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Community college students and achievement in mathematics: Predictors of success
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Content
COMMUNITY COLLEGE STUDENTS AND ACHIEVEMENT IN
MATHEMATICS; PREDICTORS OF SUCCESS
by
Jeffrey Michael Gervasi
A Dissertation Presented to the
FACULTY OF THE ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION
May 2004
Copyright 2004 Jeffrey M. Gervasi
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UMI Number: 3140474
Copyright 2004 by
Gervasi, Jeffrey Michael
All rights reserved.
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11
Dedication
I dedicate this dissertation in part to my wife Rebecca. God bless her for
putting up with my moods and absences throughout my four years at USC.
Without her love, patience, and support, I surely would not have been able to
complete such an undertaking. I have missed her dearly and I am looking forward
to the two of us returning to normal life.
I also dedicate this dissertation to my three sons Brandon, Evan, and
Curtis. Every day they make me proud to be their father and they fill my life with
a happiness I'm sure I have no right to expect.
Finally I dedicate this dissertation to my mom and dad both of whom
always drove home the importance of a college education. I hope they are proud
of their boy.
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m
Acknowledgements
I would like to recognize the faculty who served on my dissertation
committee.
Thank you Dr. Linda Serra-Hagedom. Thank you for your friendship and
for serving as the chair of my dissertation committee. Your guidance and support
were so critical to the dissertation process and quite simply I could not have done
this without you. I could never be thankful enough.
Thank you Dr. Fran Newman. I wonder if you recall our very first
conversation over the telephone. It was that conversation that hooked me and your
enthusiasm for the Ed. D. program that reeled me in. I am a USC graduate
because of you.
Thank you Dr. Melora Sundt. Your insights and ideas gave me direction
during the writing process and your keen editing made my dissertation so much
more polished. Thank you for your time and effort.
Thanks also to the wonderful faculty at USC who made four years of
graduate school difficult but fun and always interesting. A special thanks to Dr.
Tom Garrison who reminded me why I became a community college professor in
the first place. He is merely the finest teacher I have ever had.
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IV
Table of Contents
Dedication ii
Acknowledgements iii
List of Tables V
Abstract vii
Chapter 1 Introduction 1
Chapter 2 Review of the Literature 18
Chapter 3 Research Methodology 44
Chapter 4 Results 53
Chapter 5 Summary and Discussion 88
Bibliography 115
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List of Tables
Table Page
1 Percentage of All Students who Attempted
Transfer Level Math Courses 53
2 Number Reporting Highest Math Course Taken 54
3 Classification of LACCD Math Courses 55
4 General Math Participation Ratios 56
5 Math Course Participation Ratios 58
6 Frequencies by Type of Success 60
7 Frequencies by Type of Success 61
8 Percentages Success Type for All Math
by Gender and Ethnicity 62
9 Percentages Transfer Success Type by Gender and Ethnicity 63
10 Percentages Remedial Success Type by Gender and Ethnicity 64
11 Descriptive Statistics for Math Completion Ratios 64
12 Group Descriptives for Transfer Completion Ratios 65
13 Group Descriptives for Remedial Completion Ratios 66
14 Items and Scales Used in the Model 68
15 Means and Standard Deviations for Independent Variables 75
16 Regression Correlation Coefficients for Math Completion Ratios 76
17 Regression Model Summary for Total Math Completion Ratios 79
18 Summary of Regression Analysis for Variables Predicting
Total Math Course Completion Ratios 80
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VI
19 Regression Model Summary for Transfer Math
Completion Ratios 82
20 Summary of Regression Analysis for Variables Predicting
Transfer Math Course Completion Ratios 83
21 Regression Model Summary for Remedial
Math Completion Ratios 85
22 Summary of Regression Analysis for Variables Predicting
Remedial Math Course Completion Ratios 86
23 Number of Students Taking Various Levels of
Math by Semester page 99
24 Cross Tabulation of Students by Highest Math Course Taken 103
25 Number of Students Completely Successful in Transfer
Math by Gender and Ethnicity 107
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V ll
Abstract
A large majority of college degree programs and majors require students
to take courses in the mathematical sciences; consequently enrollments in
mathematics courses are among the highest of any subject. Even so, the
withdrawal and failure rates in math courses are higher than in most other courses
(Adelman, 1999b; Gold, Keith, & Marion, 1999). Failure in mathematics can
restrict students’ choices of majors and later career paths (Waits & Demana,
1988). Presently, relatively little is known about factors related to low
achievement in mathematics (Oakes, Ormseth, Bell, & Camp, 1990). Research
has shown that gaps in achievement levels between males and females and
between white, African-American, and Hispanic students are narrowing yet still
persist. This study seeks to determine the factors that predict students’
achievement in mathematics. Specifically, this study investigates the relationship
between cognitive and non-cognitive variables and achievement in urban
community college mathematics.
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CHAPTER 1
Introduction
The successful completion of one or more mathematics courses is
necessary for the fulfillment of general postsecondary education studies (Mittag &
Mason, 1999; Meeker, Fox, & Whitley, 1994), for associate’s degree completion,
certificate completion, transfer to four-year colleges and universities, and
bachelor’s degree completion. In a broader sense, many careers and academic
disciplines depend on success in mathematics (Occupational Outlook Handbook,
2001). Mechanics make use of geometry to adjust belts and tolerances, engineers
specializing in computer aided drafting must be able to bridge the gap between
two-dimensional drawings and the three-dimensional real world, and today’s
elevator engineers use “fuzzy logic” to design cars that move between floors more
efficiently (Forman & Steen, 2002). As these and other technologies advance,
they usually bring with them the expansion of applications of mathematics,
creating the need for a mathematically literate workforce (Occupational Outlook
Handbook, 2001). Indeed “the need to understand and be able to use mathematics
in everyday life and in the workplace has never been greater and will continue to
increase” (National Council of Teachers of Mathematics, 2000). The capacity to
think and reason mathematically promotes “confidence in dealing with data,
skepticism in analyzing arguments, persistence in penetrating complex problems.
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and literacy in communicating about technical matters” (Tobias, 1987, p. xviii).
To meet these challenges, community colleges offer mathematics education to
prepare students for employment, for further study in mathematics and math-
related fields, and for a fast changing world economy (Forman, 1995).
Statement of the Problem
In most institutions of higher education, mathematics is perhaps the most
critical academic program. A large majority of degree programs and majors
require students to take courses in mathematics consequently enrollments in
mathematics are among the highest of any other subject (Gold, Keith, & Marion,
1999). The problem however is that the withdrawal and failure rates in math are
also higher than those of most other courses (Adelman, 1999b; Gold, Keith, &
Marion, 1999) and little research exists to explain why (Oakes, Ormseth, Bell, &
Camp, 1990). A number of studies conducted analyzed trends and national data
sets to explore math achievement among elementary and secondary school
students. For example, according to the Nation’s Report Card Mathematics 2000
(U.S. Department of Education, 2001c), the gap in mathematics achievement
levels between fourth, eighth, and twelfth grade males and females while
relatively small still remains; similarly the gap in mathematics achievement
between fourth, eighth, and twelfth grade white, African-American,
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and Hispanic students is large and shows no evidence of narrowing over the last
ten years (U.S. Department of Education, 2001c; Education Trust, 2002). On the
other hand, gender and racial gaps in mathematical sciences and engineering
related postsecondary education have narrowed among students with similar
attributes such as those who have taken advanced math and science courses in
high school, possess high self-motivation to study math and science, and have
parents with higher levels of education and expectations. Researchers have
suggested that remaining differences between student groups are based on certain
factors that require further investigation (Nettles, 1999; U.S. Department of
Education, 2000a). Failure to succeed in mathematics can limit the choices
available to those students considering college and career decisions. Indeed
mathematics is often seen as a gatekeeper to scientific and technical academic
programs and occupations (National Research Council, 1995) and a barrier
(especially for minorities) to success in college. Furthermore, research has shown
that success in math is actually a predictor of success in college (Adelman,
1999a).
Purpose of the Study
Early studies have explored the relationship between cognitive variables
(for example scores on college entrance exams and previous math and science
courses taken in high school) and subsequent performance in college
mathematics. The results have consistently shown that differences in math
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achievement exist between males and females and between students of color and
white students (Nowell, 1998; Tate, 1997). In an effort to explain these
differences, Reyes and Stanic (1988) proposed a model of student achievement in
mathematics which suggested that non-cognitive variables such as student
attitudes about their academic ability, their expectations of success, and their
achievement-related behaviors (persistence in math courses for example) effect
their subsequent mathematical achievement. Research is necessary to test the
authors’ claim however (Reyes & Stanic, 1988). Relationships between non-
cognitive variables and measures of academic performance have been examined
but the studies were primarily conducted using elementary, middle, and high
school students (House, 1992). Few studies have examined the relationship
between non-cognitive variables and achievement in college mathematics (House,
1995b) and those that have were conducted at four-year colleges or universities
using samples of traditional-aged college students; even fewer investigated the
relationships between these variables for students of color. Furthermore, a
literature search turned up no studies that simultaneously examined cognitive and
non-cognitive variables as predictors of achievement in mathematics for students
enrolled in community colleges. The purpose of this study is to determine whether
cognitive and non-cognitive variables have any predictive value for urban
community college students’ success in mathematics. A secondary purpose of this
study is to determine if the predictive relationships between non-cognitive
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variables, cognitive variables, and success in mathematics remain constant for all
groups of students i.e. males, females, white students, African-American students,
Hispanic students, remedial math students and non-remedial math students.
Significance of the Study
California community colleges require the successful completion of
mathematics at a level equal to that necessary for the high school diploma in order
to fulfill the requirements for the associate’s degree (Academic Senate for
California Community Colleges, 2003). Generally this means California
community college students must pass elementary algebra (California Education
Code, 2003) to graduate. It should be noted that presently many California high
schools require intermediate algebra for the diploma and may soon raise the
requirement to trigonometry (Academic Senate for California Community
Colleges, 2003). As a result, the California Mathematics Council of Community
Colleges recommended to the Academic Senate for California Community
Colleges in 2002 that the requirements for the associate’s degree be raised to
include at least one college-level math course such as college algehra, statistics,
finite mathematics, or pre-calculus (Academic Senate for California Community
Colleges, 2003). A decision on raising the mathematics requirement for the
associate’s degree is currently pending. For those community college students
interested in attending any of the schools in the University of California (UC)
system or the Califomia State University (CSU) system, completion of the
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Intersegmental General Education Transfer Curriculum (IGETC) program of
courses can be used to fulfill lower-division general education requirements for
either the UC or CSU system. The IGETC program requires the successful
completion of at least one college level math course, typically statistics or higher.
For those students ineligible for admission to the UC system right after high
school because of poor academic performance, 60 semester units or 90 quarter
units of transferable college credit must be completed and of these units, 3
semester units or 4-5 quarter units must be in a college level math course
completed with a grade of C or better. Finally, mathematics is required in nearly
every university and college as part of the general education requirement
(Hagedom, Moon, Cypers, Maxwell, & Lester, 2003). Determining the factors
that predict students’ achievement in mathematics is worthy of our consideration
as many students fail or drop out of college math courses, more so than any other
academic discipline. Continued failure may perhaps compromise the nation’s
place in an expanding global society that is increasingly reliant on mathematical
sciences, technology, and complex problem solving.
The results of this study may aid administrators and faculty in determining
and developing appropriate mathematics curricula and programs designed to
maximize students’ success in mathematics.
Finally it should be noted that little research exists on urban community
college students (Bowen & Muller, 1999; Mason, 1998). We do know that many
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7
urban community college students live in poverty, many are poorly prepared for
college (National Center for Education Statistics, 1997) and/or are first-generation
college students (Rendon, 1994), some are recent immigrants and thus are not
proficient in the English language, and many come from minority groups and
historically underrepresented populations (Smith & Vellani, 1999). Minority
populations continue to grow (Smith & Vellani, 1999) and as a result will
represent a larger share of the workforce (Madison & Hart, 1990) in need of a
college education. This study will contribute to the limited research on urban
community college students and possibly lead to the expansion of such research
directly.
Research Questions
1. What is the predictive relationship between cognitive and non-
cognitive variables and achievement in urban community college
mathematics?
a. When cognitive and non-cognitive variables are considered
simultaneously, are non-cognitive variables predictive of
the outcomes of measure for student success?
2. Are the predictive relationships between cognitive and non-
cognitive variables and success in mathematics similar for all
groups of students, males, females, white students, African-
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American students and Hispanic students? In other words, are the
equations similar for all groups?
3. Are the predicative relationships between cognitive and non-
cognitive variables and success in mathematics similar for
remedial level math courses versus transfer-level math courses?
Urban Community Colleges
In order to address the research questions, data from the Transfer and
Retention of Urban Community College Students (TRUCCS) project will be
subjected to secondary analyses to be described in chapter 3. The TRUCCS
project, funded by the Field Initiated Studies (OERl R305T000154) and the
Lumina Foundation, is a five-year longitudinal study of approximately 5,000
community college students in urban Los Angeles. Data were collected from
students across nine campuses comprising the Los Angeles Community College
District (LACCD). The TRUCCS project seeks to advance new definitions of
achievement that are more consistent and applicable to urban community college
students and the present study will add to that new knowledge.
Briefly, urban communities are characterized by excessive unemployment,
minimal education on the part of its citizens, racial/ethnic and linguistic diversity,
and a high percentage of recent immigrants (Oromaner & Fujita, 1993). Examples
include New York City, Chicago, and Los Angeles. Situated within or very near
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such communities, urban community colleges have been described as “gateways
to democracy” (Bowen & Muller, 1999, p. 2) because they provide citizens access
to higher education that might otherwise he denied to them at other institutions
and they train students in the skills necessary for upward mobility in society
(Bowen & Muller, 1999; Hirose-Wong, 1999; Smith & Vellani, 1999). Often
urban community colleges serve as the last chance for many students if for no
other reason than the community colleges’ open-door philosophy (Cardenas &
Warren, 1991; Nielsen, 1991; Smith & Vellani, 1999).
