seven telephone interviews. The interviews were recorded with verbal consent and
later transcribed, de-identified, coded, and analyzed. Out of the seven interviewees, six provided
consent to participate in a classroom observation. The second phase of data collection consisted
of six class observations that supplemented the data collected through the interviews. The study
also included an analysis of relevant documents identified in Chapter 3.
The findings presented in this chapter have been organized by assumed knowledge,
motivation and organizational influence type. Each influence category is further organized by
influence, whether a gap was validated, and then by findings for each data instrument. Findings
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 88
include data from interviews, followed by data from observations, and documents. Additionally,
tables have been included as needed to provide a visualization of the data.
Definition of Gap Validation
Each of the influences discussed in this chapter will have gaps that were validated, not
validated, or unable to validate based on the findings presented. In analyzing the data, a gap for
each influence was considered validated if the interview or observation data suggested a gap in
50% or more of the respondents and was confirmed by one or more instruments. If the threshold
was not met, then the gap was not considered validated. “Validated” indicates that a gap has been
found in one of the influences and that the influence should be addressed in order for faculty to
implement the intermediate algebra for statistics course according to the stakeholder goal. When
a gap is determined to be “not validated,” the data indicate that things are working and no
changes are needed. “Unable to validate” refers to situations when there is not enough data
collected to determine whether a gap exists or not, and indicates that further study is needed.
Participating Stakeholders
The participating stakeholders consisted of math faculty at Community College Z who
taught the intermediate algebra for statistics course during the current or a previous term. The
researcher agreed to maintain the confidentiality of participants, and, therefore, each of the
participants has been assigned a pseudonym and is referred to throughout this chapter as R+
corresponding participant number (ie. R1). This labelling allowed data and quotes to be selected
and presented from the interviews and observations accordingly. In addition, presented in Table
10 is basic demographic data, such as gender and whether the participant was a full-time or part-
time faculty member. Presented in Table 11 are the years of teaching experience for each
respondent.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 89

Table 10.
Summary of Participant Gender and Faculty Status
Data Collection Instrument
Gender Faculty Status
Female Male Full-time Part-time
Interviews 5 2 5 2
Observations 4 2 5 1

Table 11.
Respondent Years of Teaching Experience
Respondent Years of Teaching
Respondent 1 18
Respondent 2 30
Respondent 3 18
Respondent 4 19
Respondent 5 20
Respondent 6 10
Respondent 7 16

Findings for Knowledge Influences
The assumed knowledge influences previously presented in Chapter 3 were evaluated
using a combination of data from interviews, observations, and documents. Each influence used
a specific combination of data sources that were also outlined in Chapter 3.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 90
Assumed factual knowledge influences
Faculty need to know the goal. A gap was not validated for this influence. A
combination of data collected from interviews and document analysis revealed that faculty
possessed factual knowledge of the goal of improving math transfer eligibility of students and
the role of the intermediate algebra for statistics course in improving the success of those
students placed into math remediation. Therefore, no gap was found.
Interview Findings. Responses from six of the seven interviews indicated that faculty
possessed factual knowledge of the goal and the role of the intermediate algebra for statistics
course. When asked “can you describe any goals of the department?”, R2 replied “You know,
overall it's students being successful.” R2 further stated, “right now, because we have the
statistics side pretty well figured out, we're starting to focus a lot more on STEM.” R6 also
shared a similar response, “we have a good handle on the statistics pathway. We have our
intermediate algebra to statistics, which is very successful.” Additionally, R1 acknowledged that,
“redesigned the placement process” was a big goal and that the statistics pathway was the focus
starting in 2012. R3 added context with the following:
One of our current goals is to improve the placement process for students. We have been
working on that for a couple of years. The most impactful work that our department is
doing right now is on the direct placement of students into transfer level statistics. We are
working on increasing the number of students who complete a transfer level math class.
Since the majority of our students are in a non-STEM majors, the appropriate pathway
for them is our statistics pathway. We are also looking at trying to improve the pathway
for our STEM students as well, but that work is not as far along as the placement work
that we do.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 91
When respondents were asked to describe the purpose of the intermediate algebra for
statistics course, five of the seven respondents replied with a response centered around preparing
students for statistics. Further, R1 replied that the course helps with, “shortening the timeline”
and that “students need a quicker way to get them through.” In their response, R4 elaborated on
the purpose behind the course by stating that, “the overwhelming purpose of the class was to
address the huge amount of students that were failing out of community colleges because of a
traditional math cycle, traditional developmental math” and R4 continued by stating, “we wanted
something that could condense the pipeline.”
During the interviews respondents also revealed three current practices that are used to
share information across all math faculty. The first practice is the use of regular math department
meetings. According to R7, “I've been to some, but I don't go to them on a regular basis. There
are some adjuncts that do.” The second practice according to R7, “before the semester starts, we
always have a retreat, which is like a two hour meeting with, everybody's invited.” The third
practice is that there is a course coordinator for each course.
Document Analysis. Evidence of the goal was found in multiple document. According to
2012 Basic Skills Action Plan, a planning document found on Community College Z’s website,
the college at the time focused on evaluating student progress through the developmental math
course sequence. The result was the development of a course that combined components of the
Elementary Algebra and Intermediate Algebra courses that students would need for statistics. The
goal was to improve student success and progression through developmental math to transfer
level statistics. The 2015-16 Fact Book also supported the rationale for development of the
intermediate algebra for statistics course by presenting an analysis of the program to date. In the
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 92
2014 Comprehensive Institutional Self Evaluation Report, the intermediate algebra for statistics
course was identified as one of the new programs developed to improve student learning.
Assumed conceptual knowledge influences
Faculty need to know the content of course curricula. A gap was not validated for this
influence. Data collected from interviews, observations, and document analysis revealed that
faculty possessed conceptual knowledge of the mathematical content of the new intermediate
algebra for statistics course curriculum. Therefore, no gap was found.
Interview Findings. Responses from all seven of the interviews indicated that faculty
possessed conceptual knowledge of the course content, with six of the seven respondents
identifying a majority of the concepts in their response. When respondents were asked about that
curriculum of the intermediate algebra for statistics course, three of the seven respondents (R2,
R3, and R4) described the course as, “data analysis” in addition to identifying other course
concepts. For example, R1 stated that, “In the beginning the math is arithmetic” and then
includes, “non-linear models” along with exercises in “affective domain” to help students learn
“how to deal with stress.” According to R2 the course includes, “mean, median, standard
deviation, but then we get to linear regression. Then we do the scatter plots and the residual
plots, but then we also do non-linear regression.” In their response, R2 shared that non-linear
regression is, “something you would never cover in a statistics class at this level, we do in our
pre-statistics class so that it's intermediate algebra” and that the course is designed to take
students “right up to where we get into probability theory.”
When asked the same question, R3 replied that the course includes, “some intermediate
algebra topics, such as exponential functions, logarithmic functions, quadratic functions, to
introduce students to an application of these non-linear functions in a statistics environment” and
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 93
that students are introduced to these concepts, “in a just in time remediation format.” In their
response, R4 shared that students, “should be able to analyze categorical data, be able to analyze
categorical relationships, and two-way tables.” Additionally, R4 stated that, “students analyze the
relationships when linear patterns kind of break down. And we saw other kinds of patterns
emerging like logarithmic patterns or exponential patterns, even quadratic patterns.” R5 and R7
also highlighted the same concepts as other respondents, but focused more on the processes used
to teach the concepts to students, such as numerical analyses, writing assignments, and affective
domain/growth mindset activities.
Observation Findings. Evidence collected during the observations that indicated the
faculty knew the mathematical content of the course. R3 presented course concepts and math
formulas to the students and when asked a question, adjusted the steps in the formula to better
guide student learning. R4 started the course with writing on the board while reviewing math
concepts and then drew ad hoc scatterplots to describe different curves and their relationships.
R5 spent time describing form, direction, and strengths of regression and during other times
during the course presented on the y-intercept while alternating between walking around the
room and writing on the board. R2 reviewed concepts for exam 2 while posing direct questions
to the students to set up a live demonstration on the projector using the StatCrunch software.
Document Analysis. Evidence of faculty knowledge of the mathematical concepts was
supported by and found in multiple documents. The course outline of record

identified the
following mathematical concepts: formulas and algebraic expressions; linear equations and
inequalities in one and two variables; analyzing and producing data; simple statistics and graphs;
functions; and probability. Additionally, the course outline of record identified both methods of
instruction, such as lecture and distance education and methods of evaluation, such as exams,
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 94
quizzes, presentations, projects, and written assignments. The syllabus, course outline of record,
and activity worksheets for all four courses of developmental math provided evidence that the
combination of mathematical concepts was unique to the intermediate algebra for statistics
course. Faculty knowledge of statistics and graphs, linear equations, data analysis in combination
was not combined in the other courses.
Assumed procedural knowledge influences
Faculty need to know how to adapt their instruction. A gap was not validated for this
influence. Data collected from interviews and observations revealed that faculty possessed the
procedural knowledge of how to adapt their instruction to meet the needs of developmental math
students. The evidence presented indicated the pedagogy of the new course curriculum and
training incorporated the procedural knowledge of how to adapt instruction as part of the
standard practice for this course. Therefore, no gap was found.
Interview Findings. The interview responses to the question “Can you describe how the
students in a class may influence how you teach the course material?” revealed a variety of
responses. Four of the seven respondents acknowledged that that adapt to their students while the
three remaining respondents described how the course pedagogy was designed differently and
included both technology and interaction.
R1 stated that, “the flow is really determined by the students in the course. In the back of
my mind I might make adjustments on that day and it varies.” R5 shared that they use technology
such as “Kahoot” and “Plickers” in the class to conduct “formative assessments” and that “the
use of technology is a key component to a real-life experience with data.” R6 explained that “if
the students don't understand something, you do have to pause and talk about it a little more,
maybe balance your time a little differently, and try to get everyone back on speed.”
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 95
R3 acknowledged that some students are “very uncomfortable with algebra, and fearful,
and come in with self-sabotaging behavior” and in those instances R3 is there “to help them
understand that this course is different than an algebra course.” R3 stated that they are “much
more attentive to those fears than I was when I was teaching the traditional STEM curriculum”
and that those fearful students “help me in terms of what I design, how I present, how I teach,
and how I engage students in the material.”
R2 responded differently stating that, “they [students] influence it a little bit, but not a
lot” and that in a typical class there is a discussion “about what happened the day before” and
review of prior concepts. R2 expanded on their response by providing context of the course:
Day one, they’re given a data set, they’re given 40 minutes to work on it. I put them into
groups, and they're presenting at the end of day one. That isn't going to be influenced by
who's in the class, because I want to get them into data really quickly, and I want to get
them into group work. Every day in class, the first thing I do is rearrange the class, and
put them into groups. That's independent of who's in the class, because I need them to
know everyone in the class. Because they have to do a lot of group and presentations. So,
the class is fairly independent of who's in it, and it's discovery.
R7 replied that prior to teaching the course they went to training and they thought to
themselves that, “I knew how to teach a math course the other way, but this is so different.”
While multiple respondents provided some context of the course, R4 provided a clear description
of the development of intermediate algebra for statistics and why it was different. According to
R4, the development of the course included “not only changing curriculum, changing the topics
we're teaching, but we did a really big study on how to actually teach mathematics effectively.
We changed pedagogy rather drastically.” The pedagogical changes R4 described included
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 96
“using technology in the class” such as “statistics technology and statistics software” and “lots of
group projects, group activities where they're working on real data and trying to learn something
from the data.” Additionally, R4 stated that the course incorporates “productive struggle where
we don't always give them the answer right away.” R6 shared that they use the assignments or “a
Kahoot quiz in class” to check in on students and make adjustments to the course to cover where
students are struggling.
Observation Findings. Evidence collected during the observations indicated that faculty
knew how to adapt their instruction to the students in the class. Table 12 presents the prevalence
of the use of non-clicker and clicker questions during the course. The data shows that all
respondents used non-clicker questions and their prevalence ranged from 3% to 43% of the time.
Table 13 presents the prevalence of follow-up/feedback on clicker questions or activities, which
occurred between 14% to 33% of the class time. R3 during the course at one point adjusted the
steps in a formula to better guide students in learning the formula. R5 used Kahoot, an online
clicker question platform to conduct a review of course concepts and check-in on student
learning. Additionally, all respondents (R1, R2, R3, R4, R5, and R6) moved through the class
checking in on students and answering questions. In Table 14 we can see that the prevalence of
the practice of moving through class guiding ongoing student work during active learning tasks
ranged from 10% to 63% of class time.
Table 12.
Prevalence of the Instructor Codes PQ - Posing non-clicker question to students and CQ -
Asking a clicker question
Observation
PQ CQ
Occurrences
Percentage of
Class Time
Occurrences
Percentage of
Class Time
Respondent 1 11 37% 0 0%
Respondent 2 13 43% 0 0%
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 97
Respondent 3 11 31% 0 0%
Respondent 4 1 3% 0 0%
Respondent 5 6 20% 4 13%
Respondent 6 2 7% 0 0%