Community colleges in general enroll nearly half of all African-American,
Native-American, and Hispanic college students (Kim, 2002; Littleton, 1998;
Saunders & Bauer, 1998). Indeed more than half of the students at community
colleges in New York, Chicago, and Los Angeles typically consist of “majority
minorities” (Smith & Vellani, 1999, p. 6), which is generally the case for most
urban community colleges (Smith & Vellani, 1999). Too, African-American,
Hispanic, and low-income students tend to be clustered in urban schools (Oakes,
Ormseth, Bell, & Camp, 1990). The LACCD represents an excellent example.
The Los Angeles Community College District is comprised of nine
community colleges: Los Angeles City College, East Los Angeles College, Los
Angeles Harbor College, Los Angeles Mission College, Pierce College, Los
Angeles Southwest College, Los Angeles Trade-Technical College, Los Angeles
Valley College, and West Los Angeles College. For the fall 2001 semester.
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10
Hispanic students represented almost half of the entire LACCD population, with
49.9% or 53,804 students enrolled in courses. In the spring 2002 semester, the
total number of Hispanic students declined by almost 6%, however there was an
overall decrease in enrollment across all racial categories. The campus with the
highest total percentage of Hispanic students was East Los Angeles, where more
than three quarters of the population were of Hispanic descent (76% percent in
fall 2001). At Los Angeles Southwest College, more than three quarters of the
population were African-American (77.5%). White students comprised the next
highest total percentage of students in the district for both recent semesters:
20.4%, or 24,276, in fall 2001, and 19.5%, or 23,629, in spring 2002 (with
African-American students not far behind: 16.9% and 16.2%, respectively). At
Pierce College, white student percentages far outweighed the number of students
in other categories: 43.9%, compared to Southwest, where only 0.6% of students
were white. Nevertheless, more students at Southwest spoke English than at any
other LACCD campus (roughly 85%) so one must be careful not to equate the
presence of a large white population with the presence of a large population for
whom English is a native language; often, white students represent immigrant
populations for whom English is a third or even fourth language. Finally, Asian
students represented the smallest total population in the LACCD for the 2001-02
academic year: roughly 14%, or 16,500. What distinguishes the Asian population
from other student racial groups, however, is that their numbers are somewhat
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more evenly distributed across the LACCD campuses; only at Southwest are they
underrepresented, where we find that 96% of the enrolled population is either
African-American or Hispanic
(http://research.laecd.edu/research/digest/SummrvFl.htm. 2002).
The Los Angeles County Area
Ethnic composition
According to the U.S. Department of Census 2000, there are over 9.5
million people living in Los Angeles (LA) County. Approximately 45% are
Hispanic, 31% percent are white, 13% are Asian, and 9% are African-American
(U.S. Department of Census, 2000a). Interestingly, neither Hispanic nor Latino is
considered a race by the Census. Rather, each is a cultural or ethnic classification
that overlaps with race. Persons who identify themselves as “Hispanic or Latino”
must also identify themselves with a race or combination of races. A large
number of these persons identify themselves with the racial classification “white.”
A column titled “White (Not Hispanic or Latino)” has been added to the census
survey.
Gender and Age
In LA County, 49.4% of the population are male. The median age for the
county is 32. However, 72% of the entire population are 18 years of age and over.
Of that grouping, 35.1% are males (U.S. Department of Census, 2000b).
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Languages
The Census reveals that English is the only language spoken in 45.9% of
the households in LA County. Of the remaining population, approximately 37.9%
speak Spanish, 10% speak Asian and Pacific Island languages, and 5.2% speak
other Indo-European languages (U.S. Department of Census 2000c).
Immigration
From 1998 to 1999, twenty percent of all legal immigrants resided in
either New York or Los Angeles. Further, as of 1998, 35.3% of all of Califomia’s
legal immigrants resided in Los Angeles County that year. In addition, over half
of all foreign-bom persons in LA County in 1990 entered the U.S. between 1980
and 1990. This contributes to a considerable number of first generation students in
Los Angeles (Los Angeles Almanac, 2002b). According to the U.S. Immigration
and Naturalization Service, approximately 2 million illegal or undocumented
residents reside in Califomia. The growth rate is estimated at about 100,000 per
year, since 1988. Most of these immigrants are expected to have arrived from
Mexico. Finally, the greatest percentage of undocumented immigrants is believed
to reside in Los Angeles County (Los Angeles Almanac, 2002b).
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Socioeconomic Status
Household Income. According to the 2000 Census, the median household
income is $42,189 in Los Angeles County. Households earning less than $25,000
a year represent 30% of the population. Twenty-seven percent of the households
earn between $25,000 and $50,000, 18% earn between $50,000 and
$75,000, 10% earn between $75,000 and $100,000, and 15% earn more than
$100,000 (U.S. Department of Census 2000d).
Poverty. More than 17% of the population are living below poverty level
(U. S. Department of Census, 2002d). Census data reveals that of those in
poverty, 56% are female. The ethnic rundown of those in poverty is the
following; 67% are Hispanic, 13% are White, 10% are African American, 9% are
Asian/Pacific Islander and less than 1% is Native American (Los Angeles
Almanac, 2002a). The Los Angeles institutional research website stated that the
poverty level in 1998 was defined as having an income of $8,050 or less for one
person, $10,850 or less for two people, $13,650 for three people, and $16,450 for
four. These numbers are refigured each year based on the cost of living and the
fact that poverty rates vary over time and move with general economic conditions.
The proportion of the population living below the poverty level in Califomia has
increased by over 34% between the 1990 Census and the 1996-97 periods (Los
Angeles Community Colleges Institutional Research and Information, 2002).
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Assumptions
For this study, the following assumptions are made;
1. The measures are reliable and valid indicators of the constructs being
studied.
2. The data will be accurately recorded and analyzed.
3. The subjects will be assessed in a quiet, controlled atmosphere.
4. The subjects will respond to the best of their ability.
5. The purposes, processes, and elements of the framework studied have
a degree of applicability and generalizability to the population of urban
community college students.
6. The research, data gathering, and conclusions of the study represent
“good research.”
Limitations
1. This study is limited to subjects who agree to participate voluntarily.
2. The scope of this study is limited to urban community college students
in the LACCD.
3. Findings will be generalized to urban community colleges only.
4. The data used for this study came from a structured survey instrument
and student transcripts received from the LACCD. Results will be
based on a quantitative design.
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Delimitations
1. Participants for this study were those attending one of the nine
LACCD colleges.
2. The effects to be studied are cognitive and non-cognitive variables
related to achievement in community college mathematics.
3. This study will focus only on students’ achievement in mathematics at
the community college level.
Definition of Terms
The following terms are presented and defined so as to clarify their
meaning and to operationalize their usage and interpretation in a consistent
manner throughout this study.
Academic Self-concept: A person’s conception of his or her own ability to learn
and perform an expected academic behavior that would lead to successful school
achievement (Brookover, Thomas, & Paterson, 1964).
Achievement-related expectancies: These are students’ expectancies of their
future academic performance (Vollmer, 1986), and they are typically measured by
self-ratings of the probability of earning passing grades; attaining a certificate, a
two or a four-year degree or higher; of graduating with honors; or of transferring
to a four-year institution.
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Cognitive variables: Cognitive variables are those that reflect factors such as
aptitude or achievement and typically include such items as standardized tests,
high school grade point average, and the number and type of math and science
courses taken in high school.
Non-cognitive variables: Sedlacek and Brooks (1976) defined non-cognitive
variables as those that reflect factors other than aptitude or achievement and
include a positive academic self-concept, high self-confidence in one’s
intellectual abilities, a realistic self-appraisal, and a preference for making long-
range goals.
Remedial math courses: Math courses are defined as remedial if they are termed
by the LACCD student information systems directory as compensatory and
developmental, pre-collegiate, adult elementary and secondary basic skills, or
basic skills. Often these courses are below the level of trigonometry and pre
calculus.
Organization of the Study
Chapter 1 begins with an introduction followed by the statement of the
problem; the purpose and significance of the study; the questions to be answered;
descriptions of urban community colleges, the Los Angeles County area, and the
Los Angeles Community College District; the assumptions, limitations, and
delimitations; and definitions of select terms.
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Chapter 2 is a review of recent literature to include the following topics:
(a) an introduction outlining the need for mathematics, (b) mathematics
considered from different points of view, (c) research studies and important
variables related to mathematics achievement, and (d) a brief conclusion.
Chapter 3 presents the methodology used in the study including
descriptions of the sample, the variables, and the data collection procedures. Also
included in this chapter are the methods of analysis of the data.
Chapter 4 presents the results of the study. Included in this chapter are
descriptions of the variables used in the study, results of statistical analyses, and
tables.
Chapter 5 presents a summary of the study. In addition this chapter
includes a discussion of the results and their implications.
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CHAPTER 2
Review of the Literature
This chapter provides a brief review of the literature about the variables
associated with achievement of community college students, specifically in
mathematics. Topics presented are (a) an introduction outlining the need for
mathematics, (b) mathematics considered from three different points of view, (c)
important variables related to mathematics achievement, and (d) a brief
conclusion.
Making the Case fo r Mathematics
Most degree-seeking students entering postsecondary education are
expected to take courses in mathematics either as part of a program of general
education requirements, or as part of a major degree program in mathematics or a
math-related field. Math courses also form the foundation for further study in
other fields such as the social sciences, agriculture, management, economics,
finance, or business (Tobias, 1987). Accordingly, the enrollments in math courses
are among the highest of any subject (Gold, Keith, & Marion, 1999). Interestingly
the withdrawal and failure rates in math courses are higher than in most other
courses (Adelman, 1999b; Gold, Keith, & Marion, 1999) leading to more student
frustration and dropout than in any other single academic department (Gold,
Keith, & Marion, 1999). Despite the reputation of being complex and difficult to
understand, mathematics is actually the most elementary academic program
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19
offered on most college campuses (Education Trust, 2002). Haycock (Education
Trust, 2002) found that the fastest growing part of the high school curriculum
over the last 20 years was in advanced placement (college level) courses yet over
the same time span the fastest growing part of the college mathematics curriculum
was in remedial or high school level courses. Indeed, courses once thought to be
traditional college level math courses (calculus and above) today account for less
than 30% of the math enrollments in higher education (Loftsgarden, Rung, &
Watkins, 1997).
After examining the state of mathematics education in the nation almost
15 years ago, the National Academy of Sciences concluded that America was at
risk of becoming economically and racially divided by knowledge of mathematics
(National Research Council, 1989). One year later, the nation’s govemors joined
together to establish a set of national goals making the improvement of math and
science achievement of paramount importance and declaring that by the year
2000, the United States would be first in the world in math and science
achievement (Education Trust, 2002). Ten years later the number of bachelor’s
degrees in mathematics actually declined by 20% (Education Trust, 2002). The
Third International Mathematics and Science Study (TIMSS), the largest, most
comprehensive, and most rigorous international comparison of education ever
undertaken, tested the math and science knowledge of a half-million students
from 41 nations at five different grade levels (National Center for Education
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2 0
Statistics, 1996). Results from the TIMSS study revealed that in mathematics,
U.S. eighth graders scored below the international average of the 41 TIMSS
countries and the content taught in U.S. eighth-grade mathematics classrooms was
at a seventh-grade level in comparison to other countries. In addition, according to
The Nation’s Report Card Mathematics 2000, a more recent report from the
National Center for Education Statistics (U.S. Department of Education, 2001c),
• 31% of America’s fourth graders were not able to complete a bar
graph; had difficulty shading a region so as to represent a fraction;
and could not identify which of four objects was heaviest.
• 34% of America’s eighth graders could not display data on a bar
graph; were unable to determine the exact change due back from a
purchase; and had difficulty finding the area of geometric figures.
• 35% of America’s twelfth graders had difficulty finding the
perimeter of a figure; were unable to place a dot on a number line
to represent a given fraction; and were unable to determine the cost
of renting a car given the day and mileage charges.
Kati Haycock of the Education Trust (2002) reasoned that the poor mathematical
performance of the nation’s students and the decrease in bachelor’s degrees in
mathematics could create a damaging domino effect whereby the shortage of
bachelor’s degree recipients in mathematics would lead to a shortage of
mathematically proficient teachers thus hindering efforts to raise student
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2 1
achievement in mathematics, -which in turn could lead to fewer students entering
college with plans to study mathematics or math-related fields, leading to an even
shorter supply of math majors, especially math majors interested in becoming
teachers, and so on.
The poor performance of the nation’s students in mathematics has been
followed by an increase of students entering institutions of higher education
underprepared for college level work (Hoyt & Sorenson, 2001) with more of them
taking courses in remedial mathematics than any other remedial subject (Lazarick,
1997; Southern Regional Education Board, 2000). Indeed, according to the
American Mathematical Association of Two-Year Colleges (AMATYC, 1999),
the nation’s postsecondary institutions have been annually experiencing greater
numbers of students enrolling in remedial math courses; courses that also have the
highest rates of failure, withdrawal, incompletes, and no-credit repeats than any
subject (Adelman, 1999b). It should be noted that other than studies that involve
analyses of trends and national data sets (Stage & Kloosterman, 1995), very little
evidence confirms that remedial mathematics successfully prepares students for
college-level mathematics (Wepner, 1987). Briefly, Penny and White (1998)
found that students who took remedial math from full-time instructors performed
better in college algebra than students who took remedial math from part-time
instructors but the strongest predictor of success in college algebra was the
performance in the last remedial math course. Only one study was found that
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examined the effectiveness of remedial mathematics in the community college.
Way caster (2001) studied remedial math courses in the Virginia Community
College System (made up of five different campuses) and found that in most
cases, students who had taken a remedial math course did as well as or better in
the subsequent college-level course than students who placed into the course
directly. Further, the retention rates for remedial students ranged from 62% to
81% across the five colleges over the time period from fall 1997 through spring
2000 whereas the retention rates for non-remedial students ranged from 42% to
62% over the same time period (Waycaster, 2001). The faculty involved in the
study argued that extra attention, counseling, advising, and monitoring of
students’ progress, as well as smaller class sizes, contributed to the higher level of
retention for developmental students. Finally, Waycaster (2001) examined the
proportions of graduates from the five colleges over the time period from 1993-94
to 1998-99 who took remedial courses and found that over 40% had taken some
remedial courses in their program of studies.
What are the effects of remedial mathematics on community college
students? The results of Waycaster’s (2001) study, though persuasive, do not
represent sufficient evidence to answer this question and the remaining body of
research on remedial education is silent on this issue. In addition, remedial
education has rarely been explored within the student persistence literature as a
factor that influences persistence (Easterling, Patten, & Krile, 1998), therefore this
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23
is an important area for further research. Remedial math courses “hold the
promise of opening new paths to future leaming and fulfilling careers”
(AMATYC, 1999, p. viii) for remedial students and therefore further research into
the effects of such courses is warranted, especially given that the need for such
remediation is so high. Further investigation is recommended to determine the
effects of remedial mathematics on students at the community college level
including progress of remedial program completion, time-to-completion, and the
factors that predict success in such courses.
Mathematics as gatekeeper. Mathematics often functions as a gatekeeper
to scientific and technical programs and occupations (National Research Council,
1995) and to postsecondary degrees in general. To be sure, a firm understanding
of mathematics is necessary for the study of physics, engineering, economics, and
other math-related fields but in addition it prepares one for dealing with real-
world problems, deriving solutions to those problems, formulating alternatives,
and realizing the consequences of the solutions and alternatives (Tobias, 1987).
Failure to succeed in mathematics effectively closes the door on interesting and
exciting academic majors and career opportunities for many students (Waits &
Demana, 1988) and impairs their ability to cope with the demands of a
technologically sophisticated society (National Research Council, 1989; Tobias,
1987).
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Mathematics as a barrier to success. In addition to being a gatekeeper to
academic programs and career opportunities, mathematics also acts as a barrier to
educational success especially for urban minority students who are more likely to
have insufficient academic backgrounds to prepare them for college level work
(Gainen, 1995; U.S. Department of Education, 1997c). Urban community college
students with poor academic backgrounds are often casualties of (a) racial/ethnic
prejudice and discrimination (College Board, 1999) that can lead to placement in
low-track math and science classes in high school (Oakes, Ormseth, Bell, &
Camp, 1990) and (b) attending high schools that either offer no college
preparatory curriculum (Littleton, 1998) or provide little opportunities to take
high-level advanced placement math courses (National Policy Summit, 2001;
Pema, 2002).
Mathematics as predictor o f success. An analysis of the data from the
National Educational Longitudinal Study by the U. S. Department of Education
(1997c) led to the conclusion that high school students who take algebra,
geometry, and other rigorous math courses are more likely to go on to college.
Specifically, 83% of students who took algebra 1 and geometry went on to college
within two years of completing high school whereas only 36% of students who
did not take algebra 1 and geometry went on to college after high school (U. S.
Department of Education, 1997). Similar results were discovered by Choy, Horn,
Nunez, and Chen (2000) after they analyzed data from the National Educational
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2 5
Longitudinal Study of 1988 and data from subsequent follow-up surveys in 1990,
1992, and 1994. In particular, these researchers found that taking algebra in eighth
grade was strongly associated with taking advanced math courses in high school
which in turn was found to be strongly associated with a higher likelihood of
going on to college. Pelavin and Kane (as cited in Tate, 1996) found, in their
analysis of the National Center for Education Statistics High School and Beyond
Survey data, that when minority students took advanced level math courses in
high school, they went on to attend and be successful in college at about the same
rates as white students. Moreover the researchers reported that even though more
white students than African-American or Hispanic students attended college
within four years of graduating from high school, this difference was mitigated
among those students who took geometry. Finally, in an effort to determine what
contributed most to bachelor’s degree completion, Adelman (1999b) examined
data from the High School and Beyond Sophomore cohort files and transcript
records of students from the time they were in the tenth grade in 1980 to about the
age of 30 in 1993. Adelman found that of all high school curricula, the highest
level of mathematics had the strongest continuing influence oii bachelor’s degree
completion. Further, Adelman found that completing a course beyond algebra 2
(such as trigonometry and pre-calculus) in high school more than doubled the
odds that a student who entered college would complete a bachelor’s degree.
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Presently the mathematical achievement of American students is
insufficient to sustain our nation’s place in a global technological society
(National Research Council, 1989; Tobias, 1987). Research has shown success in
mathematics to be a predictor of academic success in postsecondary education.
Consequently there is a sufficient need to determine the factors that contribute to
achievement in mathematics, the results of which may aid administrators and
faculty in determining and developing appropriate curricula and programs
designed to maximize students’ success in mathematics. The remainder of the
chapter is an explication of the relevant variables to be considered in the present
study along with the corresponding literature to indicate the line of reasoning used
for their inclusion.
Demographics
Age. Students attending community colleges are older than those attending
four-year institutions (U.S. Department of Education, 2002b). For example, in
1999-2000, 56% of undergraduates in their thirties and 63% of undergraduates 40
years old or older attended community colleges whereas 55% of undergraduates
between the ages of 19 and 23 were enrolled in four-year institutions (U.S.
Department of Education, 2002a). According to the LACCD institutional research
data base (2002), in fall 2001 half the LACCD student population was age 25 or
older. Adult students often have non-academic obligations that “educationalists”
(Richardson & King, n.d., p.69) believe may hamper one’s ability to study. For
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example adult students are more likely than younger students to have domestic,
financial, and employment commitments (Richardson & King, n.d.; U.S.
Department of Education, 2002b) leaving little time for attending to classes and
school work. Age is therefore an important factor to consider in this and other
studies of community college populations.
Gender differences. Disparities between male and female students
concerning mathematics achievement and attitudes about mathematics have been
noted in the literature. While differences in math achievement attributed to
cognitive factors still exist, they are declining, leading some researchers to
suggest that non-cognitive factors such as attitudes about mathematics and beliefs
about one’s academic ability influence persisting differences (Fennema &
Peterson, 1985; Leder as cited in Stage & Kloosterman, 1995). For example while
attitudes of females towards mathematics are similar to those of males in the early
years, they become more negative than those of males later on.
In 1990, 1992, and 1996, the National Center for Education Statistics
administered a national mathematics assessment of fourth, eighth and twelfth
grade students as part of the National Assessment of Educational Progress
(NAEP, which was also administered in 2000). In all three years, the percentage
of fourth grade females that agreed with the statement “I like mathematics” was
nearly the same as for males, 69% versus 71% respectively in 1990, 72% versus
71% in 1992, and 69% versus 70% in 1996. In grades eight and twelve those
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percentages begin to diverge with females less likely to agree with the statement.
In addition, at all three grade levels, females were less likely than males to agree
with the statement “I am good at mathematics” (U.S. Department of Education,
2000c), a phenomenon which continues into the college years (Sax, 1994).
Furthermore the literature has been fairly consistent in finding that females have
lower confidence in their math abilities than males (Greene, 1999). Such attitudes
may explain why females (a) are less likely than males to choose higher-level
math courses in high school (Meece, Wigfield, & Eccles, 1990), (b) take fewer
math courses overall than males (Magdalena & Suarez, 1985), and (c) avoid
majoring in math and science in college (U.S. Department of Education, 1997a).
This is especially troubling in light of previous observations, namely, that taking
advanced math courses in high school increases the likelihood of enrolling in
college.
Differences by ethnicity. While students of color have positive attitudes
towards mathematics in early grades, these attitudes have not resulted in high
mathematics achievement (Beane, 1985). Afriean-American and Hispanic
students enrolled in public schools have not reached the same achievement levels
in mathematics as their white counterparts as measured by such typical criteria as
standardized achievement tests, course grades, and enrollment in advanced math
courses (Valverde, 1984; Jones, Burton, & Davenport, 1984). For example,
according to the N AEP 2000 (U. S. Department of Education, 2001c) assessment
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of mathematics achievement of fourth, eighth, and twelfth grade students across
the nation, white and Asian/Pacific Islander students scored higher on average
than African-Ameriean and Hispanic students. The gaps in mathematies
achievement between these groups have shown no evidenee of narrowing over the
last ten years (U.S. Department of Edueation, 2001b; Edueation Trust, 2002). On
the other hand, racial gaps in mathematical sciences and engineering related
postsecondary education have narrowed among students but only insofar as they
exhibited similar attributes sueh as taking advaneed math and seience courses in
high school, possessing high self-motivation to study math and scienee, and
having parents with higher levels of education and expectations (Nettles, 1999;
U.S. Department of Education, 2000a), attributes that are not typically associated
with urban community college students.
Socioeconomic status (SES). Reyes and Stanie (1988) argued that SES (for
example the type of eommunity in which the student lives, parents’ level of
edueation, and parents’ oceupations) was an important factor to consider in any
research pertaining to aeademic aehievement because of the “disproportionate
number of minority group members who are low in SES and the disproportionate
number of majority group members who are high in SES.” (p. 26). Researehers
who do not consider SES as an important factor for community college students
may unintentionally eompare the aeademic achievement of eeonomically
disadvantaged African-Ameriean or Hispanic students with the academie
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achievement of economically advantaged white students (Yando, Seitz, & Zigler
as cited in Reyes & Stanic, 1988). According to the National Assessment of
Educational Progress mathematics trend assessments taken in 1978, 1982, 1986,
1990, and 1992, the average mathematics proficiency scores of all students living
in advantaged urban communities were higher than those of students living in
disadvantaged urban communities. Furthermore, using data from the 1992 second
follow-up of the longitudinal High School and Beyond survey. Green, Dugoni,
Ingels and Cambum (1992) found that the proportion of high SES students at the
low-proficiency level in mathematics (8.6%) was lower than that of medium SES
students and low SES students (25.1%, and 46.1% respectively). Green et al.
(1992) also found a strong relationship between parents’ level of education and
mathematics proficiency using the same data. Specifically, as parents’ level of
education increased, so did the proportion of their children who demonstrated a
high mathematics proficiency score while the proportion of students
demonstrating a low proficiency score decreased as their parents’ education
increased. Finally Hagedom, Siadat, Fogel, Nora, and Pascarella (1999) found
that students placed in remedial math courses were more likely to come from
families with lower incomes and educational levels, receive less encouragement
to go to college than those students that placed in non-remedial math courses, and
to live in neighborhoods and attend high schools that were predominantly non
minority.
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Many urban community college students are first-generation college
students (Hirose-Wong, 1999; Rendon, 1994; Stovall, 2000) meaning that their
parents have attained at most a high school education (U.S. Department of
Education, 2001a) and as a result, their parents, like the students themselves, are
uninformed about college, course, and program selections (Cisneros, 1996).
According to the College Board (1999), educationally sophisticated parents are
more likely to assist their children early on by reading to their children at young
ages, seeking help and guidance early in diagnosing leaming disabilities, and
finding tutors if necessary from the time their children are in grade school through
the high school years. In contrast, parents of poor and minority students and first-
generation students often lack the education and skills necessary to help their
children with the same types of support and encouragement (Hom & Nunez,
2000; Mehan, Hubbard, Lintz, & Villanueva as cited in Jun & Tiemey, 1999).
Evidence suggests, however, that completing an advanced mathematics course in
high school helps to mitigate the disadvantages of first-generation students (U.S.
Department of Education, 2001a). For example, among 1992 high school
graduates whose parents did not attend college, 64% who completed an advance
math course beyond algebra 2 enrolled in a four-year college compared to 34%
who had completed math courses up to and including algebra 2 only (U.S.
Department of Education, 2001a) further adding to the endorsement of
mathematics as an agent of success.
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Background
Cognitive variables. Cognitive variables such as college entrance exam
scores, high school grades, and high school class rank have been found to be
associated with math and science achievement (House, 2000; Nora & Rendon,
1990). American College Testing (ACT) scores have been shown to be
significantly and positively correlated with students’ final grade point average in
college algebra (Kohler, 1973), calculus (Edge & Friedberg, 1991), finite
mathematics (House, 1995c), and introductory college chemistry (House, 1993d).
Ozsogomonyan and Loftus (1979) studied a sample of university freshmen
enrolled in general chemistry and determined that 35% of the variance in final
general chemistry grades was explained by math scholastic aptitude test (SAT-M)
scores, chemistry pretest scores, and high school chemistry grades. Similarly,
Craney and Armstrong (1985) found SAT-M scores, high school chemistry
grades, and scores on the American Chemical Society’s Toledo exam to be
positive predictors of grades in general college chemistry. Baron and Norman
(1992) found high school class rank and average achievement test scores
(measured by the mean of three College Entrance Examination Board
achievement tests) to be the strongest predictors of students’ cumulative grade
point average for a sample of university freshmen. House (1993d) found that the
number of years of high school math taken was a significant predictor of eaming a
passing grade in a university freshman introductory chemistry course. Lastly
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Tartre and Fennema (1995) studied certain cognitive and affective (non-cognitive)
variables and the mathematics achievement of students from grade six through
grade twelve and found that prior mathematics performance was the strongest
single predictor of subsequent mathematics achievement.
Except for the study by Tartre and Fennema, the samples in the
aforementioned studies were taken from traditional university freshmen and none
of the studies, Tartre and Fennema’s included, considered ethnicity in their
analyses. These types of exclusions are problematic when studying urban
community college students because, unlike their traditional four-year
counterparts, many of them are poorly prepared for college (National Center for
Education Statistics, 1997), and/or are first-generation college students (Hirose-
Wong, 1999; Rendon, 1994; Stovall, 2000), some are recent immigrants and thus
are not proficient in the English language, and many come from minority groups
and historically underrepresented populations (Smith & Vellani, 1999).