Table 13.
Prevalence of the Instructor Code FUp - Follow-up/feedback on clicker question or activity
Observation Occurrences Percentage of Class Time
Respondent 1 9 30%
Respondent 2 6 20%
Respondent 3 5 14%
Respondent 4 5 17%
Respondent 5 10 33%
Respondent 6 5 17%

Table 14.
Prevalence of the Instructor Code MG - Moving through class guiding ongoing student work
during active learning task
Observation Occurrences Percentage of Class Time
Respondent 1 10 33%
Respondent 2 3 10%
Respondent 3 5 14%
Respondent 4 16 53%
Respondent 5 11 37%
Respondent 6 19 63%

Faculty need to know how to teach math effectively. A gap was not validated for this
influence. Data collected from interviews and observations revealed that faculty possessed the
procedural knowledge of how to teach math effectively. The evidence presented indicated the
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 98
pedagogy of the course incorporated best practices and research during development and all
faculty learned to structure and teach the course with a degree of consistency. While variations
existed between courses, there was consistent use of equipment, technology, and activities to
promote student learning of the course concepts. Therefore, no gap was found.
Interview Findings. When asked to “describe how you work with students in
developmental math courses to help them learn the material?” R1 replied that they “take different
steps to work on the activity” such as having the students use magnets to show results on the
board and then checking in, asking questions, and adjusting. R2 shared a story of a student that
wasn’t strong writing answers down but was able to verbalize the answers and concepts well and
how this changed their thinking. R2’s reflection of this incident was, “I realized my paper tests
weren't good. They were measuring one type of learning, and so in developmental math the key
is lots of different types of assessments and making people feel comfortable.” R4 replied, “we've
always had an emphasis on work and not on exams.” R3 added that the course introduces
research on “fixed and growth mindset as a starting point for students” and that there are “a
number of assignments that deal with students' affective needs.” R2 also added:
The other way to teach developmental students is they help each other. I tell them I can
get half of them through, but they have to help the other half through. And so they have to
work in teams, and they like working in teams. They like helping each other. But that's
sort of a methodology of the class.
R3 stated that “we intentionally build community in the class” and “I'm not the only
teacher in the room, but that we try and learn from each other and create that teamwork
environment.” These comments indicate that the course is taught using techniques that differ
from other math courses at the college. R4 shared that they are “big proponent that teachers need
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 99
a little bit of freedom in the classroom” and that “there is a little bit of variability” as “some
teachers do more projects than others” but that overall “we teach the class pretty much the
same.” One reason for the consistency was the amount of training, R4 stated that “from the very
beginning, knew that we were going to have to wholesale train math teachers to teach” and
“constant training of faculty was huge for us.”
R5 shared that students have access to video lectures outside of class so “once they come
to class they don't have to do that part I can jump in with activity.” Once in the class R5 stated
that they “try to scaffold questions” and “try not to give them [students] the answers but provide
them with questions to think about how to get the answer.” R6 stated that they use “technology to
really gauge their [students] understanding, to really do those checks for understanding is
absolutely essential.” R7 shared that if “the class was not able to grasp the concept” then they
would adjust and use “a lecture series” or “a different set of activities.” R4 stated that they “went
from four exams to six smaller exams” and that for projects they “broke down into more isolated
ideas.”
Observation Findings. Evidence collected during the observations indicated that faculty
knew how to teach math effectively. All classes were held in a computer lab where each student
had access to a computer during class to access online materials, lessons, data, and statistical
software to complete assignments. All courses were observed during the same week, however
each class was at a different point in the course. R1 structured the course around two activities
that focused on scatterplots, correlations, and lurking variables. R1 started the course by having
the students work on the first activity in groups while R1 moved through the class checking in.
As the students completed the assignment, they placed their answers on the board using magnets.
Then R1 lead a discussion on the first activity focusing on student data and their answers and
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 100
then moving on to lines, linear relationships, correlations, and rationale for each scatterplot along
with posing questions to the students before moving on to next activity. R1 structured the
remaining class around three additional activities following a similar pattern, taking time to
elaborate on student questions and mathematical concepts as needed.
The courses of R2, R3, and R5 were structured similarly. R2 and R3 both incorporated
student presentations in addition to the student activities, where a group of students presented
together one group at a time. R2 listened to the student presentations and then provided feedback
and asked the student presentation group a series of questions moving on to questions for the
entire class. R4 structured the course activities similarly but incorporated a student data poster
activity where students worked in groups to create a poster. The students then placed their
posters around the room and all groups presented their poster as if they were at a conference
presenting their work describing their data, rationale, curves, and relationships.
R4 started the class by reviewing previous concepts and drawing scatterplots to describe
various mathematical curves and the steps to calculate in the StatCrunch software while
explaining log, exponential, and quadratic curves. R4 then described the next activity and then
the students begin working independently on the activity while R4 moved throughout the room
answering questions, providing guidance, and checking in. R6’s course was structured as a
flipped classroom where students accessed the lecture component of the course online in the
learning management system and worked on assignments in class. R6 therefore spent more time
moving through the classroom as evidenced in Table 14 answering student questions such as,
what is a parabola. During the class as students finished their assignments they turned them in
through the learning management system.
Faculty need to know how to align instructional activities to performance. A gap was
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 101
not validated for this influence. Data collected from interviews, observations, and document
analysis revealed that faculty possessed procedural knowledge of how to align instructional
activities to performance in the new intermediate algebra for statistics course. Therefore, no gap
was found.
Interview Findings. Responses from six of the seven interviews indicated that faculty
possessed procedural knowledge of how to align instructional activities to performance.
Additionally, three of the seven respondents described how the course was designed to
implement a new pedagogy to teach mathematics effectively. The course included in class
activities, group work, projects, presentations, and the use of technology (R2, R3, and R4, R6).
When asked to “describe how the instructional activities help you reach the student learning
objectives of the course?” R4 replied, “we have activities that are based around students working
on some real data and solving some kind of problem solving and analyzing the data in class.” R6
provided an example of the instructional activity:
So we do a lot of hands-on stuff. I tend to like to do something hands-on and then I
bounce to technology. So, let's say I'm doing scatter plots, in which I just did this week, I
can have them Google search their car on their MPG for city versus highway. And then I
have them Google search their dream car for their MPG, highway versus city. And we
make a scatter plot for the highway versus the city.
Observation Findings. Evidence collected during the observations indicated that faculty
knew how to align instructional activities to performance. In Table 14 above, the data presented
the prevalence of instructors moving throughout the classroom checking in with students during
active learning activities. In Table 15, we see that the in-class instructor practices also included
lecturing and real-time writing on the board behaviors that ranged between 20% to 53% and 0%
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 102
to 47% respectively. In Table 16 data is presented that shows the activities of students including
both listening to the instructor and independently thinking or problem solving. Table 17 shows
the prevalence of students working in groups and student presentations in the classroom. This
indicates that instruction is being paired with in-class assignments.
For example, R1 used in-class discussions that incorporated both lecture and posing
questions to review lines, linear relationships, correlations, and scatterplots. R1 then provided
students with a worksheet activity to practice what they had learned. In another example, R3
used an online quiz to assess student learning and then followed with a review of the quiz results.
The review included content and concepts, math formulas, writing on the overhead screen to
explain concepts visually, and asking students questions to understand where they struggled to
allow the instructor to adjust their material in response.
Table 15.
Prevalence of the Instructor Codes Lec - Lecturing and RtW - Real-time writing on board, doc.
projector, etc.
Observation
Lec RtW
Occurrences
Percentage of
Class Time
Occurrences
Percentage of
Class Time
Respondent 1 16 53% 14 47%
Respondent 2 8 27% 5 17%
Respondent 3 18 50% 12 33%
Respondent 4 9 30% 9 30%
Respondent 5 13 43% 10 33%
Respondent 6 6 20% 0 0%

Table 16.
Prevalence of the Student Codes L - Listening to instructor/taking notes, etc. and Ind - Individual
thinking/problem solving.
Observation L Ind
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 103

Occurrences
Percentage of
Class Time
Occurrences
Percentage of
Class Time
Respondent 1 16 53% 8 27%
Respondent 2 7 23% 3 10%
Respondent 3 18 50% 0 0%
Respondent 4 9 30% 5 17%
Respondent 5 11 37% 13 43%
Respondent 6 7 23% 17 57%

Table 17.
Prevalence of the Student Codes WG - Working in groups on worksheet activity and SP -
Presentation by student(s)
Observation
WG SP
Occurrences
Percentage of
Class Time
Occurrences
Percentage of
Class Time
Respondent 1 8 27% 0 0%
Respondent 2 0 0% 8 27%
Respondent 3 3 8% 7 19%
Respondent 4 10 33% 4 13%
Respondent 5 3 10% 1 3%
Respondent 6 0 0% 0 0%

Document Analysis. Evidence of faculty knowledge of how to align instructional
activities was supported in multiple documents. The college conducted a training on how to teach
statistics and a review of the training agenda included an introduction to teaching statistics,
resources such as textbooks, sample schedules, sample exams, sample notes, activities, and
projects. The training agenda also included sections on grading, course pacing, and technology
including software, data, and support contacts. The agenda also included the Guidelines for
Assessment and Instruction in Statistics Education College Report 2016 (GAISE College Report
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 104
ASA Revision Committee, 2016), which is focused “on what to teach in introductory courses and
then on how to teach those course” (p. 3). The open learning initiative (OLI) textbook developed
by R4, provides both the traditional concepts as well as an introduction that incorporates
guidance on teaching pre-statistics or intermediate algebra for statistics, how to use technology in
the classroom, and problem sets to help students understand the concepts.
Findings for Motivation Influences
The assumed motivation influences previously presented in Chapter 3 were evaluated
using data from interviews. Each influence used specific combination of interview questions that
were also outlined in Chapter 3.
Assumed expectancy value influences
Faculty need to value implementing intermediate algebra for statistics. A gap was not
validated for this influence. Data collected from interviews revealed that faculty valued
implementing the intermediate algebra for statistics course. Therefore, no gap was found.
Interview Findings. Responses from six of the seven interviews indicated that faculty
valued implementing the intermediate algebra for statistics course. When asked “why you teach
the intermediate algebra for statistics course?” R2 replied “Statistics is so fun to teach” and
added that they “don't want that to be the barrier to them [students] getting a college degree.”
When asked the same question R3 replied, “this seemed to be a more impactful way to
incorporate I guess the elements that I thought were really critical for students to be exposed to,
writing, presentation skills, incorporating real world examples to contextualize it for students.”
R4 shared that “there's many answers to that question” and that “it's really about the students.”
R4 also added that their “specialty is in developmental math curriculum” and that the
“developmental math curriculum in this country is appalling” and that they “wish to be a part of
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 105
this whole redesign process” in an effort “to try to fix the system.” R5 also added that their
“specialty is statistics and they [college] recognize that and I absolutely love it too.” In
responding to the same question, R6 stated, “I think it's fun and it's interesting and I like it.” R7
was not teaching the course during the current semester, but responded to the same question
with, “It's a fun course and, you know I always tell [the students], because right now I teach the
class you would be in before you head into that class.”
Faculty need to value improving student success. A gap was not validated for this
influence. Data collected from interviews revealed that faculty valued improving student success.
Therefore, no gap was found.
Interview Findings. Evidence collected from the interviews indicated that faculty valued
improving student success. When asked “why you teach the intermediate algebra for statistics
course?” R2 replied “I enjoy watching the growth of students.” R6 responded to the same
question with, “you know most of our students are going to this pathway” and added, “I think
that we need to have good instructors who are able to teach in this way to have these kind of
results.”
When interviewees were asked “What do you do to help your students be successful in
courses you teach?” R2 replied, “I help any student that comes to me who asks for help or I
become notified they need help.” R2 added that they “make it student project to help other
students” and that “one of the biggest impacts for students who are struggling is to have other
students help.” R4 shared that the California Acceleration Project is focused on the “idea of
active intervention” and that often “when a student is struggling, teachers have a tendency to
wait for the student to jump out to you.” R4 stated that when students are struggling, “I’m going
to go and see that student, and I'm going to make them come and see me and we're going to work
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 106
on stuff.” R3 was also focused on student success but shared the following experience:
Because I had worked in the business environment and that was where I went first before
I came back to teaching, I could see the need for having good teamwork skills, being able
to work with others. Because when I was an auditor, I worked in teams. That's all we did
was we worked in teams. We needed to be able to communicate our findings and
summarize that information and deliver it to clients. It's very important that students be
able to not only have technical skills, but to also be able to deliver it in a format that is
understandable to others, whether it's written or oral.
Assumed self-efficacy influences
Faculty need to believe they are capable of effectively delivering instruction. A gap
was not validated for this influence. Evidence collected from interviews revealed that faculty
believe that they are capable of effectively delivering instruction. Therefore, no gap was found.
Interview Findings. Six of the seven interviews indicated that faculty possessed belief
that they are capable of effectively delivering instruction. When asked “How confident do you
feel about your ability to deliver instruction for the intermediate algebra for statistics course?”,
R1 replied “fairly confident” while R7 replied “I felt pretty confident.” When asked the same
question R6 replied, “one to ten, I'd say ten.” R2 stated “I feel pretty comfortable with it, because
I'm always checking in with students.” R4 also felt, “pretty confident to deliver the material” but
acknowledged that “there's always more to learn.” R3 stated, “I’m much more confident now
than when I started,” however R3 shared that they, “spent a lot of time in the past six years being
mentored.” The remaining respondent, R5 shared that their confidence “depends on the day that
you ask” and that “some days, I feel like I am just a winner” while at other times they think
“what can I do better? I suck at this. How can I get through to the student?"
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 107
Assumed attributional influences
Faculty need to believe that student outcomes can be attributed to their instruction.
A gap was not validated for this influence. According to Cohen et al. (2003), effective teachers
review the work of students and repeat material if needed. Data collected from interviews
revealed that faculty believed that student outcomes can be attributed to their instruction.
Therefore, no gap was found.
Interview Findings. The evidence collected during the interviews indicate that six of the
seven interviewees attributed faculty and/or instructional materials to the student outcomes.
When asked “What do you believe are the factors that lead to better student outcomes?” R1
replied that “this [course] is something different that takes something different from faculty.” R2
referenced the importance of “having good instructional materials” along with group work and
projects. In addition, R3 stated, “I think addressing affective needs of students, teacher
acknowledgement of that is very, very important. Understanding that students are fearful, and
that our actions can either make things better or make things worse for students.”
The role of faculty was also addressed when R4 replied, “I think it's a major problem
when teachers themselves aren't comfortable with the material” and R4 also stated that “faculty
being trained is a huge issue.” When asked the same question R6 shared that, “even though it's
the pedagogy that's driving it, I think it's the faculty who have gone in for the trainings and
learned about the different pedagogies.” R6 also added, “I want to say faculty, because being
faculty is a constant evolution of our own teaching, and every semester I'm looking at that past
activity and saying what can I do to make it better.” R5 during the interview shared that it was
their job to get the students through the class.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 108
Additionally, two respondents (R5 and R7) shared that student outcomes could be
attributed to students. R5 shared a story of a student that did not do well in class and how that
student had not done all their work. R7 replied, “first of all, you need to come to class” and that
“students will find all kind of reasons why they couldn't come” however, “being in class, first of
all, is actually really is very important because you miss out on a lot of this stuff.”
Findings for Organization Influences
The assumed organizational influences previously presented in Chapter 3 were evaluated
using a combination of data from interviews and documents. Each influence used a specific
combination of data sources that were also outlined in Chapter 3.
Assumed cultural model influences
There is a culture that supports implementing new courses to improve student
success. A gap was not validated for this influence. Data collected from interviews and document
analysis revealed that there is a culture at Community College Z that supports implementing new
courses to improve student success. Therefore, no gap was found.
Interview Findings. The interview responses to the question “How supportive is the
college toward developing new courses to improve student success?” revealed that five of the
seven respondents (R1, R2, R3, R4, and R6) viewed the college as supportive. R1 replied that the
there was a “high level of support” and in the case of the intermediate algebra for statistics
course the college made funding available for statistics training and for professional
development. R2 shared that the college was “very supportive” and the support was “from the
Chancellor down.” R3 agreed that the college was “very, very supportive” and added that there
was “administrative support even from the top.” R3 also shared an example about how “the
chancellor had come into one of our meetings that we had and brought us some goodies while we
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 109
were working and has been so supportive of our efforts to create this statistics pathway.” R6
shared a similar example:
A week before classes were starting, we were having a meeting, we're going over last-
minute stuff and our Chancellor came in, sat with us, and told us how great she thinks the
work we're doing is and that she's really excited to see how this progresses.
R6 shared that the having “the Chancellor come and speak to us with her busy schedule,
to show that support” was “I think, absolutely amazing.” R4 also stated that the college was
“very, very supportive” and that the “administration has been hugely on board. Even counseling,
they were very, very supportive, because I think right from the beginning they started to see the
power of this.” R4 added that “this [course] was gonna be a game changer for all those thousands
of students that are failing out of community colleges, especially our college.”
R4 described the support for the intermediate algebra course further as “whatever we
need, you know. If we need training, they're gonna come up with people to train. If we need
computer labs, they're gonna come up with money to get more computer labs.” R4 also shared
that “it's always been a very high priority at our college of fixing this really bad developmental
math system.”
In answering the same question R5 and R7 focused on their experience with the
intermediate algebra for statistics course. R7 shared that being new to teaching the intermediate
algebra course, the existing faculty “always made it known that they were very grateful for us to
do the course” and that “they were always available.” R5 shared that the course leads make
themselves available and that “they offer training on the flipped classroom, the use of Canvas.
They provided the video notes. They actually provided the entire [course] shell.”
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 110
Document Analysis. Evidence of a culture that supports implementing new courses to
improve student success was supported in the college’s program and curriculum development
procedures. The procedures outline that faculty initiate program and curricula changes and
submit those changes through existing approval processes established by curriculum committee
and academic senate. Additionally, the policies outline how the committee is responsible for
ensuring that “curriculum is academically sound, comprehensive, and responsive to the evolving
needs of the institution and the community.”
There is a culture that believes underprepared students can complete math
coursework. A gap was validated for this influence. Data collected from interviews revealed that
there is a culture at Community College Z that does not fully believe underprepared students can
complete math coursework. Therefore, a gap was found.
Interview Findings. The interview responses to the question “What is the general feeling
in the department about students in the developmental math course, and the likelihood that they
will be successful?” revealed a variety of responses. Six of the seven interviews (R1, R2, R3, R4,
R5, and R6) indicated that they believe that underprepared students can complete math
coursework. Table 18 presents the perception of student pass rate percentage for the intermediate
algebra for statistics course. However, four of the seven interviews (R1, R2, R4, and R6) or 57%
shared that the belief has not been fully embraced on the STEM side of the math department.
Table 18.
Respondent Perception of Student Pass Rate Percentage
Interview Perceived of Student Pass Rate Percentage
Respondent 1 75-85%
Respondent 2 90%
Respondent 3 70%
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 111
Respondent 4 70%
Respondent 5 87%
Respondent 6 70%
Respondent 6 60%