Many urban community college students, especially African-American
and Hispanic students, have been subjected to prejudice and discrimination
stemming from the belief that they are educationally inferior (Beane, 1985; Klein,
2000; Sanchez, 2000) resulting in lowered achievement expectations by their
teachers and counselors early in their academic careers (Beane, 1985; National
Policy Summit, 2001; U.S. Department of Education, 1998), no matter that they
may be academically equal to high-achieving white students (National Policy
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Summit, 2001). This is especially true in the area of mathematics (Oakes,
Ormseth, Bell, & Camp, 1990; Robinson, 1996). Often times, as a result of such
misconceptions, teachers and counselors discourage these students from taking
rigorous college preparatory courses in high school (Checkley, 2001; The College
Board, 1999; Klein, 2000). A study of data from the National Science
Foundation’s 1985-1986 National Survey of Science and Mathematics Education
(Oakes, Ormseth, Bell, & Camp, 1990) found that in schools where African-
American, Hispanic, and low-income students were the majority, these students
were often placed in low-track programs limiting their access to typical
mathematics courses that would prepare them for college. This may be a large
reason why students of color are often over-represented in remedial and low-level
high school math classes (U.S. Department of Education, 1996b). Furthermore,
Oakes et al. (1990) found that 67% of disproportionately minority high school
math classes were more likely to be judged as low-ability classes by their teachers
rather than as high-ability whereas more than 50% of disproportionately white
high school math classes were judged to be of high-ability versus just 10% for
disproportionately minority high school math classes.
In addition to being steered away from taking advanced math courses in
high school, academically prepared students of color may simply not have access
to such courses in the first place (Pema, 2000). Schools with majority minority
populations have more limited math and science curricula than schools dominated
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by white students (Gainen, 1995; Oakes, Ormseth, Bell, & Camp, 1990) and
research has shown access to such courses to decline as minority enrollments
increase (Oakes, Ormseth, Bell, & Camp, 1990).
Finally, urban community colleges enroll many students who are not
proficient in the English language (Ignash, 1992). Consider for example Los
Angeles County where 44.6% of the population is of Hispanic or Latino descent
and 3,330,935 people reported speaking Spanish at home (U.S. Census Bureau,
2003). Of this subpopulation, 32.4% reported that they spoke English “not well”
or “not at all” (U.S. Census Bureau, 2003). When juxtaposed against the tedious
college application process which often includes scheduling and taking college
entrance exams and filling out application and financial aid forms (Cabrera & La
Nasa, 2000), being of limited English proficiency can pose a formidable obstacle
to students’ initial access to college (Luna, 2002). Once in college, students with
limited English proficiency may find themselves placed in a number of remedial
reading and writing courses. Taking remedial courses however tends to increase a
student’s time-to-degree completion and/or goal completion (Adelman, 1999b) as
well as stress students’ and families’ financial resources (Legislative Analysts
Office, 2001; Payne & Lyman, 1998), perhaps forcing students to consider
leaving school. A report by the National Center for Education Statistics (U.S.
Department of Education, 2001b), found that students assigned to any remedial
reading course were less likely to complete a two-year degree compared to
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36
students who took two or fewer remedial courses in mathematics only (the rates
were 34% versus 45% respectively). Furthermore, among those students who
took any remedial reading, 67% of them also took remedial math and 42% of
them enrolled in three or more remedial courses (U.S. Department of Education,
2001b) lending support for the view that remediation can increase the time
necessary for students to reach their intended objectives because of the amount of
additional course work they face.
Non-cognitive variables. The relationships between non-cognitive
variables such as academic self-concept and achievement-related expectancies
and measures of academic performance in college have been examined. Academic
self-concept refers to a person’s conception of his or her ability to learn and
perform a given academic behavior that would lead to successful school
achievement (Brookover, Thomas, & Paterson 1964). Willemsen (1995)
explained that a positive self-concept “motivates persistent effort in the face of
possible frustration and it infuses the classroom experience with some quality that
both makes it more enjoyable and facilitates focus on the material” (p. 17). With
respect to math courses, this means that the student with a positive self-concept,
what Willemsen calls an T can’ attitude, has the expectation of eventual success
and mastery when initial attempts at problem solving fail (Willemsen, 1995).
Mathematics self-concept has been found to be a positive predictor of
mathematics-related educational and career choices (Hackett and Betz, 1989), of
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persistence in math (Sherman, 1980), and performance on tests of math
achievement (Astin, 1993). There is also ample evidence showing that overall
academic self-concept may be causally linked to academic achievement (Sax,
1994). Academic self-concept was found to predict achievement test scores of
elementary school students (Lyon & Macdonald, 1993), middle school students
(Lyon, 1993), and high sehool students (Lyon & Macdonald, 1990; Mboya,
1986). For example academic self-concept was found to be significantly and
positively related to the academic performance of seventh grade students, even
after controlling for IQ scores (Brookover, Thomas, & Paterson, 1964) although
the sample consisted of white students only. Similarly, for a sample of African-
American students ranging in age from 17 to 45 and enrolled in an adult education
class, academic self-concept was found to be significantly and positively related
to course grades (Mangieri & Olsen, 1977). Similar results were also found for
college students. Trippi and Stewart (1989) found that confidence in the ability to
prepare for tests and in reading ability were significant predictors of science
course grades for a sample of African-American university freshmen enrolled in
the fall semester of 1985 and 1986. The same researchers also found that
expectations of performing well academically during the first year of college and
confidence in understanding lectures were both found to be significant positive
predictors of persistence. In other words, African-American students who
expected to perform well academically during their first year of college and who
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expressed confidence in their ability to understand lectures were more likely to
persist than those not expecting to perform well nor expressing confidence in their
ability to understand lectures. Gerardi (1990) studied 98 minority and low SES
engineering students enrolled in one of the City University of New York (CUNY)
colleges to answer the research question: Is academic self-concept an important
and significant predictor of academic success (defined as students’ grade point
average after three semesters) among minority and low SES college students? Of
the four independent variables, high school grade point average (HSGPA), CUNY
math assessment test scores, CUNY reading assessment test scores, and academic
self-concept, only academic self-concept was significantly correlated (r = 0.57, p
< 0.01) with students’ grade point average after three semesters. In addition, a
multiple regression analysis indicated that academic self-concept was the only one
of the four predictor variables to enter the equation significantly with a beta value
of 0.582 compared to CUNY reading scores (P= 0.018), CUNY math scores (|3=
0.017), and HSGPA ((3= 0.016). Because the sample size was so small, the
results are quite limited in their generalizability to other student populations,
nevertheless the findings here are similar to the results of other studies and
warrant a replication using a larger sample to determine if findings would be
identical.
In an effort to examine the relationship between academic self-coneept,
achievement-related expectancies, and mathematics performance of academically
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39
underprepared students (all having similar SES backgrounds), House (1993a)
found that students with higher academic self-concept earned significantly higher
grades in college algebra but achievement-related expectancies (making at least a
B average ands graduating with honors) were not significant predictors, perhaps
because the students in the sample had unrealistic expectations for their success in
mathematics (House, 1993a). In a separate study of 484 new university freshmen.
House (1993c) found that students’ academic self-concept, expectations of
graduating with honors, and expectations of eaming at least a B average in college
were significantly correlated with eaming a passing grade in either biology or
geology. Furthermore, using multiple regression analyses to determine the best
predictors of course achievement for all students, males only, and females only,
academic self-concept was the only variable to enter the equations significantly.
The findings are limited in their generalizability to community college
populations since the sample was taken from only one institution and contained
only traditional-aged freshmen, and the researcher did not take into consideration
SES or ethnicity.
To study the predictive relationship between nine items measuring
achievement-related expectancies ( expectations of eaming at least a B average in
college, graduating with honors, failing one or more courses in college, needing
tutoring assistance, eaming a bachelor’s degree, needing extra time to eam a
degree, transferring to another college, dropping out of college temporarily, and
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4 0
dropping out of college permanently) and students’ cumulative grade point
averages after two, four, and eight semesters of college enrollment. House
(1993b) chose a sample of 2,480 new university freshmen all of which completed
their first two semesters, 1,964 of which completed four semesters, and 1,651 of
which completed eight semesters. Multiple regression analysis was used for the
entire sample and separately for males and females. House found that
expectations of earning at least a B average in college and graduating with honors
were the first two variables to significantly enter the regression equations for two,
four, and eight semesters when the entire sample was considered. House also
found gender differences, namely that expectations of needing tutoring assistance
significantly entered each multiple regression equation for females after two, four
and eight semesters but that item did not enter any of the equations for males. The
sample was taken from only one large Midwestern university, included only
traditional-aged university freshmen, and did not contain a sufficient amount of
minority students to explore any meaningful analyses all of which serve to limit
the generalizabilty of these results to community college students. For example,
expectations of dropping out of college temporarily, of dropping out permanently,
and of transferring to another institution did not enter any of the regression
equations for two, four, and eight semesters of work for all students, males
separately, and females separately and yet these are very real possibilities for
community college students. Indeed many community college students transfer
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41
(“drop out”) before completing a degree (Bean & Metzner, 1985), or enroll in
courses but do not complete them, perhaps planning to return later and finish
(Hagedom, Maxwell, Pickett, Moon, Brocato, & Sax, 2000), or they intend to
take only one or two courses without pursuing a degree (Bean & Metzner, 1985).
Similar results between self-concept variables, achievement-related
expectancies, and subsequent academic achievement were found for college
chemistry (House, 1994), calculus (House, 1995d), finite mathematics (House,
1995b), college composition (House & Prion, 1998), and cumulative grade point
average after one year in college (House, 1995a). Even so there is a dearth of
studies that examine the relationship between non-cognitive variables and
achievement in college mathematics (House, 1995b) and those that have were
conducted at four-year colleges or universities, used samples of traditional-aged
college students, and failed to investigate relationships between these variables
for minority students. Even fewer studies have simultaneously examined
cognitive and non-cognitive variables as predictors of math achievement even
though favorable results have been discovered. Eor example House (1995b)
investigated the predicative relationship between cognitive variables (high school
math course work and admissions test scores) and non-cognitive variables
(academic self-concept and achievement expectancies) and achievement in a
finite math course taken in the first year of college. Self-concept of math ability
was the most significant predictor of earning a passing grade and of eaming the
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4 2
highest possible grade. House (1995b) also found self-concept items to be better
predictors of success than the achievement expectancies and the number of years
of high school math taken. Hagedom, Siadat, Nora, and Pascarella (1997) studied
cognitive and non-cognitive factors and math achievement and concluded that (a)
first-year gains in mathematics were best predicted by the student’s commitment
to completing a bachelor’s degree and enrollment in higher-level mathematics
courses, (b) women were more likely to achieve higher gains in math if they were
actively involved in campus activities whereas participation in fraternities had a
negative effect on math gains for men, and (c) full-time enrollment and high goal
commitment to complete the bachelor’s degree were especially important
predictors of math achievement for minority students. While this study included
both two-year and four-year college students in the sample, the authors did not
differentiate their findings according to institutional type (two-year versus four-
year) in their analyses.
Conclusion
The poor mathematical performance of the nation’s students has increased the
need to study mathematics achievement in order to determine its contributing
factors. A literature search turned up no studies that examined the relationship
between non-cognitive variables and achievement in community college
mathematics or any studies that simultaneously examined cognitive and non-
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4 3
cognitive variables as predictors of achievement in mathematics for students
enrolled in urban community colleges. To be sure there has been very little
research examining the same for four year college and university students.
Nevertheless, the evidence gained from existing studies would seem to
corroborate the model posed by Reyes and Stanic (1988), namely that non-
cognitive variables such as student attitudes about their academic ability, their
expectations of success, and their achievement-related behaviors (persistence in
math courses for example) have a positive influence on their subsequent
mathematics achievement. These results lend support for examining the same
factors in community colleges.
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CHAPTER 3
Research Methodology
This chapter will provide a description of the research methods and sample used
in the study. The research questions will first be presented and followed by the
conceptual framework. Also included are descriptions of the research population,
the research design, the instrumentation, and data analysis techniques.
Research Questions
1. What is the predictive relationship between cognitive and non-cognitive
variables and achievement in urban community college mathematics
courses?
a. When cognitive and non-cognitive variables are
considered simultaneously, are non-cognitive variables
predictive of the outcomes of measure for student
success?
2. Are the predictive relationships between cognitive and non-cognitive
variables and success in mathematics similar for all groups of students,
males, females, white students, African-American students, and Hispanic
students? In other words, are the equations similar for all groups?
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3. Are the predicative relationships between cognitive and non-cognitive
variables and success in mathematics similar for remedial level math
courses versus transfer-level math courses?
Conceptual Framework
The framework for this study was based in part on the model by Reyes and
Stanic (1988) that proposed that non-cognitive variables such as students’
attitudes about their academic ability, their expectations of success, and their
achievement-related behaviors influence their subsequent mathematical
achievement. Furthermore this study was based on the research by Hagedorn,
Siadat, Nora, and Pascarella (1997) that found cognitive and non-cognitive
variables to be predictive of postsecondary mathematics achievement. This study
was also based on the work by Hagedorn, Siadat, Fogel, Nora, and Pascarella
(1999) that found differences in math achievement between students enrolled in
remedial math courses and students enrolled in non-remedial math courses.
Finally, this study was based on the research by House (1993a, 1993b, 1993c,
1993d, 1994,1995a, 1995b, 1995c, 1995d, 2000) that found npn-cognitive
variables such as academic self-concept and achievement-rel ated expectancies to
be predictors of achievement in various four-year college courses.
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46
Methodology
Research Population
The TRUCCS project, funded initially by the Field Initiated Studies
(OERIR305T000154) and subsequently by the Lumina Foundation, is a five-
year, longitudinal study of community college students in urban Los Angeles that
seeks to advance new definitions of achievement that are more consistent and
applicable to urban community college students. The theoretical population is
urban community college students. The accessible population consists of students
attending any of the nine community colleges in the LACCD. The research
population is meant to generalize to other urban community college districts in
cities such as New York, Chicago, Dallas, and Miami.
Research Design
The present study used data gathered by the TRUCCS project. Members
of the TRUCCS project research team and several volunteers administered a
survey across 241 classrooms spanning the nine colleges of the LACCD in the
spring semester 2001. Participating classrooms were chosen using a stratified
random sampling method that relied on three levels of English courses (two levels
below transfer, one level below transfer, and transfer level) as well as
occupational programs stratified by gender predominance (Hagedorn, Maxwell, &
Moon, 2002). Stratified sampling is necessary to make sure that certain subgroups
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4 7
in the population are adequately represented in the sample (Gall, Borg, & Gall,
1996). Students were also requested to sign a release that would allow access to
their transcript files. Of the 5,000 students surveyed, 4,967 agreed to permit
access to their transcripts (Hagedom, Maxwell, & Moon, 2002).
Instrumentation
A 47-item survey instrument was developed specifically for the purpose of
gathering information from urhan community college students and administered
during the spring 2001 semester. The survey instrument was constructed in such a
way as to reflect the influence of the existing literature on community college
students and, after a pilot study and subsequent revisions, was administered to
approximately 5,000 students attending the LACCD (Hagedom, Maxwell, &
Moon, 2002).
Variables
Dependent variable
An important matter to consider for the analyses was how to measure
academic achievement for community college students. For example, should
achievement be measured by degree attainment as it often is for students attending
four-year institutions? Not necessarily since many students attend community
colleges for reasons other than obtaining a degree (Bean & Metzner, 1985).
Should achievement be measured in terms of grade point average (GPA)? Grimes
and
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Antworth (1996) argued that because community college students “exhibit
extensive withdrawals and retakes” (p. 349), college GPA alone would be a
misleading statistic suggesting instead that academic success should be defined in
terms of a student’s course completion ratio. Course completion ratios represent a
continuous measure determined by dividing the number of courses attempted into
the number of courses completed with a passing grade. Researchers have
suggested that a community college student’s course completion ratio is a more
relevant measure of his or her persistence (North, 1988) and one that better
describes the student’s behavior in college (Hagedom, Maxwell, & Moon, 2002).
For example, because graduation rates at community colleges tend to be low due
to transfer or stop out behaviors, course completion ratios offer a more
appropriate definition of academic success (Logan, 1997). Furthermore, the
TRUCCS project researchers argued the course completion ratio to be “ideal for
the community college environment because it flexes to accommodate part-time
enrollment that is prevalent among community college students” (Hagedom,
Maxwell, & Moon, 2002, p. 4). The dependent variable for the statistical analyses
will be the student’s math course completion ratio, the number of math courses
attempted from fall 2000 through winter 2002 divided into the number of math
courses successfully completed with a passing grade. The data to compute this
measure was obtained from the transcript file provided by the LACCD.
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4 9
Independent Variables
Demographics. Demographic variables used to represent students’
background measures included age, gender, ethnicity, and SES. Students’ ages
were recorded as of September 2002 and measured continuously. Gender was
coded as 1 for males and 2 for females. Ethnicity was coded with a 1 for
Asian/Pacific Islanders, 2 for African-American students, 3 for Hispanic students,
and 4 for white students. SES was measured by using several survey items that
asked students about their parents’ educational backgrounds and occupations.
Parents’ occupation was then assessed and assigned a numerical score between 0
and 100 based on the Nam-Powers-Terrie Occupational Status Scores Index, a
commonly used index for the hierarchical ranking of occupations. Briefly, this
index, which relies completely on data from the U.S. Census, provides the
research community with a consistently defined and up to date set of measures of
the socioeconomic status of detailed census occupations (Nam & Terrie, 1994).
Occupational status scores are derived using several indicators which include the
occupation’s median income level and median educational level. Median
educational level is determined by a measure of educational attainment rather than
the number of years of schooling so as to reflect specific degrees such as the
bachelor’s , master’s, professional, and doctorate (Nam & Terrie, 1994).
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Cognitive variables. Cognitive variables included students’ highest math
course taken as indicated on the survey instrument (participants chose from
calculus, pre-calculus, trigonometry, algebra 2, geometry, algebra 1, and one
response that combined basic math, business math, or pre-algebra), highest
placement test score for mathematics, highest placement test score for English,
college grade point average from fall 2000 up to and including winter 2002,
students’ self-report of their overall average grade in high school, and whether or
not the student took remedial math courses. Students who took remedial math
courses were coded with a 1 whereas those who took no remedial math courses
were coded with a 0.
Push/Pull variables. Push variables refer to students’ study behaviors and
experiences that tend to push them toward positive academic achievement. Survey
items used to measure this construct included studying in groups inside and
outside of class, asking the instructor questions, speaking up during class
discussions, studying for tests early on rather than at the last minute, and
completing homework assignments. Pull variables represent environmental
factors such as domestic and employment obligations that may tend to divert a
student’s attention from his or her studies. Research has shown that environmental
factors, especially employment, have negatively affected persistence (Grimes &
Antworth, 1996; Walleri as cited in Grimes & Antworth, 1996; Webb, 1988) and
degree completion (Nippert, 2000) for community college students and Borglum
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51
and Kubala (2000) found that many community college students preferred to
spend no more time on campus than was necessary due to employment
responsibilities. Pull variables included two dichotomous items, being employed
and having children, and one scale labeled as obstacles.
Non-cognitive variables. Non-cognitive variables included achievement-
related expectancies, academic self-concept, and uncertainty about career choices
and college major. All three constructs were measured using items from the
survey instrument. Uncertainty was included in the analyses because it may be
that failure to pass required math courses will lead students to change their
intended major (from a mathematically-based major to a non-mathematically-
based major) and/or to change their intended choice of career. This phenomenon
has been reported among students attending four-year institutions (Hewitt &
Seymour, 1991).
Data Analysis
This study used both descriptive and inferential statistics to investigate the
existence and extent of relationships among selected variables. Factor analysis
was performed to isolate and identify suitable scales. Confirmatory factor analysis
was performed to test the reliability of the scales. Correlation coefficients were
computed to investigate the relationship between predictor variables and
achievement in mathematics. Two-way analysis of variance (ANOVA) was used
to compare mean transfer completion ratios and remedial completion ratios both
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5 2
by gender and ethnicity. Finally, ordinary least-squares multiple regression
analysis was performed to determine the relative contribution of specified
variables to success in mathematics and the model was executed separately for all
math courses, remedial math courses, and transfer-level math courses. Multiple
regression analysis was appropriate for this study because there was more than
one potential predictor, as is often the case in educational research (Shannon &
Davenport, 2001). Statistical analyses were performed using SPSS 11.0 and the
level of significance established for all tests was at p < 0.05.
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CHAPTER 4
Results
Descriptive analysis
Overall, the TRUCCS sample included 4,720 students of which 39% were
males and 70% were under the age of 30. Almost half of the students surveyed
(47.7%), had never attempted a math course. Of those students who did attempt a
math course, 41% had taken at least one remedial level math course whereas only
16% had taken a transfer level math course. Table 1 includes the percentages of
all students surveyed who had attempted a transfer level math course by gender
and ethnicity.
Table 1
Percentage of All Students who Attempted Transfer Level Math
Courses
Male
Gender
Female
Asian 21 18
African-American 10 18
Hispanic 51 52
White 12 7
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Table 2 contains the numbers of students surveyed who indicated the highest math
course they had taken at the time of the survey (N = 3,212). Corresponding
percentages are in parentheses.
Table 2
Number Reporting Highest Math Course Taken__________
Calculus 212 (6.6)
Pre-calculus 204 (6.4)
Trigonometry 275 (8.6)
Algebra 2 751 (23.4)
Geometry 368 (11.5)
Algebra 1 532 (16.6)
Basic math 721 (22.4)
All math courses offered through the LACCD were classified into 4 groups by the
TRUCCS project researchers: Level 0 represented three levels below transfer,
level 1 represented two levels below transfer, level 2 represented one level below
transfer, and level 3 represented transfer level. In addition, levels 0, 1, and 2 have
been further classified as being either basic remedial (levels 0 and 1) or
intermediate remedial (level 2). Table 3 describes the types of courses in each
level.
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Table 3
Classification of LACCD Math Courses
Courses Level Description
100-
112 0 Arithmetic through Pre-algebra
113 -
118 1
Introductory Elementary Algebra, Elementary
Algebra
120-
125 2 Geometry, Intermediate Algebra
132-
291 3
Introductory Statistics, Calculus, Differential
Equations,
Math Analysis for Business and Social Sciences,
Trigonometry, Pre-calculus
Further descriptive analyses at this point must be done with care. Consider
that many community college students withdraw from and repeat courses (Grimes
and Antworth, 1996). Some may fail a lower level course only to enroll in a
higher level course and pass it. Simply stating who is taking what courses would
be a misleading statistic. A better indicator of what courses students are taking
i
would be participation ratios. For example for all students who have taken math
courses, their overall math course participation ratio would be defined as the total
number of math courses attempted divided by the total number of all courses
attempted. Similarly, the transfer level math course participation ratio would be
defined as the number of transfer level math courses attempted divided by the
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total number of all math courses attempted. In the same way, the remedial
participation ratio would be defined as the sum of the number of level 0, 1, and 2
courses attempted divided by the total number of all math courses attempted. We
could refine this further by finding the participation ratio for level 0 courses only
as the number of level 0 math courses attempted divided by the total number of
remedial math courses attempted and so on. An attempt is defined as only those
courses for which students earned a letter grade (A, B, C, D, F, or P). Courses
dropped without a letter grade were deleted from the analyses. This was done to
avoid including students who often register for classes only to drop them after the
first day in an effort to shop for (or avoid) certain instructors or perhaps to create
the ideal schedule (Hagedom, Maxwell, & Moon, 2002). Letter grades of A, B, C,
and P represent passing grades. Table 4 shows the frequencies for overall
participation ratios for mathematics, that is, the number of math courses attempted
divided by the total number of all courses attempted.
Table 4
General Math Participation Ratios
Scale Frequency
0 2252
0.01 - 0.24 2022
0.24 - 0.49 379
0.50 - 0.74 61
0.75 - 0.99 1
1 5
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As can be seen from Table 4, five students had an overall participation ratio of
1.00 meaning that the only courses they attempted were math courses whereas
almost half of the students in the sample (2,252) had an overall participation ratio
of 0 meaning that of all the courses they attempted, none were math courses.
To further illustrate the usefulness of employing participation ratios,
consider the enrollment history of one participant, student X, over the period from
fall 2000 through summer 2002. Transcript data revealed that this student
registered for 29 courses, dropped 17 of them, attempted 12, and passed eight. A
look at this student’s math course enrollment activity further revealed the
following: In August 2000, student X registered for, attempted, and passed
MATH 105, a level 0 course. In December 2000 student X registered for MATH
112, a level 0 math course, dropped the course two days later, and then registered
for the same course but in a different section completing it with a C grade. In July
2001, student X registered for MATH 115, a level 1 eourse, dropped it four days
later, registered for the same course but a different seetion, and finally dropped it
without penalty. In September 2001, student X registered for another level 0 math
course, MATH 100, and completed it with a passing grade P. In October 2001 the
student registered for MATH 113, a level 1 math course, and completed it with a
failing grade F. In December 2001 the student registered for MATH 114, dropped
it two days later, registered for the same course but a different section, and later
dropped it without penalty. Finally, in February 2002, student X registered for
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MATH 113 again, dropped it eight days later, registered for it again but in a
different section and dropped it later without penalty. To summarize, student X
registered for eleven math courses, attempted four of them, and passed three. The
three courses passed were level 0 courses. The failed course was level 1. Student
X’s overall participation ratio would be the total number of math courses
attempted, four, divided by the number of all courses attempted, 12, for a value of
0.33. Therefore, of all courses student X attempted, one third of them were math
courses. Restricting our attention to just math courses, student X ’s level 0 and
level 1 participation ratios would be 0.75 and 0.25 respectively. That is, of all the
math courses this student attempted, 75% of them were level 0 courses.
Table 5 gives the frequencies for level 0, 1, 2, and 3 math course participation
ratios.
Table 5
Math Course Participation Ratios
Scale
Course Level
Remedial
(0)
Remedial
(1)
Remedial
(2)
Transfer
(3)
0 1724 1462 1787 1721
0.01 - 0.24 1 3 3 0
0.25 - 0.49 78 103 112 51
0.50 - 0.74 209 326 290 148
0.75 - 0.99 7 4 0 6
1 449 570 276 542
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As can be seen from this table, 542 students had a Transfer (level 3) participation
ratio of 1.00 meaning that all of the math courses they attempted were transfer
level courses.
Total math success, transfer level math success, and remedial level math
success were measured respectively by course completion ratios for all math
courses; level 3 math courses; and levels 0, 1, and 2 math courses combined. The
TRUCCS project adopted the following typology for assessing course completion
ratios;
• A course completion ratio of 0 is defined as No Success
• A course completion ratio of more than 0 but less than 0.33 is defined as
Little Success
• A course completion ratio of 0.33 or higher but less than 0.66 is defined as
Moderate Success
• A course completion ratio of 0.66 or higher but less than 1.00 is defined as
Substantial Success
• A course completion ratio of 1.00 is defined as Complete Success
(Hagedom, Maxwell, & Moon, 2002)
To illustrate, recall the example of student X who registered for eleven math
courses but attempted only three level 0 courses and one level 1 course. This
student received a passing grade in all level 0 courses but failed the level 1 course.
This student would have a total math completion ratio of 0.75 and be typed as
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6 0
meeting substantial success. The student’s level 0 completion ratio would be 1.00
( three level 0 courses completed with a passing grade divided by three level 0
courses attempted) but the student’s level 1 completion ratio would be 0 ( no level
1 courses completed with a passing grade divided by one level 1 course
attempted). This student would then be typed as meeting complete success in
basic remedial math courses. Table 6 contains the frequencies for completion
ratios for all four levels of math courses.
Table 6
Frequencies by Tvpe of Success
Success
Scale
Course Level
Remedial
(0)
Remedial
(1)
Remedial
(2)
Transfer
(3)
No success 265 436 240 219
Little 1 0 0 2
Moderate 59 76 41 66
Substantial 3 2 0 9
Complete 416 492 400 451
As can be seen from this table, 492 students had a level 1 completion ratio of
1.00. These students completed all of their level 1 courses with passing grades
and therefore they would be typed as Completely Successful in level 1 courses.
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61
Table 7 contains the frequencies and percentages of students meeting the different
types of success for all math course completion ratios, transfer level (level 3)
ratios, and remedial (levels 0, 1, and 2 combined) level ratios together for ease of
comparison.