Assumed cultural setting influences
The organization supports a standard approach to improve math remediation. A gap
was validated for this influence. Data collected from interviews and document analysis revealed
that the organization did not support a standard approach to improve math remediation.
Therefore, a gap was found.
Interview Findings. Data collected from the interviews indicated that the organization
does not support a standard approach to improve math remediation. When asked “Tell me about
the college’s approach to math remediation?” R2 described the approach as “a data focused
campus conversation, with the math department leading the way” while R7 replied “I'm not the
one to really know what the college's approach is.” When asked the same question, R3 stated:
we have been looking at both our STEM and our non-STEM sequence. Most of the
attention has been on the non-STEM sequence because we have a higher percentage of
students who are non-STEM. We've been working on developing the statistics pathway,
which then is reducing the number of classes that students need to take and the
developmental level courses. As a result of changes that we've been making to our
placement policy, we are now getting some data about how our STEM students are doing,
too. We are starting to look more closely at the pre-algebra and algebra courses that we
offer. We had moved arithmetic to noncredit in Fall 2015, I believe. That reduced our
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 112
pathway by one, but we're now having very beginning conversations about the pre-
algebra and what we're going to do with our pre-algebra class.
R4 provided additional insight by stating, “the one thing that's been really big with us is
that we've split our approach. We don't approach students. We don't remediate students the same
way for everybody, which is the problem that most colleges have.” R4 elaborated:
Remedial math is not something that most students even need or will use ever in their
life. But the 75% of students that don't need calculus, we're putting them into our
intermediate algebra for stats and our regular stat classes. And what we found, we kept
looking at data and tweaking placement in terms of what students need intermediate
algebra for statistics. And what we're finding out is that less and less. So a lot of students
now, what we've done is we're placing them directly into stats. They're bypassing our
intermediate algebra for statistics class, and they're going straight into statistics.
R6 replied to the same question by sharing that “the college is really into innovation and
trying something new” and that lead to the intermediate algebra for statistics course. However,
math remediation at Community College Z includes courses other than statistics. R4 shared that
“on the STEM side, we honestly still haven't fixed STEM.” Additionally, R4 stated that there
have been efforts that have “condensed our arithmetic and pre-algebra into one class.” Now
according to R4, math remediation went from “four levels for the STEM students to three levels”
but that the issue is still not fixed and “that's actually our big project right now.”
Document Analysis. There was no evidence located in any of the documents that the
organization supports a standard approach to improving math remediation. In the college’s
factbook an analysis of the intermediate algebra for statistics course identifies the course as an
approach to improve the remediation pathway for non-STEM students. However, the same
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 113
analysis identified the current non-statistics structure of courses as the appropriate sequence for
students pursuing a STEM pathway. Additional research briefs show that the college is also
focused on improving the placement process to improve math remediation. According to the
research briefs, the college uses data to evaluate student success rates and placement data to
determine what changes to implement to the placement data. The research briefs also identify the
application of curricular revisions and accelerated pathways as approaches to improve math
remediation at Community College Z.
The organization provides resources to support academic and professional
standards. A gap was not validated for this influence. Data collected from interviews and
document analysis revealed that the organization provides resources to support academic and
professional standards. Therefore, no gap was found.
Interview Findings. Data collected from the interviews indicated that the organization
provides resources to support academic and professional standards. When asked “what kind of
resources are available to support you in maintaining academic and/or professional standards?”
R2 replied, “there’s conferences, there’s mentoring” and R2 also shared that “there’s a planning
committee that sort of provides funding for activities so there’s financial support for activities.”
In addition, R2 stated that “student equity folks are very supportive too and institutional research
has been exceptionally supportive with data requests and doing presentations.” R3 also
mentioned funding and stated, “we've been very lucky at the college to have access to basic skills
funding.” R3 also shared:
We have the Basic Skills Outcomes Transformation grant as well, and we use funding for
that to pay for professional development. We have student equity funding, so it was really
good timing in terms of us creating the pre-statistics course and training faculty because it
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 114
was at a time where we had lots of resources to be able to pay for funding or pay for
training for faculty and sustain the training as well.
When asked the same question R4 shared that “one of the big issues is the training. The
training takes a lot of hours and a lot of effort” and that they are “hoping that the new book for
intermediate algebra, for statistics, is gonna help us decrease the amount of training that we have
to do.” R4 stated that a book for the intermediate algebra for statistics “was huge” because “we
had no book, so a lot of stuff that we covered in trainings are now in the book.”
R5 replied that the college is “putting their money where their mouth is, and all of their
professional development that they fund, it's amazing.” According to R5, the college “believe in
training and professional development and support of their instructors.” R7 stated “we get a lot
of workshops that are available to us” and described how “throughout the whole semester, you
can get faster e-mails, professional developments, stuff like that. Also, in the statistics area they
have conferences you can go to. They advertise that.” R6 also spoke about professional
development:
We do a lot of professional development. It's waned over the years, just because we have
the same instructors teaching the classes and I wish there was more. It's funny because
we offer a lot of professional development. We offer things on how to teach differently
and different technologies…
Document Analysis. Evidence that the organization provides resources to support
academic and professional standards was supported in multiple documents. The college has an
official professional development program that offers employees the opportunity to attend
various trainings throughout the year. In addition, through the flexible calendar program, each
full time permanent faculty member is obligated to complete 41 hours of FLEX activities per
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 115
academic year. Specifically, the Faculty Development Committee develops schedules and
activities for professional development. Through this program the math department has hosted a
number of trainings in support of the intermediate algebra for statistics course. An example of a
training included a workshop that was designed to improve statistical understanding and provide
attendees with best practices for teaching statistics. A copy of the agenda for another statistics
training identified a set of resources such as textbooks, sample schedules, sample exams, sample
notes, activities, and projects. The training also introduced the Guidelines for Assessment and
Instruction in Statistics Education College Report 2016 (GAISE College Report ASA Revision
Committee, 2016), that focuses on content and techniques for teaching introductory statistics.
Training resources also include the open learning initiative (OLI) textbook on pre-statistics or
intermediate algebra for statistics that was developed by R4.
Table 19.
Validated Influencers Table
Assumed Influences
Validated, Not Validated,
or Unable to Validate
Knowledge (Factual)
Faculty need to know the goal.
Not Validated
Knowledge (Conceptual)
Faculty need to know the content of course curricula.
Not Validated
Knowledge (Procedural)
Faculty need to know how to adapt their instruction.
Not Validated
Faculty need to know how to teach math effectively. Not Validated
Faculty need to know how to align instructional activities to
performance.
Not Validated
Motivation (Expectancy Value)
Faculty need to value implementing intermediate algebra for
statistics.
Not Validated
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 116
Faculty need to value improving student success. Not Validated
Motivation (Self-Efficacy)
Faculty need to believe they are capable of effectively
delivering instruction.
Not Validated
Motivation (Attribution)
Faculty need to believe that student outcomes can be attributed
to their instruction.
Not Validated
Organization (Cultural Models)
There is a culture that supports implementing new courses to
improve student success.
Not Validated
There is a culture that believes underprepared students can
complete math coursework.
Validated
Organization (Cultural Settings)
The organization supports a standard approach to improve
math remediation.
Validated
The organization provides resources to support academic and
professional standards.
Not Validated

Conclusion
Chapter 4 presented all of the data collected from the interviews, observations, and
document analysis to evaluate the knowledge, motivation and organizational influences affecting
the ability of math faculty to implement the intermediate algebra for statistics course. For the
knowledge influencers, no gaps were validated. For the motivation influencers no gaps were
validated. For the organizational influencers, gaps were validated for two influencers while no
gaps were validated for the remaining two organizational influencers. In Chapter 5,
recommendations and solutions will be presented to address the validated gaps to improve the
ability of math faculty to implement the intermediate algebra for statistics course.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 117
CHAPTER FIVE: SOLUTIONS, IMPLEMENTATION AND EV ALUATION PLAN
The purpose of this study was to evaluate the extent that the math faculty at Community
College Z was meeting its goal of implementing 100% of the content for the intermediate algebra
for statistics course using 100% appropriate pedagogy. The Clark and Estes (2008) gap analysis
framework was chosen to be the primary framework for this study. In Chapter Four, the findings
from data collected were used to answer Research Question 1, what are the knowledge,
motivation and organizational influences affecting the ability of math faculty to implement 100%
of the content for the intermediate algebra for statistics course using 100% appropriate
pedagogy? Each of the 13 influences that were initially identified during the literature review
were evaluated based on data collected from interviews, observations, and document analysis.
Based on the findings, two validated gaps were found and both gaps were in organizational
influences.
This chapter addresses Research Question 2, what are the recommendations for
organizational practice in the areas of knowledge, motivation, and organizational resources? The
recommendations and implementation plan provided are based on the New World Kirkpatrick
Model (J. D. Kirkpatrick & Kirkpatrick, 2016), which was used as a framework for providing
recommendations for closing the two validated gaps. Community College Z can consider using
the provided recommendations to help faculty in the math department to implement the
intermediate algebra for statistics course.
Recommendations for Practice to Address KMO Influences
Knowledge Recommendations
There were no recommendations made for knowledge influencers, since there were no
validated gaps.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 118
Motivation Recommendations
There were no recommendations made for motivation influencers, since there were no
validated gaps.
While there were no gaps in these two areas of knowledge and motivation influences,
there were plenty of promising practices identified in the findings. The stakeholder of focus for
this study were the math faculty that taught the intermediate algebra for statistics. The distinction
of stakeholder is important since the following validated organization gaps and recommendations
are focused not on the stakeholders of this study, but instead on the larger organizational unit of
the entire math department, which includes those faculty that teach math remediation in the
STEM pathway. The following gaps and recommendations, therefore address the issue of
transferring the practices found within the stakeholder of focus to the larger organization unit. As
such, the following implementation and evaluation plan is designed to assist new faculty in
teaching the existing intermediate algebra for statistics course at Community College Z or for
other colleges looking to train faculty to engage in the process and practices of inquiry.
Organization Recommendations
Introduction. According to Clark and Estes (2008) three organizational factors that can
be a source of organizational performance gaps include work processes, material resources, and
value streams. Further, organizations are composed of complex and interacting systems that have
their own culture and understanding the influences affecting the conditions of an organization is
important to improving organizational performance (Clark & Estes, 2008; Rueda, 2011).
Gallimore and Goldenberg (2001) propose cultural models and cultural settings to describe the
shared mental models and the settings where culture exists. Clark and Estes (2008) also propose
that organizational culture sits between existing processes and resources and efforts to improve
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 119
organizational performance. Table 20 depicts the assumed organizational influences that were
validated in chapter four. Table 20 also presents the recommendations for each of the influences
based on theoretical principles found in the literature.
Table 20.
Summary of Organization Influences and Recommendations
Assumed
Organization
Influence
Validated
Gap?
Principle and Citation
Context-Specific
Recommendation
Cultural Models:
There is a culture that
believes underprepared
students can complete
math coursework.
Yes Organizational performance
increases when beliefs and
knowledge are focused on
achieving organizational
goals (Clark & Estes, 2008)

Creating clear pathways
connects the skills required
during remediation to
improve student success
(Fong et al., 2015; Hodara &
Jaggars, 2014)

Department dean will
provide faculty with
information on student
success data, effective
pedagogy, and
instructional tools.

Department dean will
communicate how
faculty practices
contribute to
improving student
outcomes in math
remediation to
increase faculty buy-in
and ensure curriculum
alignment.
Cultural Settings:
The organization
supports a standard
approach to improve
math remediation.
Yes Organizational performance
increases when processes
and structures are aligned
with goals (Clark & Estes,
2008)

Approaches to improving
student outcomes in math
remediation include:
curriculum alignment,
acceleration, and statistics
Department dean will
lead monthly faculty
meeting on course
content and how
resources can be used
to solve student
success problems.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 120
pathways (Davidson &
Petrosko, 2015; Hern, 2012;
Hern & Snell, 2014; Valdez
& Marshall, 2013).

Cultural Model. As math faculty at Community College Z look to implement a new
course that would improve student outcomes in math remediation it is important that there is a
culture that believes underprepared students can complete math coursework. Clark and Estes
(2008) suggest that organizational performance increases when beliefs and knowledge are
focused on achieving organizational goals. This suggests that the organization needs to create a
place where faculty can refer to references and resources on student success data, effective
pedagogy, and instructional tools.
In a study of students from eight community colleges, Fong et al. (2015) use student data
to build a model to explain the successful progression of students through the developmental
math course sequence. The community college district’s office of institutional research provided
quantitative data for a sample of 54,879 students that had been assessed and placed into a
developmental math course. Using quantitative analysis and a logistic regression, the researchers
found, “that students who enter at lower developmental levels are attempting and passing the
higher courses at rates comparable to those who are initially placed in higher levels—if they
attempt those levels” (p. 739). This would suggest that creating a place where faculty can refer to
references and resources on student success data, effective pedagogy, and instructional tools
could reaffirm that underprepared students are capable of completing math coursework.
Cultural Setting. To improve math remediation, community colleges often implement
and combine interventions at their own pace. Therefore it is important that the organization
supports a standard approach to improve math remediation. Clark and Estes (2008) suggest that
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 121
organizational performance increases when processes and structures are aligned with goals. This
suggests that the organization needs to facilitate a faculty discussion forum to share and review
standard approaches to improving student outcomes in math remediation to ensure curriculum
alignment and increase faculty buy-in on solving student success problems.
Clark and Estes (2008) stated that processes, resources, and value streams can be the
source of organizational performance gaps. In the case of math remediation at Community
College Z, the implementation of the intermediate algebra for statistics course is only one of the
interventions currently in use to improve math remediation. However, other approaches such as
curriculum alignment, acceleration, and statistics pathways also exist to improve math
remediation (Davidson & Petrosko, 2015; Hern, 2012; Hern & Snell, 2014; Valdez & Marshall,
2013). At Community College Z math courses are offered in an accelerated format to improve
student success rates. As such, it appears that the literature would support the need for the
organization to share and review approaches to improving student outcomes in math remediation
and increase faculty buy-in on solving student success problems.
Integrated Implementation and Evaluation Plan
Implementation and Evaluation Framework
The New World Kirkpatrick Model (2016) was used to inform the implementation and
evaluation plan of this study and is based on Kirkpatrick’s (2006) earlier four levels of training
and evaluation (J. D. Kirkpatrick & Kirkpatrick, 2016). J. D. Kirkpatrick and Kirkpatrick (2016)
identify four levels of training and evaluation in the New World Kirkpatrick Model: Level 1
(Reaction), Level 2 (Learning), Level 3 (Behavior), and Level 4 (Results). In this model, it is
proposed that evaluation plans reverse the order of the four levels during the planning phase,
thereby ensuring that “the focus on what is most important” is maintained (J. D. Kirkpatrick &
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 122
Kirkpatrick, 2016, p. 11). By starting with the goals of the organization through Level 4 (Results)
and working in reverse towards Level 1 (Reaction), training and evaluation efforts can be better
aligned to organizational goals. The alignment is accomplished by first focusing on a) outcomes
and the indicators of those outcomes, b) then defining the behaviors that support those identified
indicators, and c) then looking at the learning needed to achieve the desired behaviors through
training that is favorable to trainees (J. D. Kirkpatrick & Kirkpatrick, 2016). Utilizing each of the
four levels in a training and evaluation plan in the reverse order helps to stay focused on the
goals and outcomes by guiding each phase in the training package to deliver measurable results
in support of the overall organizational goal (J. D. Kirkpatrick & Kirkpatrick, 2016).
Level 4: Results and Leading Indicators
Table 21 shows the proposed Level 4: Results and Leading Indicators in the form of
outcomes, metrics and methods for both external and internal outcomes for Community College
Z or other institutions attempting to institute a similar intervention. If the internal outcomes are
met as expected as a result of the training and organizational support for faculty implementation
of the intermediate algebra for statistics course, then the external outcomes should also be
realized.
Table 21.
Outcomes, Metrics, and Methods for External and Internal Outcomes
Outcome Metric(s) Method(s)
External Outcomes
1. Increase math transfer
eligibility of
developmental math
students.
1a. The number of students
successfully completing
intermediate algebra for
statistics.
Solicit data, i.e., course success
rate, each semester from the
Office of Institutional Research.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 123
1b. The number of
developmental math students
successfully enrolling in and
completing a transfer-level math
course.
Solicit data, i.e., course
enrollment success rate, each
semester from the Office of
Institutional Research.
2. Increased number of
intermediate algebra for
statistics course sections.
2. The number of intermediate
algebra for statistics course
sections offered per semester.
Track the number of
intermediate algebra for
statistics course sections offered
each semester.
Internal Outcomes
3. Increase math
department faculty
participation in training.
The number of faculty
participating in training.
Department dean will track
faculty participation in training
events.
4. Increase number of
intermediate algebra for
statistics faculty.
The number of faculty that
attend training on intermediate
algebra for statistics.
Course lead will track faculty
participation in intermediate
algebra for statistics training
events.
5. Monthly math
department workgroup
meeting on student
success.
The amount of resources spent
on department led student
success initiatives.
Solicit data from department
dean/accounting on resources
expended for department led
student success initiatives.

Level 3: Behavior
Critical behaviors. The stakeholders of focus are the math faculty implementing the
intermediate algebra for statistics course. The first critical behavior is that math faculty will work
with each other in a problem-solving approach to improve student success. The second critical
behavior is to increase faculty involvement in professional development training. The third
critical behavior is to increase faculty check-in with students to review course progress. The
specific metrics, methods, and timing for each of these outcome behaviors appears in Table 22.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 124
Table 22.
Critical Behaviors, Metrics, Methods, and Timing for Math Faculty
Critical Behavior Metric(s) Method(s)
Timing
1. Math faculty will
work with each other
in a problem-solving
approach to improve
student success.

The number of faculty
participants at each
meeting.

1. Course Lead will
track the faculty
participation for each
meeting.
1. Ongoing –
monthly.

2. Increase faculty
involvement in
professional
development training.

The number of faculty
that have attended a
training each
semester.
2. Course Lead will
track the faculty
participation for each
training.
2. Ongoing – every
semester.
3. Increase faculty
check-in with students
to review course
progress.
The number of
students check-ins.

3. Faculty shall
document the number of
check-ins for each
student.
3. During each
course – weekly.

Required drivers. Math faculty that teach the intermediate algebra for statistics course
require the support of their course lead, fellow faculty, department dean, and the organization to
reinforce, encourage, reward, and monitor what they learned in the training. Reinforcement
provides training participants a reminder of what they learned and additional training.
Encouragement provides coaching and mentoring to support the behaviors learned during
training. Rewards are the incentives for participants to practice what they learned in training.
Rewards should be established for achievement of performance goals to enhance the
organizational support of math faculty. Additionally, monitoring creates a system of
accountability to monitor the performance of training participants to implement what they
learned. Table 23 shows the recommended drivers to support critical behaviors of math faculty
that teach the intermediate algebra for statistics course.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 125
Table 23.
Required Drivers to Support Math Faculty’s Critical Behaviors
Method(s) Timing
Critical Behaviors Supported
1, 2, 3 Etc.
Reinforcing
Job aid including course
curricula and mathematical
concepts.
Ongoing 2, 3
Job Aid including checklist
for student follow-up.
Ongoing 1, 2, 3
Training on course
preparation, goal setting, and
student follow-up
Annually 2, 3
Faculty report out their work
on improving student success
in department meetings
Monthly 1
Encouraging
Mentoring from other math
faculty during check-
ins/report outs.
Monthly 1
Feedback and coaching from
Course Lead.
Monthly 1, 2
Rewarding
Training cost incentive when
faculty participate in training.
Training-based as applicable

2
Reassigned time incentive
when faculty participate in
training.
Training-based as applicable

2
Monitoring
Office of Institutional
Research will track and report
student performance data for
intermediate algebra for
statistics course.
Monthly 1, 3
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 126
Department dean and course
lead can assess faculty
alignment with implementing
training goals.
Monthly 1, 2, 3

Organizational support. To ensure that the required drivers are implemented the
organization will provide the following support. First, the organization will create a policy that
describes a process of inquiry that can be used to identify when new courses are needed and
outlines how a new course should align to the vision and goals of the institution to improve
student success. Second, the organization, specifically the department dean, will provide faculty
with information on student success data, effective pedagogy, and instructional tools.
Additionally, the department dean will communicate how faculty practices contribute to
improving student outcomes in math remediation to increase faculty buy-in and ensure
curriculum alignment. The department dean will also lead monthly faculty meeting on course
content and how resources can be used to solve student success problems. Finally, the
organization will provide financial resources to expand faculty participation in professional
development.