Table 7
Frequencies by Tvpe of Success
Success
Type
Total Transfer Remedial
f F f P f P
No success 840 34 219 29.3 696 36.1
Little 14 0.6 2 0.3 9 0.5
Moderate 380 15.4 66 8.8 288 15
Substantial 82 3.3 9 1.2 46 2.4
Complete 1152 46.7 451 60.4 887 46.1
As can be seen from this table, of all the students who attempted a math course,
1,152 (46.7%) were completely successful in all of the math courses they
attempted whereas 840 students (34%) were completely unsuccessful in all of the
math courses they attempted. Of all students who attempted a transfer level math
course, 451 (60%) were completely successful whereas 219 (29%) failed all of
their transfer level math courses.
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Table 8 contains the percentages of students meeting each success type in all math
courses by gender and ethnicity for those students who identified themselves as
either male or female, and either Asian, African-American, Hispanic, or white.
Table 8
Percentages Success Type for All Math by
Gender and Ethnicity
Type
Asian
African-
American Hispanic White
Male Female Male Female Male Female Male Female
No success 35.5 27.5 41 41.4 39.9 35.2 24 25
Little 1.3 1.1 0.8 0.2 1
Moderate 7.9 9.9 9 16.8 15 17.8 21.3 12.5
Substantial 2.2 4 2.9 3.8 4 2.7 3.8
Complete 55.3 59.3 46 38.1 41.3 42.8 52 57.7
Table 9 contains the percentages of students meeting each success type in
transfer math courses by gender and ethnicity for those students who identified
themselves as either male or female, and either Asian, African-American,
Hispanic, or white.
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63
Table 9
Percentages Transfer Success Type by
Gender and Ethnicity
Asian
African-
American Hispanic White
Type Male Female Male Female Male Female Male Female
No
success 20.9 14.9 25 31.9 42.2 32.8 20.8 22.2
Little 2.3 5
Moderate 11.6 8.5 10 12.8 9.8 4.4 12.5 11.1
Substantial 4.3 1 5.6
Complete 65.1 72.3 60 55.3 47.1 62.8 66.7 61.1
Table 10 contains the percentages of students meeting each success type in
remedial math courses by gender and ethnicity for those students who identified
themselves as either male or female, and either Asian, African-American,
Hispanic, or white.
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64
Table 10
Percentages Remedial Success Tvpe by Gender and
Ethnicity
Asian
African-
American Hispianic White
Type Male Female Male Female Male Female Male Female
No
success 55.6 39.6 42 42.1 38.9 36.6 27.6 23.7
Little 2.1 0.9 0.2 1.1
Moderate 8.3 9.1 16.4 13.1 17.7 20.7 12.9
Substantial 1.1 1.9 2.2 3.4 1.7 2.2
Complete 44.4 50 47.7 38.8 45.8 42.1 50 60.2
Table 11 contains the means and standard deviations for all math course
completion ratios, transfer math completion ratios, and remedial math completion
ratios.
Table 11
Descriptive Statistics for Math Completion
Ratios
M SD n
All Math 0.56 0.447 2468
Transfer 0.65 0.449 747
Remedial 0.55 0.453 1926
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A two-way ANOVA was performed to determine differences in transfer level
math completion ratios by gender and ethnicity. Group statistics are shown in
Table 12.
Table 12
Group Descriptives for Transfer
Completion Ratios
Male Female Total
Group n M SD n M SD n M SD
Asian 43 0.71 0.42 47 0.79 0.368 90 0.75 0.394
A.Araerican 20 0.66 0.446 47 0.62 0.457 67 0.63 0.451
Hispanic 102 0.53 0.475 137 0.65 0.422 239 0.6 0.473
White 24 0.73 0.419 18 0.7 0.447 42 0.72 0.416
Total 189 0.61 0.459 249 0.67 0.447 438 0.65 0.453
There was no significant main effect for gender: Females (M = 0.67) did not
achieve significantly higher transfer completion ratios than males (M = 0.61), F (l,
430) = 0.432,2 = 0.511. A significant main effect for ethnicity was found, F(3,
430) = 3.351, p = 0.019. Follow-up tests consisted of all pair wise comparisons
among the different ethnic groups. The Tukey post-hoc test was used to control
Type I error across the comparisons. The results of that analysis indicated that
Asian students (M = 0.75) had significantly higher transfer level math completion
ratios than Hispanic students (M = 0.60). No other significant differences were
found between ethnic groups. Finally, there was no significant gender by ethnicity
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66
interaction, F(3, 430) = 0.738, q = 0.530: Neither gender nor ethnicity had any
significant effect on transfer level math completion ratios.
A two-way ANOVA was performed to determine differences in remedial level
math completion ratios by gender and ethnicity. Group statistics are shown in
Table 13.
Table 13
Group Descriptives for Remedial
Completion Ratios
Male Female Total
n M SD n M SD n M SD
Asian 36 0.44 0.504 48 0.55 0.477 84 0.5 0.489
A.American 88 0.53 0.476 214 0.48 0.452 302 0.5 0.459
Hispanic 275 0.53 0.461 435 0.53 0.445 710 0.53 0.451
White 58 0.62 0.43 93 0.68 0.427 151 0.65 0.428
Total 457 0.54 0.464 790 0.54 0.45 1247 0.54 0.455
There was no significant main effect for gender: Females (M = 0.54) did not
achieve significantly different remedial level completion ratios than males (M =
0.54), F(l> 1239) = 0.608, p = 0.436. Once again a significant main effect for
ethnicity was found, F(3, 1239) = 3.517, g = 0.015. Follow-up tests consisted of
all pair wise comparisons among the different ethnic groups. The Tukey post-hoc
test was used again to control Type I error across the comparisons. The results of
that analysis indicated that white students (M = 0.65) had significantly higher
remedial level math completion ratios than Hispanic students (M = 0.53) and
African-American students (M = 0.50). No other significant differences were
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67
found between ethnic groups. Finally, there was no significant gender by ethnicity
interaction, F (3 ,1239) = 0.799, p = 0.495; Neither gender nor ethnicity had any
significant effect on remedial level math completion ratios.
Reliability analysis identified several factors representing relationships
among selected items taken from the survey instrument. Scales proposed to
represent these different factors were tested for reliability and appropriately
constructed to reduce measurement error. Table 14 contains the items and scales
used in the regression model followed by brief descriptions.
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Table 14
Items and Scales Used in the Model
6 8
Construct Description Coding, , , , Alpha
Age Age as of 9/9/02 Continuous
Gender 1 = male
2 = female
Ethnicity 1 = Asian
2 = Af. American
3 = Hispanic
4 = white
1 item
1 item
1 item
SES Socioeconomic
Status
Score between 0 and 100 1 item
based on Nam-Powers-Terrie
Occupational Status Index
HSAVG Self-report of average 1 = D or lower (poor) 1 item
High school grade 2 = C- (Below average)
3 = C (Average)
4 = C-t (Above average)
5 = B- (Good)
6 = B (Very good)
7 = B+ (Excellent)
8 = A- (Superior quality)
9 = A or A+ (Extraordinary)
Math Score Highest math Continuous 1 item
placement score
English score Highest English Continuous 1 item
placement score
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Table 14 continued
Items and Scales Used in the Model
69
Construct Description . . . Coding... Alpha
High math Highest math course
taken
1 = Basic math
2 = Algebra 1
3 = Geometry
4 = Algebra 2
5 = Trigonometry
6 = Pre-calculus
7 = Calculus
1 item
GPA
Remedial
Grade point average
If the student took
remedial math
1 = yes
0 = no
1 item
1 item
Achievement- Get a BA/BS
Related Exp.
Transfer to a 4-year
college or university
Self-concept Expect to earn good
grades
1 = Definitely not
2 = Probably not
3 = Maybe
4 = Probably
5 = Definitely
1 = Strongly agree
2 = Disagree
3 = Slightly disagree
4 = Not sure
.7277
(2 items)
.8304
(8 items)
Understanding what
is taught is important 5 = Slightly agree
6 = Agree
I keep trying even 7 = Strongly agree
when frustrated
It is important to
finish my courses
I am very determined
to reach my goals
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Table 14 continued
Items and Scales Used in the Model
70
Construct Description Coding Alpha
Self-concept I feel most satisfied
when I work hard to
achieve something
Success is due to effort
Uncertainty
I know I can leam
all the skills taught
in college
Change career choice 1 = Definitely not
2 = Probably not
Change college major 3 = Maybe
4 = Probably
5 = Definitely
.7649
(2 items)
Wait until the day
before an assignment
is due before starting
Study at least 2 or 3
Days prior to tests
Behaviors Wait until the day 1
2
3
4
5
6
7
Always complete
homework assignments
; Strongly agree
: Disagree
Slightly agree
: Not sure
: Slightly agree
; Agree
: Strongly agree
5 items
Declared a major
Permanently stop
attending college
Employment 1 = employed
0 = unemployed
1 item
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71
Table 14 continued
Items and Scales Used in the Model
Construct Description Coding Alpha
Children 1 = one or more children
0 = no children
1 item
Obstacles Parking 1 = Not a problem
Transportation 2 = Small problem
Family responsibility 3 = Medium problem
Job-related 4 = Large problem
Paying for college 5 = Very large problem
Scheduling classes
Understanding English
Difficulty of classes
.8331
Participation Number of times ask
instructor questions
1 = 0/no times
2 = 1 time
3 = 2 times
4 = 3 times
.7391
(2 items)
Number of times
speak up during class 5 = 4 times
discussion 6 = 5 or more times
Study habits Number of times 1 = 0/No times
telephoned/emailed 2 = 1 time
students about studies 3 = 2 times
4 = 3 times
Studied in small 5 = 4 times
groups outside of 6 = 5 or more times
class
.6680
(4 items)
Helped another student
understand homework
Worked in small groups
during class time
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72
Independent Variables
The independent variables were blocked into four groups and entered into
the regression model in the following order.
Demographics. The first block contained students’ background measures
and included age, gender, ethnicity, and SES.
Cognitive variables. The second block of variables represented cognitive
variables and included students’ highest math course taken as indicated on the
survey instrument, highest placement test score for mathematics, highest
placement test score for English, college grade point average from fall 2000 up to
and including winter 2002, students’ self-report of their overall average grade in
high school, and whether or not the student took remedial math courses.
Push/Pull variables. The third block of variables included two scales used
to measure push variables and were labeled as Study habits and Participation. Pull
variables were measured with two dichotomous items, being employed and
having children, and one scale labeled as Obstacles.
Non-cognitive variables. The fourth block included three scales used to
represent the constructs for achievement-related expectancies, self-concept, and
uncertainty about career choice and college major. Five single items taken from
the survey instrument were also included in this block: studying two or three days
prior to tests, always completing homework assignments, waiting until the day
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73
before an assignment is due before starting it, declaring a college major, and
deciding to permanently stop attending college.
The fourth block was entered last in the regression analyses to control for
the other three yet even so the ordering makes sense. For example the
demographic variables represent characteristics of students before or at the point
of college entry that might have some influence on their academic success and
therefore their completion ratios. The cognitive variables represent a bridge
between students’ previous academic backgrounds (usually high school) and
access to college level studies. The pull variables employment, having children,
and the obstacles scale represent issues that students must face while attending
college and which may influence completion ratios. The push variables are the
academic habits students adopt while navigating through college. The non-
cognitive variables achievement-related expectancies, academic self-concept, and
uncertainty are the attitudes student may be likely to adopt depending on whether
they are successful or not as they proceed through college. The five single items
included in this block, studying two or three days prior to tests, always
completing homework assignments, waiting until the day before an assignment is
due before starting it, declaring a college major, and deciding to permanently stop
attending college are all variables that might suggest a student’s ability to manage
their time effectively, their willingness to proceed with college even if success in
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74
their courses is difficult to come by, or their decision to change their course of
studies or leave college altogether.
Regression analysis was performed on completion ratios for all math
courses, transfer level math courses, and remedial level math courses to determine
the predictive relationships between the independent variables and success in
math. Descriptive information for the independent variables is included in Table
15 followed by correlation coefficients in Table 16.
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Table 15
Means and Standard Deviations for
Independent Variables
75
Variables
Total Transfer Remedial
M SD
M
SD M
Age 26.37 8.025 25.04 6.797 26.72 8.233
Gender 1.62 0.487 1.59 0.494 1.63 0.484
African-American 0.17 0.378 0.14 0.350 0.19 0.390
Asian 0.11 0.311 0.23 0.420 0.06 0.241
Hispanic 0.56 0.497 0.52 0.501 0.58 0.494
SES 42.71 23.551 43.31 24.138 42.10 23.233
HSAVG 5.19 1.776 5.72 1.767 5.04 1.747
Math Score 2.57 1.060 3.17 1.093 2.36 0.961
English
Score 3.32 1.140 3.45 1.172 3.30 1.123
High math 3.09 1.780 4.26 1.715 2.71 1.596
GPA 2.82 5.343 2.86 0.674 2.82 5.934
Remedial 0.81 0.394 0.32 0.467
Employment 0.70 0.458 0.67 0.471 0.71 0.454
Children 0.33 0.472 0.24 0.431 0.36 0.479
Obstacles 15.90 5.456 16.19 5.681 15.80 5.405
Participation 2.60 1.228 2.53 1.188 2.62 1.238
Study habits 1.91 0.838 1.98 0.907 1.89 0.817
ARE 0.17 0.678 0.39 0.510 0.14 0.701
Self-concept 6.22 0.660 6.28 0.632 6.22 0.659
Uncertainty -0.01 0.894 -0.04 0.887 0.02 0.901
Q37_19 3.17 1.756 3.24 1.729 3.12 1.760
Q37_04 4.83 1.688 4.92 1.685 4.81 1.699
Q37_07 5.74 1.259 5.79 1.323 5.74 1.250
Q37_22 5.26 1.769 5.32 1.779 5.26 1.770
Q10_05 1.32 0.669 1.27 0.648 1.31 0.664
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Table 16
Regression Correlation Coefficients
for Math Completion Ratios
76
Total Transfer Remedial
Age 0.119
*
0.096 0.134
*
Gender 0.013 0.043 0.002
African-American -0.029 -0.039 -0.007
Asian 0.035 0.065 -0.043
Hispanic -0.046 -0.049 -0.031
SES -0.003 0.021 -0.018
HSAVG 0.119
*
0.088 0.106
*
Math Score 0.102
*
0.037 0.068
English Score 0.090
*
0.009 0.111
> K
High math 0.201
*
0.106
*
0.177
*
GPA 0.016 0.530
*
0.000
Remedial -0.146
*
-0.090
Employment -0.063
*
-0.057 -0.048
Children 0.036 0.002 0.054
Obstacles -0.060
*
-0.073 -0.056
Participation 0.021 0.000 0.025
Study habits -0.017 0.019 -0.030
ARE 0.050 0.036 0.046
Self-concept 0.092 0.029 0.114
Uncertainty 0.011 0.066 0.013
Q37_19 -0.072
*
-0.068 -0.085
*
Q37_04 0.081
*
-0.037 0.108
*
Q37_07 0.156
*
0.145
*
0.148
*
Q37_22 -0.041 -0.122
*
-0.019
Q10_05 -0.008 0.048 -0.029
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77
The analysis included 1,000 students who attempted any math course and who
had valid responses to each of the independent variables selected for regression.
Similarly, the analysis included 282 students who had taken transfer level math
and who had valid responses to each of the independent variables selected for
regression. Finally, the analysis included 808 students who had taken remedial
level math courses and who had valid responses to each of the independent
variables. According to the results displayed in Table 16, age, self-report of
average grade in high school, math and English placement test scores, highest
math course taken, academic self-concept, studying at least two or three days
prior to tests, and always completing homework assignments were all positively
correlated with total math course completion ratios whereas taking any remedial
math courses, being employed, obstacles, and waiting until the day before an
assignment was due before starting it were negatively correlated with total math
course completion ratios. The highest math course taken, GPA, and always
completing homework assignments were positively associated with higher
transfer level math course completion ratios however declaring a college major
was negatively associated with transfer level math course completion ratios. Age,
self-report of average high school grade, math and English placement test scores,
academic self-concept, studying at least two or three days prior to tests, and
always completing homework assignments were all positively correlated with
higher remedial level completion ratios. Waiting until the day before an
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7 8
assignment was due before starting it was associated with lower remedial math
completion ratios. Achievement-related expectancies were not significantly
correlated with any of the dependent variables.
The method proposed by Pedhazur (1982) to check for gender interactions
and ethnicity interactions was employed in this study. For example, to test for
interaction between gender and the other independent variables, cross products
were computed using the following form: gender*independent variable. Once
defined, these new variables were collected into a fifth block and added to the
regression analyses for all three dependent variables while the gender variable
was removed. Block 5, the check for interactions by gender, was not significant
for any of the dependent variables. The gender variable was then replaced in
Block 1 for subsequent analyses. Similarly, to test for interaction between
ethnicity and the other independent variables, cross products were computed
using the following form: ethnic group * independent variable. Once defined, these
new variables were collected to form a fifth block and added to the regression
analyses for all three dependent variables. Block 5, the check for interactions by
ethnicity, did not reach significance in any case. These results indicated that only
three regression analyses needed to be conducted, one for each dependent
variable, and that conducting any further regression analyses on gender and
ethnicity separately were unnecessary.
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7 9
Table 17 contains a model summary of the results of the regression
calculated to predict students’ total math course completion ratios based on the
four predictors (blocks).
Table 17
Regression Model Summary for Total Math Completion
Ratios
Model R R2 SE
R2
Change
F
Change dfl df2
Sig.F
Change
Demographics 0.145 0.021 0.4443 0.021 3.535 6 993 0.002 *
Cognitive 0.286 0.082 0.4316 0.061 10.891 6 987 0 *
Push/Pull 0.304 0.092 0.4302 0.01 2.254 5 982 0.047 *
Non-cognitive 0.335 0.112 0.4273 0.02 2.725 8 974 0.006 *
Table 18 contains a summary of the regression analysis for the variables
predicting total math course completion ratios and includes the standardized and
unstandardized regression coefficients as well as the standard errors.
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80
Table 18
Summary of Regression Analysis for Variables Predicting Total Math
Course Completion Ratios
B SE
P
(Constant) 0.037 0.199
Age 0.007 0.002 0.128 *
Gender -0.005 0.031 -0.005
African-American -0.046 0.049 -0.039
Asian -0.048 0.058 -0.034
Hispanic -0.013 0.042 -0.014
SES -0.001 0.001 -0.032
HSAVG 0.009 0.008 0.034
Math Score 0.001 0.015 0.003
English Score 0.033 0.012 0.083 *
High math 0.047 0.009 0.188 *
GPA 0.001 0.003 0.008
Remedial -0.087 0.041 -0.077 *
Employment -0.071 0.030 -0.073 *
Children 0.032 0.032 0.034
Obstacles -0.002 0.003 -0.030
Participation -0.004 0.013 -0.012
Study habits -0.021 0.019 -0.039
ARE 0.008 0.023 0.012
Self-concept 0.016 0.026 0.024
Uncertainty 0.020 0.018 0.040
Q37_19 -0.008 0.009 -0.033
Q37_04 0.008 0.009 0.030
Q37_07 0.039 0.014 0.111 *
Q37_22 -0.014 0.009 -0.054
Q10_05 0.011 0.023 0.016
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81
A significant regression equation was found (ANOVA F(25, 974) = 4.914, 2 <
.05), with an R-square of .112 meaning that the model explained 11.2% of the
variance in students’ total math course completion ratios. All four blocks
significantly increased the predictive ability of the final model. Even so, review of
the beta weights in the table of coefficients. Table 18, indicates that only six of
the variables, age, highest English placement scores, highest math course taken,
having taken any remedial math courses, being employed, and always completing
homework assignments, significantly contributed to the model. The contributions
of the other independent variables were no more than would be expected by
chance. The highest math course taken was the best positive predictor of total
math course completion ratios. The next best positive predictor was age followed
in order by always completing homework assignments and highest English
placement scores. Having taken remedial math courses and being employed were
both negative predictors of total math completion ratios.
Table 19 contains the model summary of the results of the regression
calculated to predict students’ transfer math course completion ratios based on the
four predictors (blocks).
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8 2
Table 19
Regression Model Summary for Transfer Math Completion Ratios
Model R
R2
SE
R2
Change
F
Change dfl df2
Sig.F
Change
Demographics 0.136 0.019 0.4485 0.019 0.865 6 275 0.521
Cognitive 0.563 0.317 0.3784 0.298 19.559 6 269 0 *
Push/Pull 0.572 0.327 0.3789 0.011 0.844 5 264 0.519
Non-cognitive 0.588 0.346 0.3795 0.018 0.903 8 256 0.515
Table 20 contains a summary of the regression analysis for the variables
predicting transfer math course completion ratios.
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83
Table 20
Summary of Regression Analysis for Variables Predicting
Transfer Math Course Completion Ratios
B SE
(Constant) -0.227 0.359
Age 0.002 0.004 0.035
Gender 0.077 0.051 0.084
African-American 0.077 0.100 0.060
Asian 0.058 0.089 0.055
Hispanic 0.068 0.083 0.076
SES 0.000 0.001 -0.022
HSAVG -0.028 0.015 -0.111
Math Score -0.011 0.026 -0.026
English
Score -0.027 0.021 -0.072
High math 0.004 0.016 0.014
GPA 0.385 0.039 0.579 *
Remedial -0.148 0.057 -0.154 *
Employment 0.004 0.053 0.004
Children -0.013 0.059 -0.012
Obstacles -0.007 0.004 -0.084
Participation -0.021 0.024 -0.055
Studychabits 0.028 0.030 0.057
ARE 0.057 0.053 0.064
Self-concept 0.032 0.050 0.045
Uncertainty 0.001 0.031 0.002
Q37_19 -0.012 0.015 -0.047
Q37_04 -0.027 0.017 -0.103
Q37_07 0.003 0.022 0.008
Q37_22 -0.021 0.016 -0.082
Q10_05 0.030 0.040 0.043
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84
A significant regression equation was found (ANOVA F(25, 256) = 5.414, g <
.05), with an R-square of .346 meaning that the model explained 34.6% of the
variance in students’ transfer math course completion ratios. The addition of
Block 2, cognitive variables, was highly significant whereas Blocks 1, 3 and 4,
demographics, push/pull variables and non-cognitive variables respectively, did
not significantly increase the predictive ability of the model. Furthermore, the
table of coefficients. Table 19, indicates that only two of the variables, GPA and
taking remedial math courses, significantly contributed to the model for transfer
math course completion ratios. The contributions of the other independent
variables were no more than would be expected by chanee. A student’s GPA was
the best and only positive predictor of transfer math completion ratios whereas
having taken remedial math courses was a negative predictor of transfer math
completion ratios.
The results of the regression calculated to predict students’ remedial level math
course completion ratios based on the four predictors are contained in Tables 21
and 22.
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85
Table 21
Regression Model Summary for Remedial Math Completion
Ratios
Model R SE
W
Change
F
Change dfl df2
Sig.F
Change
Demographics 0.16 0.024 0.4517 0.024 3.301 6 801 0.003 *
Cognitive 0.28 0.078 0.4405 0.053 9.232 5 796 0 *
Push/Pull 0.3 0.087 0.4396 0.009 1.642 5 791 0.147
Non-cognitive 0.33 0.107 0.437 0.02 2.211 8 783 0.025 *
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86
Table 22
Summary of Regression Analysis for Variables Predicting Remedial Math
Course Completion Ratios
B
(Constant) -0.133 0.219
Age 0.007 0.002 0.126 *
Gender -0.039 0.035 -0.041
African-American -0.034 0.054 -0.029
Asian -0.117 0.075 -0.062
Hispanic -0.010 0.047 -0.011
SES -0.001 0.001 -0.039
HSAVG 0.011 0.010 0.044
Math Score 0.007 0.017 0.015
English Score 0.042 0.014 0.103 *
High math 0.055 0.011 0.191 *
GPA 0.000 0.003 -0.006
Employment -0.073 0.035 -0.073 *
Children 0.045 0.037 0.048
Obstacles -0.001 0.003 -0.015
Participation -0.010 0.015 -0.027
Study habits -0.024 0.022 -0.043
ARE 0.007 0.025 0.011
Self-concept 0.027 0.030 0.039
Uncertainty 0.023 0.020 0'045
Q37_19 -0.007 0.010 -0.028
Q37_04 0.015 0.010 0.057
Q37_07 0.033 0.016 0.091 *
Q37_22 -0.008 0.010 -0.032
Q10_05 0.003 0.026 0.005
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8 7
A significant regression equation was found (ANOVA F(24, 783) = 3.920, q <
.05), with an R-square of .107 meaning that the final model explained 10.7% of
the variance in students’ remedial math course completion ratios. Block 3,
push/pull variables, did not significantly increase the predictive ability of the
model however Blocks 1, 2, and 4, demographics, cognitive and non-cognitive
variables respectively, explained significant amounts of the variation in remedial
math completion ratios. Even so, the table of coefficients indicates that only five
of the variables, age, highest English placement scores, highest math course
taken, being employed, and always completing homework assignments,
significantly contributed to the final model for remedial math course completion
ratios. The contributions of the other independent variables were no more than
would be expected by chance. The highest math course taken was the best
positive predictor of remedial math completion ratios followed in order by age,
highest English placement scores, and always completing homework assignments.
Being employed was the only significant negative predictor.
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8 8
CHAPTER 5
Summary and Discussion
This final chapter restates the research problem and reviews the major
methods used in the study. The major sections of this chapter summarize the
results and discuss their implications.
Statement of the Problem
In most institutions of higher education, mathematics is perhaps the most
critical academic program. A large majority of degree programs and majors
require students to take courses in mathematics consequently enrollments in
mathematics are among the highest of any other subject (Gold, Keith, & Marion,
1999). The problem however is that the withdrawal and failure rates in math are
also higher compared to most other courses (Adelman, 1999b; Gold, Keith, &
Marion, 1999). Failure to succeed in mathematics can limit the choices available
to those students considering college and career decisions. Mathematics is often
seen as a gatekeeper to scientific and technical academic programs and
occupations (National Research Council, 1995) and a barrier (especially for
minorities) to success in college.
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8 9
Purpose of the Study
The purpose of this study was to determine whether cognitive and non-
cognitive variables had predictive value for urban community college students’
success in mathematics. A secondary purpose of this study was to determine if the
predictive relationships between non-cognitive variables, cognitive variables, and
success in mathematics remained constant for all groups of students i.e. males,
females, white students, African-American students, Hispanic students, remedial
math students and non-remedial math students.
Research Questions
1. What is the predictive relationship between cognitive and non-cognitive
variables and achievement in urban community college mathematics?
b. When cognitive and non-cognitive variables are
considered simultaneously, are non-cognitive variables
predictive of the outcomes of measure for student
success?
2. Are the predictive relationships between cognitive and non-cognitive
variables and success in mathematics similar for all groups of students,
males, females, white students, African-American students, and Hispanic
students? In other words, are the equations similar for all groups?
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9 0
3. Are the predicative relationships between cognitive and non-cognitive
variables and success in mathematics similar for remedial level math
courses versus transfer-level math courses?
Methodology
Research Population
The TRUCCS project, funded initially by the Field Initiated Studies
(OERIR305T000154) and subsequently by the Lumina Foundation, is a five-
year, longitudinal study of community college students in urban Los Angeles that
seeks to advance new definitions of achievement that are more consistent and
applicable to urban community college students. The theoretical population is
urban community college students. The accessible population consisted of
students attending any of the nine community colleges in the LACCD. The
research population is meant to generalize to other urban community college
districts in cities such as New York, Chicago, Dallas, and Miami.