Level 2: Learning
Learning goals. Following completion of the recommended solutions, the math faculty
will be able to:
1. Identify the goal of the intermediate algebra for statistics course. (D)
2. Identify the content of course curricula and describe the included mathematical
concepts. (D)
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 127
3. Adapt their instruction through course preparation, goal setting, and student follow-
up. (P)
4. Teach math effectively by deconstructing math concepts. (P)
5. Align instructional activities to course performance goals. (P)
6. Value implementing intermediate algebra for statistics. (V)
7. Value improving student success. (V)
8. Indicate self-efficacy in effectively delivering instruction. (SE)
9. Believe that student outcomes can be attributed to their instruction. (A)

Program. The learning goals listed in the previous section, will be achieved through job
aids, training, and exercises that will increase the knowledge and motivation of the learners,
math faculty, to implement 100% of the content for the intermediate algebra for statistics course
using 100% appropriate pedagogy. The program will be ongoing and will consist of information,
job aids, and training workshops. First, each semester on an ongoing basis intermediate algebra
for statistics math faculty will be provided with information and job aids that outline the goal of
the intermediate algebra for statistics course and its role in the developmental math sequence. In
addition, job aids will be provided that describe the mathematical concepts included in the
curricula of the intermediate algebra for statistics course.
The math faculty will also be provided with an all-day in-person training workshop at the
beginning of the school year where they will learn and practice how to deconstruct math
concepts and plan to match instructional activities and course content to reach course objectives.
The training will include topics on effective instructional techniques and the use of scaffolding to
enhance the learning experience. Additionally, during the training scenarios will be used for
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 128
faculty to practice and receive feedback on course preparation, goal setting, and student follow-
up. As part of the training there will be immediate and delayed private feedback on mathematical
discourse, productive struggle, student engagement, and sense-making to demonstrate the
connection between faculty instruction and student outcomes and how individual efforts and
instructional practices contribute to student success.
Components of learning. The knowledge, skills, and motivation of math faculty are
important to implementing the intermediate algebra for statistics course. The knowledge, skills,
and motivation gained in training can be applied to solving the challenges faced by math faculty.
Therefore, it is important to evaluate the declarative and procedural knowledge being taught to
participants based on their training participation. Additionally, it is also important that math
faculty value the training, are committed, and confident in their knowledge and skills so that they
can apply their training on the job. Table 24 lists the evaluation methods and timing for each
component of learning.
Table 24.
Components of Learning for the Program
Method(s) or Activity(ies) Timing
Declarative Knowledge “I know it.”
Survey items using scaled and open-ended items At the end of the workshop
Knowledge checks through whole group discussions. During the in-person workshop

Procedural Skills “I can do it right now.”
Demonstrate procedural skill using scenarios to successfully
perform practice activities.
During the workshop
Feedback from peers during training scenarios. During the workshop
Attitude “I believe this is worthwhile.”
Group discussions on why it is important to improve student
success.
During the workshop
Discussions of the value of what they are being asked to learn. During the workshop
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 129
Confidence “I think I can do it on the job.”
Survey items using scaled items At the end of the workshop
Discussions following practice and private feedback. During the workshop
Commitment “I will do it on the job.”
Survey items using scaled items At the end of the workshop
Ask math faculty to create an individual action plan on how they
will implement what they learned.

At the end of the workshop

Level 1: Reaction
It is important to determine how the participants react to the training to identify the
quality of the training and if the training was acceptable to participants. Table 25 lists the
methods for evaluating the engagement, relevance, and satisfaction of the training from math
faculty.
Table 25.
Components to Measure Reactions to the Program
Method(s) or Tool(s)
Timing
Engagement
Observation by instructor/facilitator During the workshop
Attendance at training workshop At the start of the workshop
Training workshop evaluation At the end of the workshop
Relevance
Pulse-check with participants via discussion During the workshop
Training workshop evaluation At the end of the workshop
Customer Satisfaction
Pulse-check with participants via discussion During the workshop
Training workshop evaluation At the end of the workshop

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 130
Evaluation Tools
Immediately following the program implementation. Following the in-person training
workshop, participants will complete a short post-training evaluation. The evaluation will contain
scaled and opened-ended items to measure participants’ Level 1 reactions on training relevance,
engagement, and satisfaction. The post-training evaluations will also measure participants’ Level
2 learning by gathering information on their declarative knowledge, procedural skills, attitudes,
confidence, and commitment. Appendix E shows the post-training evaluation instrument that the
instructor will use to gather data on performance on Level 1 and Level 2 indicators.
During the in-person training workshop the instructor track attendance, observe
participation, and conduct pulse-checks to measure Level 1 reactions to the training workshop.
Level 2 learning will be evaluated during in-person training using declarative knowledge checks
during discussions and practicing procedural skills with peer feedback. Level 2 attitudes and
confidence will be evaluated in discussions with participants following live practice and
feedback. Level 2 commitment will be evaluated through the creation of individual action plans.
Delayed for a period after the program implementation. Approximately 90 days after
the implementation of the training workshop the organization will administer a survey. The
survey will contain 5 scaled items using the Kirkpatrick Blended Evaluation (J. D. Kirkpatrick &
Kirkpatrick, 2016) approach to measure participant’s perspective on the relevance and
satisfaction of the training (Level 1), the ability to teach math curricula in intermediate algebra
for statistics (Level 2), application of the training to teaching the intermediate algebra for
statistics course (Level 3), and the extent to which their application of training content has
positively impacted results (Level 4). Appendix F is the Blended Evaluation instrument that
addresses all four Kirkpatrick levels.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 131
Data Analysis and Reporting
The Level 4 goal for math faculty to implement the intermediate algebra for statistics
course is measured by analyzing and reporting key performance indicators (KPIs). Each
semester, the reviewer will compile the data from various internal sources for each of the KPIs
listed in Table 26 below. Additionally, Table 26 list each of the metrics and the type of graphical
representation to be used in a dashboard for reporting and communicating with college
administrators and faculty. Figure 5 below presents an example dashboard that will be used to
monitor progress and serve as an accountability tool. Similar dashboards will be created to
monitor Levels 1, 2 and 3.
Table 26. Possible Key Performance Indicators for Internal Reporting and Accountability
Key Performance Indicator
(KPI)
Metric Frequency
Dashboard
Representation
Developmental math student
math transfer eligibility
Course Success Rate Semester Gauge on completion
rate
Number of course sections
offered
Number of course
sections
Semester Bar chart on the
number of course
sections
Faculty participation in
training.
Number of faculty
participants
Semester Gauge on the number
of faculty participants
Training resources Training costs Semester Bar chart on costs of
training