Research Design
This dissertation used data gathered by the TRUCCS project. A survey
instrument was administered across 241 classrooms spanning the nine colleges of
the LACCD in the spring semester 2001. Participating classrooms were chosen
using a stratified random sampling method that relied on three levels of English
courses (two levels below transfer, one level below transfer, and transfer level) as
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91
well as occupational programs stratified by gender predominance (Hagedom,
Maxwell, & Moon, 2002). Of the 5,000 students surveyed, 4,967 also agreed to
permit access to their transcripts (Hagedom, Maxwell, & Moon, 2002).
Instrumentation
A 47-item survey instrument was developed specifically for the purpose of
gathering information from urban community college students and was
constmcted in such a way as to reflect the influence of the existing literature on
community college students. The survey underwent a pilot study and subsequent
revisions and was finally administered to approximately 5,000 students attending
the LACCD (Hagedom, Maxwell, & Moon, 2002).
Variables
Dependent variable
Determining how to measure academic achievement or success for
community college students can be problematic. Many students attend community
colleges for reasons other than obtaining certificates or degrees thus making
certificate or degree attainment an inappropriate measure of success. Moreover,
Grimes and Antworth (1996) argued that because community college students
“exhibit extensive withdrawals and retakes” (p. 349), college GPA alone would
also be an inappropriate measure of achievement or success. Instead, researchers
have suggested that a community college student’s course completion ratio, a
continuous measure determined by dividing the number of courses attempted into
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92
the number of courses completed with a passing grade, would be a more relevant
measure of his or her persistence (North, 1988) and one that would better describe
the student’s academic progress (Hagedom, Maxwell, & Moon, 2002). Because
graduation rates at community colleges tend to be low due to transfer or stop out
behaviors (Logan, 1997), a student’s course completion ratio would offer a more
appropriate definition of his or her academic success. The TRUCCS project
researchers reasoned that the course completion ratio was an appropriate measure
of success for the community college setting because it would “flex to
accommodate part-time enrollment that is prevalent among community college
students” (Hagedom, Maxwell, & Moon, 2002, p. 4). The dependent variable for
this study was defined as the student’s math course completion ratio, the number
of math courses attempted from fall 2000 through winter 2002 divided into the
number of math courses successfully completed with a passing grade during that
time. The data to compute this measure was obtained from the student transcript
file provided by the LACCD.
Independent Variables
Demographics. Demographic variables used to represent students’
background measures included age, gender, ethnicity, and socioeconomic status
(SES). Students’ ages were recorded as of September 2002 and measured
continuously. Gender was coded as 1 for males and 2 for females. Ethnicity was
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93
coded as a 1 for Asian/Pacific Islanders, 2 for African-American students, 3 for
Hispanic students, and 4 for white students. SES was measured by using several
survey items that asked students about their parents’ educational backgrounds and
occupations. Parents’ occupation was then assessed and assigned a numerical
score between 0 and 100 based on the Nam-Powers-Terrie Occupational Status
Scores Index, a commonly used index for the hierarchical ranking of occupations.
Cognitive variables. Cognitive variables included students’ highest math
course taken as indicated on the survey instrument (participants chose from
calculus, pre-calculus, trigonometry, algebra 2, geometry, algebra 1, and one
response that combined basic math, business math, or pre-algebra), highest
placement test score for mathematics, highest placement test score for English,
college GPA from fall 2000 up to and including winter 2002, students’ self-report
of their overall average grade in high school, and whether or not the student took
remedial math courses.
Push/Pull variables. Push variables refer to students’ study behaviors and
experiences that tend to push them toward positive academic achievement. Survey
items used to measure this construct included studying in groups inside and
outside of class, asking the instructor questions, speaking up during class
discussions, studying for tests early on rather than at the last minute, and
completing homework assignments. Pull variables represent environmental
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factors such as domestic and employment obligations that may tend to divert a
student’s attention from his or her studies. Pull variables included two
dichotomous items, being employed and having children, and one scale labeled as
obstacles.
Non-cognitive variables. Non-cognitive variables included achievement-
related expectancies, academic self-concept, and uncertainty about career choices
and college major. All three constructs were measured using items from the
survey instrument. Uncertainty was included in the analysis because it may be
that failure to pass required math courses will lead students to change their
intended major (from a mathematically-based major to a non-mathematically-
based major) and/or to change their intended choice of career, a phenomenon that
has been reported in four-year institutions (Hewitt & Seymour, 1991).
Data Analysis
This study used both descriptive statistics and inferential statistics to
investigate the existence and extent of relationships among selected variables.
Factor analysis was performed to isolate and identify suitable scales.
Confirmatory factor analysis was performed to test the reliability of the scales.
Correlation coefficients were computed to investigate the relationship between
predictor variables and subsequent achievement in mathematics. Two-way
analysis of variance was used to compare mean transfer completion ratios and
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95
remedial completion ratios both by gender and ethnicity. Finally, ordinary least-
squares multiple regression analysis was performed to determine the relative
contribution of specified variables to success in mathematics and the model was
executed separately for all math courses, remedial math courses, and transfer-
level math courses. Statistical analyses were performed using SPSS 11.0 and the
level of significance established for all tests was at p < 0.05.
Discussion
Currently there exists very little research that examines the relationship
between non-cognitive variables and achievement in college mathematics (House,
1995b). Still fewer studies have simultaneously examined cognitive and non-
cognitive variables as predictors of math achievement. In either case, those
studies that have examined such relationships were conducted at four-year
colleges or universities using samples of traditional-aged college students. The
literature is silent on these issues where community college students are
concerned.
Within the context of the first research question concerning the predictive
relationship between cognitive and non-cognitive variables and achievement in
urban community college mathematics, the correlations between each predictor
variable and subsequent total math course completion ratios indicated that
cognitive and non-cognitive variables were significantly correlated with math
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achievement. Specifieally, the highest math course taken, highest placement test
scores for mathematies and for English, and students’ self-report of their overall
average grade in high school, were significant positive correlates of total math
completion ratios. This finding is consistent with previous studies on four-year
college and university students that found college entrance exam scores (Baron
and Norman, 1992; Craney and Armstrong, 1985; Edge & Friedberg, 1991;
House, 1995c; House, 2000; Kohler, 1973; Nora & Rendon, 1990), high school
grades (Craney and Armstrong, 1985; Ozsogomonyan and Loftus, 1979), and the
number of years of high school math taken (House, 1993d) to be positively
associated with math and science achievement. Having taken remedial math
courses was negatively eorrelated with total math completion ratios perhaps
suggesting that math remediation in the LACCD is not adequately preparing
students to succeed in subsequent math courses.
Starting to study at least two or three days prior to tests and always
completing homework assignments were significant and positive non-cognitive
correlates of total math completion ratios as one would expect. Waiting until the
day before an assignment was due before starting it was a negative correlate of
total math completion ratios, and again this was to be expected. Finally, whereas
academic self-concept was significantly correlated with total math completion
ratios, achievement-related expectancies (getting a bachelor’s degree and
transferring to a four-year college) were not. Self-concept develops through
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constant self-evaluation in different situations (Shavelson & Bolus, 1982). For
students this means weighing verbal and nonverbal reactions of significant
people, namely teachers, to make evaluative judgments (Woolfolk, 1998). The
LACCD math faculty should be informed that encouraging their students,
especially at times when the topics are most difficult, contributes to the students’
self-concept which in turn may positively affect their achievement in
mathematics. Achievement-related expectancies were not significantly correlated
with total math completion ratios which may suggest that while student transfer is
an integral part of the LACCD function, it may not be the most important in the
eyes of its students. More will be said about achievement-related expectancies
later in the discussion.
When transfer level math completion ratios were compared to remedial
level math completion ratios, cognitive and non-cognitive predictors were found
to be significant however the number of predictors that reached significance was
different. For example the highest math course taken and always completing
homework assignments were the only two significant positive correlates
commonly associated with transfer and remedial level math course completion
ratios. College GPA was a significant positive correlate of transfer math
completion ratios but not for remedial level. Declaring a college major was a
significant negative correlate of transfer level completion ratios but it did not
reach significance at all for the remedial level. It seems somewhat contradictory
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that declaring a college major would be negatively associated with transfer level
math completion ratios. It may be that many of the declared majors were
occupational and as such did not call for a transfer level math course to satisfy
degree or certificate requirements. It may also be that once a student formerly
declares a major, possibly non-math related in nature, he or she may be more
inclined to focus time and energy on that course of study perhaps compromising
the amount of effort put forth in non-major courses.
Age, self-report of average high school grade, highest math course taken,
math and English placement test scores, academic self-concept, studying at least
two or three days prior to tests, and always completing homework assignments
were all positively correlated with remedial level completion ratios whereas
waiting until the day before an assignment was due before starting it was
associated with lower remedial math completion ratios.
After examining the results of the regression analyses, the reader may
have noticed the similarities in the predictors that reached significance in the
remedial case and the case of all math courses. A clue to why this might be so is
given by the transcript data, some of which is summarized in Table 23. This table
contains a snapshot of the number of students taking the various levels of
mathematics at any of the nine LACCD colleges from fall 2000 through winter
2002.
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Table 23
Number of Students Taking Various Levels of Math by Semester
Remedial Remedial Remedial
Level 0______ Level 1 _______ Level 2_______ Transfer
Fall 2000 44 40 20 24
Winter 2001 27 49 22 5
Spring 2001 735 843 480 576
Summer 2001 135 236 137 210
Fall 2001 362 506 486 656
Winter 2002 28 38 45 50
As we see from this table, in any one semester there were more students taking
remedial math courses than there were taking transfer level math courses. Thus it
is not surprising that the results for total math completion ratios should echo the
results for remedial level completion ratios. In both cases the results of the
regression analyses showed that older students tended to have higher completion
ratios. Research has shown that adult students tend to earn better grades than
younger students (Moffatt, 1993) and younger students tend to academically
perform better when in the presence of older students (Darkenwald & Novak,
1997; Dobie, 1993) so perhaps it is not surprising that age was found to be a
positive predictor of remedial and total math achievement in this study. It may be
that older students had better achievement results in remedial mathematics
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because they simply repeated courses they once took in high school. Indeed many
remedial students graduate from high school a number of years before attending
college and only need to take a refresher course in math (Hardin, 1988; Ikenberry,
1999; Boilman, Eaton, Otte, & Thomas, 1999; Schrag, 1999; Southem Regional
Education Board, 2000). Furthermore it seems reasonable that older students have
more life and occupational experiences which they can connect to new
information and create meaning, a process known as elaboration (Woolfolk, 1998)
and one that can apply to all students. Briefly, Woolfolk (1998) explained that the
more students elaborate new information with previous knowledge and
experiences, whether by translating information into their own words, by creating
their own examples, or by drawing a relationship, the deeper their understanding
of the new information and the better the recall of that information. This would
suggest that LACCD math teachers supplement assigned exercise sets that stress
routine calculations with problems that ask students to search for meaning and
understanding. Following are two such examples;
• Explain in your own words how the vertical line test works
(Bittinger & Ellenbogen, 2002, p. 538).
• The following “proof’ shows that 0.5 < 0.25. Explain the error
(Aufmann, Barker, & Lockwood, 2000, p. 670)
1 <2
1 * log 0.5 < 2 * log 0.5
log 0.5 < log (0.5)^
0.5 < 0.25
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101
Higher English placements scores contrihuted to higher total and remedial
math completion ratios. English placement scores are an indication of students’
ability to read and write in English yet nearly half (46%) of the students surveyed
responded that English was not their native language. To he sure mathematics
requires the ability to analytically solve problems hut it also requires the ability to
read the problems. Reading is the critical area for most remedial students as it is
associated with additional remediation in writing and mathematics (Adelman as
cited in Hoyt, 1999; NCES, 2001). A report by the National Center for Education
Statistics on the condition of education 2001 (NCES, 2001) found that students
assigned to any remedial reading were less likely to complete a two- or four-year
degree compared to students who took two or fewer remedial courses in
mathematics only (the rates were 34% versus 45% respectively). Further, among
those students who took any remedial reading, 67% also took remedial math and
42% enrolled in three or more remedial courses (NCES, 2001) suggesting that
when students have difficulty reading, all other skills suffer (Merisotis & Phipps,
2000). Consider the following exercises that might appear in any elementary
algebra textbook: “Find the decimal approximation rounded to the nearest
thousandth” or “Find A (T B given A = {-4, -2, 0, 2}”. These statements might
present a difficult challenge for those students not proficient in the English
language. The LACCD mathematics faculty must consider the possibility that for
many of their students, poor performance in math may not necessarily be related
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to the math content but to a language barrier. A possible solution might be to
designate English 21 English Fundamentals or the equivalent as a prerequisite to
the level 0 and level 1 remedial math courses. English 21, a course offered at each
of the nine LACCD colleges, introduces students to the fundamentals of academic
reading, writing, and thinking. By requiring evidence of successful performance
in English 21 or the equivalent before attempting a math course, students would
presumably be sufficiently prepared in English and thus able to focus more
intently on the mathematical content.
The highest math course taken was found to positively predict total and
remedial math achievement. Students indicated their highest math course taken on
the survey instrument by choosing from seven possihilities: calculus, pre-calculus,
trigonometry, algebra 2, geometry, algebra 1, and one response that combined
basic math, business math, and pre-algebra. Twenty-three percent of the students
surveyed indicated that algebra 2 was their highest math course taken. Algebra 2,
geometry, algebra 1, and basic math are all remedial courses so it may be that
students who took remedial math courses from fall 2000 through winter 2002
were successful in their remedial level math courses prior to the survey and were
successful in subsequent remedial math courses or the students were unsuccessful
in their remedial math courses prior to the survey and were repeating them,
perhaps performing better the second (or third) time around. Table 24 indicates
the cross tabulations of students by highest math course taken.
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Table 24
Cross Tabulation of Students by Highest Math Course Taken
Basic
Algebra
1 Geometry
Algebra
2 Trig.
Pre
calculus Calculus
Basic 721
Algebra 1 285 532
Geometry 263 272 368
Algebra 2 450 494 421 751
Trigonometry 195 216 208 206 275
Pre-calculus 137 153 148 150 116 204
Calculus 135 145 144 141 131 129 212
As can be seen in this, of the 212 students who indicated that calculus was the
highest math course they attempted, 129 of them also took pre-calculus, 131 