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 132

Figure 5. Example KPI Dashboard
Summary
The New World Kirkpatrick Model (J. D. Kirkpatrick & Kirkpatrick, 2016) was used as a
framework to develop this study’s recommended solutions, implementation strategies, and
evaluation plan. The model is based on Kirkpatrick and Kirkpatrick’s earlier four levels of
training and evaluation with the application of the four levels in reverse order to maintain
alignment and focus on the organizational goal (J. D. Kirkpatrick & Kirkpatrick, 2016). As a
result, the recommended solutions, implementation strategies, and evaluation plan each
contribute to ensuring that math faculty gain the knowledge, motivation, and organizational
support to implement the intermediate algebra for statistics course. The training package that was
developed is designed to deliver measurable results that can be monitored through critical
behaviors after math faculty participated in training. Training helps math faculty gain knowledge
and learn skills along with developing the attitude, confidence, and commitment to apply what
was learned.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 133
According to the J. D. Kirkpatrick and Kirkpatrick (2016), evaluating the training
program requires asking and answering three questions for each of the four levels, “Does the
level of ….. meet expectations? If so, then why? and If not, then why not?” (p. 122). For Level 1
(Reaction) and Level 2 (Learning) a formative analysis conducted by the trainer during training
can be conducted to assess whether the training is meeting expectations. If the training is meeting
expectations, then the trainer can conduct a pulse check to identify was is increasing the
reactions and learning. If the training is not meeting expectations, the trainer can use the pulse
checks to identify what is inhibiting participation and learning. For Level 3 (Behavior),
determining if the training is meeting expectations will be based on a delayed survey and
measuring on the job performance through the mentoring, coaching, and check-ins that occur
after training to identify what is inhibiting or promoting math faculty from utilizing what they
learned during their training. For Level 4 (Results) an evaluation on if the training is meeting
expectation will be based on the data collected during the delayed survey. If the training is
meeting expectations, then the course lead and college administrators can solicit feedback on
what is increasing performance. If the training is not meeting expectations, then the course lead
and college administrators can solicit feedback on what behaviors would help improve
performance.
Strengths and Weaknesses of Approach
The Clark and Estes (2008) gap analysis model used in this study provided a framework
that specifically identified the knowledge, motivation, and organizational influences affecting
faculty. The result was a research study that provided a comprehensive examination of the
influences to identify recommendations specific to research site. Additionally, the findings from
the Clark and Estes (2008) gap analysis model combined with the New World Kirkpatrick Model
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 134
(J. D. Kirkpatrick & Kirkpatrick, 2016) aligned to address an ongoing issue identified in the
literature, faculty professional development. However, the Clark and Estes (2008) gap analysis
model demonstrates a limitation when applied to an organization that has minimal validated gaps
in the assumed influences as was found in this study.
Limitations and Delimitations
This study focused on expanding the existing understanding of the ability of faculty to
implement a new course to improve math remediation by analyzing a set of knowledge,
motivation, and organizational influences identified in the literature. However, as with all
research studies, this research study contained some elements that remained out of the control of
the researcher and are identified as limitations. This study includes those limitations associated
with the data collection methods.
According to Creswell (2014), each form of data collection has inherent strengths and
weaknesses that may influence the data collected. In this study, the use of interviews as the
primary method of data collection introduces a known limitation into the research design. The
information presented by a participant during an interview is filtered through the participant’s
perspective (Merriam & Tisdell, 2016). Therefore, while it is assumed that the data collected
from participants was truthful, there remains the potential for bias in each response as
participants knowingly select which information to share as they responded to the interview
questions.
The use of course observations also presented a limitation in the data. During data
collection, the presence of an observer in the classroom altered the start of one course as one
instructor took a few minutes to introduce the observer at the start of the course. In a second
course, the classroom projector had been stolen and a replacement projector took 20 mins to
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 135
locate and install. The observation protocol was designed to measure the behavior of both the
students and instructor as they engage in the course content during the course session. In these
two courses, the behavior of the instructor and students may have been influenced with respect to
the content.
Another limitation was the lack of access to certain documents for analysis. The research
design included document analysis as a method to gather data about existing procedures,
policies, training, etc. However, during the study some documents were not available including
previous student testimonials/evaluations and certain training policies. The lack of access to
these documents limit the ability of the researcher to verify data collected during interviews and
observations.
A delimitation of the study involved the selection of math faculty that taught the
intermediate algebra for statistics course. By selecting the faculty that taught the intermediate
algebra for statistics course as the stakeholder group, the study is focused on a small group
considered non-STEM math faculty as compared to STEM math faculty or even the larger
system of California Community Colleges. Thereby, the focus on this small stakeholder group
potentially reduces the generalizability of the findings to other faculty groups.
Recommendation for Further Inquiry
During the data collection process, it was clear that the intermediate algebra for statistics
course was considered a non-STEM math course while traditional math remediation courses
were considered STEM math courses. The data further suggests that this distinction could play a
role in the acceptance and/or applicability of the tools, techniques, and pedagogy used for the
implementation of the intermediate algebra for statistics course by STEM related math
remediation courses. Therefore, it is recommended that future research explore the extent that
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 136
STEM and non-STEM courses differ in faculty implementation and faculty preparation. In
addition, it is also recommended that future research also explore how community colleges can
improve STEM related math remediation to improve student success.
This study revealed that those faculty engaged in implementing the intermediate algebra
for statistics course demonstrated a number of promising practices. However, another
recommendation for further inquiry is the based on the organizational gaps identified in this
study’s findings. The organizational gaps that were found, were associated with the larger math
department that included math faculty not associated with teaching the intermediate algebra for
statistics. In the findings, it was clear that the math faculty who taught intermediate algebra for
statistics had engaged in a process of inquiry leading to the practices and beliefs used to teach the
course including a standard approach to improve math remediation and the belief that
underprepared students can complete math coursework. However, the findings also revealed that
those practices and beliefs had not transferred to the larger organizational culture.
To overcome the organizational gaps found with the larger group in this study, the
application of Kotter’s (2007) steps for transforming organizations could serve as a framework
that can be applied to the STEM math faculty. In particular, is the step of establishing a sense of
urgency as this step triggers the motivation and effort needed to address the issue in the first
place. In this case, creating a sense of urgency within the larger math department should help
those teaching math remediation in the STEM pathway recognize that existing student outcomes
need to be improved. Two additional and important steps include creating a vision and
communicating the vision (Kotter, 2007). These two steps can help to address the existing
organizational gaps associated with supporting a standard approach to improve math remediation
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 137
by developing strategies to direct efforts that support the vision of improving math remediation
and then by communicating those strategies to the larger math department.
So, while the non-stem faculty present a case study for other colleges, the STEM side of
the math faculty present an opportunity for further study as the STEM side of the department’s
remediation efforts have not engaged in a similar process. Since this study did not focus on the
larger group of math faculty within the math department, a new Clark and Estes (2008) gap
analysis study to specifically identify the knowledge, motivation, and organizational influences
affecting the larger math department is recommended.
Conclusion
This study sought to evaluate the ability of math faculty at a local community college to
implement an intermediate algebra for statistics course designed to designed to shorten the basic
skills math pathway and improve student success. The Clark and Estes (2008) gap analysis
model was used as the methodological framework to identify the 13 knowledge, motivation and
organizational influences affecting the ability of faculty to implement the course. The
knowledge, motivation and organizational influences were evaluated through a review of the
literature, interviews, classroom observations, and document analysis. Of the 13 influences
identified, only two validated gaps were found in the data and both were tied to the larger
organizational culture that included those involved with the implementation of developmental
math courses designed for the traditional STEM pathway. This would suggest that while the
faculty at Community College Z have incorporated those practices identified in the literature as
part of the implementation of the intermediate algebra for statistics course, the lessons learned
have not transferred to all courses in the developmental math sequence. Additionally, this study
used the New World Kirkpatrick Model (J. D. Kirkpatrick & Kirkpatrick, 2016) as a framework
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 138
to develop recommended solutions, implementation strategies, and an evaluation plan for
implementing the intermediate algebra for statistics course that could be used to train additional
faculty or as a model for other institutions attempting to adopt a similar math remediation
intervention.
Another point is that while this study focused on the implementation of the intermediate
algebra for statistics course, there was little data or discussion collected regarding the initial
motivation or conditions that prompted and supported the creation of the course. However, the
little evidence that was collected revealed that the process centered around a revelation of the
data and the intrinsic motivation of faculty at the college to do something about improving
student success in the math remediation gatekeeper course. Depending on who you speak with at
the college, the faculty spark can be tied to either an individual or a highly supportive group of 4-
5 faculty members collaborating with each other. In either case, what is commonly understood by
those at the college regarding the development of the intermediate algebra, is that the data drove
a sense urgency to do something. According to Kotter (2007), establishing a sense of urgency
through an evaluation of the facts triggers the motivation and effort needed to address the issue
in the first place.
The initial student success data in math remediation at Community College Z, appears to
have provided a catalyst for faculty to drive change, as the data demonstrated disparities in
student equity. Harris and Bensimon (2007), point out that developing a sense of responsibility
among practitioners to address race-based inequities in higher education outcomes can be
accomplished by creating a level of awareness that the gaps exist through the use of evidence. In
this case, the combination of initial student outcome data and the sense of urgency drove faculty
to engage in a process to address the existing issues with student outcomes. From the data
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 139
collected in this study, the faculty that taught non-STEM math remediation courses worked
together as a team to find and implement a solution. From the literature, we understand that in
teams, collaboration and the relationships that are built can be beneficial by supporting good
problem solving and increasing peer support and accountability (Bensimon & Neumann, 1993).
The findings from this study revealed a number of promising practices for implementation of the
intermediate for algebra course that included an ongoing process of inquiry and serves as an
example of the faculty driven change that can be accomplished.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 140
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IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 151
APPENDIX A
Request for Interview Participation
Greetings,
You have been selected to participate in a one-hour interview of Community College Z
mathematics faculty that teach the intermediate algebra for statistics. The interview is one part of
a doctoral research project being conducted through USC’s Rossier School of Education. The
purpose of this interview is to gain a better understanding of the key influencing factors affecting
the ability of faculty to fully implement the intermediate algebra for statistics course. As part of
the math faculty delivering instruction for the intermediate algebra for statistics course, you
possess valuable information and experience to inform this study.
Your participation in this interview is completely voluntary. Your identity will be kept
confidential, and a pseudonym will be used in the final report. All information collected during
the interview will be treated confidentially, only the researcher/doctoral candidate and
dissertation chair will have access to the raw data.
If you decide to participate, I will be asking for your permission to record the interview,
to more accurately capture your perspectives. After the interview, you will have an opportunity to
review the transcripts. You may decline to answer any questions and you can stop the interview
at any time or choose to withdrawal from the study completely.
I hope you are willing to participate in an interview to help us better understand how to
successfully scale transformational programs that dramatically assist student success. I have
received IRB approval from both USC and your district process. I would greatly appreciate your
participation, and if so please click the link below to schedule an interview.
usepowwow.com/xxxxxxxxx
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 152
If you would like to schedule an alternate time, please contact the researcher at either
cgmontoy@usc.edu or (559) 301-0822 to set a day and time for the interview that will
accommodate your schedule.

Thank you in advance for your participation.

Sincerely,

Carlos Montoya
Doctoral Candidate – Rossier School of Education
University of Southern California

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 153
APPENDIX B
Stakeholder Interview Protocol
Name (Pseudonym):

Location of Interview:

Date/Time of Interview Start:

Introduction for Interview
Hello, my name is Carlos Montoya. I am a graduate student at the Rossier School of
Education at the University of Southern California. I would like to thank you for agreeing to
participate in this interview. The purpose of this interview is to understand the key factors
affecting the ability of faculty to implement the Intermediate Algebra for Statistics Course.
When we scheduled this interview, you suggested that this would be a good time for the
interview – is that still the case? (if yes, continue; if no, try to reschedule). As previously
discussed, this interview should take no longer than 60 minutes. You do not have to answer any
questions you do not want to, and you may stop the interview at any
In addition, everything you say will be treated confidentially and only members of the
study team will have access to the data. With your permission, I would like to record this
interview, so that I can accurately capture your perspectives. Once the recordings are transcribed
and any identifying information is removed, the recordings will be deleted. Do I have your
permission to record the interview?

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 154
Interview Questions for Stakeholders

Interviewee Background.
1) Tell me a little about your background, I'm interested in learning about what led you to teach
this course?
a) Probe: How long have you been in your present position?
b) Probe: How long have you been at this institution?
c) Probe Adjunct: What type of work do you do besides teach this course?

Factual Knowledge Questions.
2) Tell me about the math department.
a) Probe: Can you describe any goals?
b) Probe: To what extent do you collaborate? Is there any team teaching? How are faculty
evaluated? What kind of criteria are used? Is workload evenly shared or distributed?
3) Can you describe the purpose of the intermediate algebra for statistics course?

Conceptual Knowledge Questions.
4) Tell me about the curriculum of the intermediate algebra for statistics course?
a) Probe: How is it organized, what is included, how it differs from other courses?

Procedural Knowledge Questions.
5) Can you describe how the students in a class may influence how you teach the course
material?
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 155
6) Describe how you work with students in developmental math courses to help them learn the
material?
7) Can you describe how the instructional activities help you reach the student learning
objectives of the course?

Expectancy Value - Motivation Questions.
8) Tell me about why you teach the intermediate algebra for statistics course?
9) What do you do to help your students be successful in courses you teach?
a) Probe: Tell me about why you choose to take those steps?

Self-Efficacy - Motivation Questions.
10) How confident do you feel about your ability to deliver instruction for the intermediate
algebra for statistics course?
11) What percentage of students do you think will be able to pass the course you are teaching?
a) Probe: What accounts for that pass rate?
b) What do you think would help those not passing?

Attribution - Motivation Questions.
12) What do you believe are the factors that lead to better student outcomes?
a) Probe: What impact, if any, do instructional materials, teaching methods, or experience
have?

Cultural Models - Organizational Questions.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 156
13) How supportive is the college toward developing new courses to improve student success?
a) Probe: Can you share an example?
14) What is the general feeling in the department about students in the developmental math
course, and the likelihood that they will be successful?
a) Probe: Could they all learn this material or are there some who will never get it?
b) Probe: Who or what is responsible for their success or failure?

Cultural Settings - Organizational Questions.
15) Tell me about the college’s approach to math remediation?
16) What kind of resources are available to support you in maintaining academic and/or
professional standards?
a) Probe: What has been helpful, what's missing, if anything?
17) Can you describe any training that is available to faculty?
a) Probe: Are there any rewards for participation? How often do you participate? Why or
why or why not?
18) When you are successful with your students, to what extent is that noticed by the department
or college?

Concluding Questions.
19) Is there anything else you would like to add that I did not get a chance to ask you about?
20) Would you be willing to let me sit in one day and observe the class?

Thank you for taking the time to share your thoughts and experiences with me.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 157
APPENDIX C
Stakeholder Observation Protocol
5

Date and time of Observation: _______________________________________________
Name (Pseudonym):

Course No./name/section: _____________

Number of students present:

Observer’s location:

Classroom and background
a) Room location and layout (e.g., type of student seating, instructor on podium, etc.).

b) Note if there is anything unusual about this class/lecture (e.g., quiz day, first day of
semester, etc.)

c) (Optional, if known) What goes on out of class? Homework? Pre-readings? Labs?
Projects? Other? Explain briefly.

5
Adapted from Smith MK, Jones FHM, Gilbert SL, and Wieman CE. 2013. The Classroom Observation Protocol
for Undergraduate STEM (COPUS): a New Instrument to Characterize University STEM Classroom Practices.
CBE-Life Sciences Education, Vol 12(4), pp. 618-627; www.cwsei.ubc.ca/resources/COPUS.htm
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 158

Narrative Description of Course / Field Notes
a) The structure of the lesson (e.g., how the instructor sequenced material, does material
build over the course session)
b) The range and type of activities that occurred.
c) Dialog/behaviors that illustrate faculty adapting instruction to students.
d) Explanations of course concepts are understood by students.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 159
Observation Codes
Course Led By
· AS – Active Student
· ID – Instructor Delivery

Students are Doing
· L - Listening to instructor/taking notes, etc.
· Ind - Individual thinking/problem solving. Only mark when an instructor explicitly asks
students to think about a clicker question or another question/problem on their own.
· CG - Discuss clicker question in groups of 2 or more students
· WG - Working in groups on worksheet activity
· OG - Other assigned group activity, such as responding to instructor question
· AnQ - Student answering a question posed by the instructor with rest of class listening
· SQ - Student asks question
· WC - Engaged in whole class discussion by offering explanations, opinion, judgment, etc. to
whole class, often facilitated by instructor
· Prd - Making a prediction about the outcome of demo or experiment
· SP - Presentation by student(s)
· TQ - Test or quiz
· W - Waiting (instructor late, working on fixing A V problems, instructor otherwise occupied,
etc.)
· Other – explain in comments

Instructor is Doing
· Lec - Lecturing (presenting content, deriving mathematical results, presenting a problem
solution, etc.)
· RtW - Real-time writing on board, doc. projector, etc. (often checked off along with Lec)
· FUp - Follow-up/feedback on clicker question or activity to entire class
· PQ - Posing non-clicker question to students (non-rhetorical)
· CQ - Asking a clicker question (mark the entire time the instructor is using a clicker question,
not just when first asked)
· AnQ - Listening to and answering student questions with entire class listening
· MG - Moving through class guiding ongoing student work during active learning task
· 1o1 - One-on-one extended discussion with one or a few individuals, not paying attention to
the rest of the class (can be along with MG or AnQ)
· D/V - Showing or conducting a demo, experiment, simulation, video, or animation
· Adm - Administration (assign homework, return tests, etc.)
· W - Waiting when there is an opportunity for an instructor to be interacting with or
observing/listening to student or group activities and the instructor is not doing so
· Other – explain in comments

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 160
Observation Matrix
How to use observation matrix: Put a check under all codes that happen anytime in each 5
minute time period (check multiple codes where appropriate). If no codes fit, choose “o” (other)
and explain in comments. Put in comments when you feel something extra should be noted or
explained.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 161

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 162
APPENDIX D
Information/Facts Sheet for Exempt Non-Medical Research
University of Southern California
Rossier School of Education
3470 Trousdale Parkway
Los Angeles, CA 90089

INFORMATION/FACTS SHEET FOR EXEMPT NON-MEDICAL RESEARCH

EXAMINING THE FACULTY IMPLEMENTATION
OF INTERMEDIATE ALGEBRA FOR STATISTICS

You are invited to participate in a research study conducted by Carlos Montoya at the University
of Southern California. Please read through this form and ask any questions you might have before
deciding whether or not you want to participate.

PURPOSE OF THE STUDY
This research study aims to understand the key influencing factors affecting the ability of faculty
to implement the intermediate algebra for statistics course.

PARTICIPANT INVOLVEMENT
If you agree to take part in this study, you will be asked to participate in a phone interview that
should take no longer than 60 minutes. you will be asked for your permission to record the
interview for accuracy. You do not have to answer any questions you don’t want to and you can
stop the interview at any time. During the interview, you will be asked for permission to observe
a course session. Permission to be observed is not a requirement to participate in the interview and
is voluntary for the second part of the study.

CONFIDENTIALITY
Any identifiable information obtained in connection with this study will remain confidential. Your
responses will be coded with a false name (pseudonym) and maintained separately. The audio-
tapes will be destroyed once they have been transcribed. Two copies of the data will be stored on
a password-protected laptop and in a secured cloud-based backup location. At the completion of
the study, direct identifiers will be destroyed and the de-identified data may be used for future
research studies. If you do not want your data used in future studies, you should not participate.

The members of the research team and the University of Southern California’s Human Subjects
Protection Program (HSPP) may access the data. The HSPP reviews and monitors research studies
to protect the rights and welfare of research subjects.

INVESTIGATOR CONTACT INFORMATION
If you have any questions or concerns about the research, please feel free to contact Carlos
Montoya at cgmontoy@usc.edu or at (559) 301-0822.
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 163

IRB CONTACT INFORMATION
If you have questions, concerns, or complaints about your rights as a research participant or the
research in general and are unable to contact the research team, or if you want to talk to someone
independent of the research team, please contact the University Park Institutional Review Board
(UPIRB), 3720 South Flower Street #301, Los Angeles, CA 90089-0702, (213) 821-5272 or
upirb@usc.edu.

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 164
APPENDIX E
Sample Post-Training Survey Items Measuring Kirkpatrick Levels 1 and 2
Instructions: Please complete the following survey to the best of your ability. The survey will
provide the training facilitator and the college with important data to analyze the effectiveness of
the training workshop and areas that can be improved. Your feedback is valuable to make sure
the workshop is reaching its intended goals and aspirations. Thank you.

The following questions will utilize a scale, please indicate on the scale if you Strongly Disagree,
Disagree, Agree, or Strongly Agree with the item.

1. The training workshop held my interest. (L1: Engagement)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
2. What I learned from this training will help me teach intermediate algebra for statistics.
(L1: Relevance)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
3. I will recommend this training to other math faculty. (L1: Customer Satisfaction)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
4. I know the goal of the intermediate algebra for statistics course. (L2: Declarative
Knowledge)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
5. I understand that course preparation, goal setting, and student follow-up are valuable to
teaching intermediate algebra for statistics. (L2: Attitude)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 165
6. I feel confident about applying what I learned today to teaching intermediate algebra for
statistics. (L2: Confidence)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
7. I am committed to applying what I learned to teaching intermediate algebra for statistics.
(L2: Commitment)
a. Strongly Disagree, Disagree, Agree, Strongly Agree

Open -ended questions

8. What were the major concepts you learned today? (L2: Declarative Knowledge)
9. How do you plan to apply what you learned today to teaching intermediate algebra for
statistics? (L2: Procedural Skills)

IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 166
APPENDIX F
Sample Delayed Blended Evaluation Survey Kirkpatrick Levels 1, 2, 3, and 4
Instructions: Please complete the following survey to the best of your ability about the training
workshop on teaching intermediate algebra for statistics that you attended at the beginning of the
school year. The survey will provide the training facilitator and the college with important data
to analyze the effectiveness of the training workshop and areas that can be improved. Your
feedback is valuable to make sure the workshop is reaching its intended goals and aspirations.
Thank you.

The following questions will utilize a scale, please indicate on the scale if you Strongly Disagree,
Disagree, Agree, or Strongly Agree with the item.

1. The training information has been applicable to teaching intermediate algebra for
statistics. (L1: Reaction)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
2. Looking back, the training workshop provided me with a valuable learning experience.
(L1: Reaction)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
3. After the training, I was able to teach math curricula in intermediate algebra for statistics.
(L2: Learning)
a. Strongly Disagree, Disagree, Agree, Strongly Agree
4. I have successfully applied what I learned in the training workshop to teach intermediate
algebra for statistics. (L3: Behavior)
IMPLEMENTATION OF INTERMEDIA TE ALGEBRA FOR STATISTICS 167
a. Strongly Disagree, Disagree, Agree, Strongly Agree
5. I am already seeing positive results from applying what I learned. (L4: Results)
a. Strongly Disagree, Disagree, Agree, Strongly Agree

Abstract (if available)

Abstract This dissertation study examined the factors that influence the ability of math faculty at a local community college to implement a new intermediate algebra for statistics course designed to improve the math remediation pathway. A gap analysis framework was used to identify the knowledge, motivation and organizational influences found in the literature. The methodology used in this study included literature reviews, interviews, classroom observations, and document analysis. The data collected were used to determine if a gap for each influence was validated, not validated, or unable to validate based on the findings. According to the findings, two validated gaps tied to the organizational culture were found. Findings indicate that parts of the organizational culture do not believe that underprepared students can complete math coursework. It was also found that the organization does not support a standard approach to improve math remediation. The findings were used to develop recommendations specific to the validated gaps found at the college. Recommendations include that the college create a place where faculty can refer to references and resources on student success data, effective pedagogy, and instructional tools. It was also recommended that the college facilitate faculty discussions to share and review approaches to improving student outcomes in math remediation to ensure curriculum alignment and increase faculty buy-in on student success. Additionally, a training framework was used to develop an implementation and evaluation plan to train additional faculty or used as a model for other institutions attempting to adopt a similar math remediation intervention.

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Asset Metadata

Creator Montoya, Carlos G. (author)

Core Title Examining the faculty implementation of intermediate algebra for statistics: An evaluation study

School Rossier School of Education

Degree Doctor of Education

Degree Program Organizational Change and Leadership (On Line)

Publication Date 02/24/2018

Defense Date 02/15/2018

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

Tag acceleration,community college,faculty,math,OAI-PMH Harvest,Statistics,teaching

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Sundt, Melora (committee chair), Hasan, Angela (committee member), Robles, Darline (committee member)

Creator Email carlosgmontoya@gmail.com,cgmontoy@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-479704

Unique identifier UC11267298

Identifier etd-MontoyaCar-6066.pdf (filename),usctheses-c40-479704 (legacy record id)

Legacy Identifier etd-MontoyaCar-6066.pdf

Dmrecord 479704

Document Type Dissertation

Rights Montoya, Carlos G.

Type texts

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

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA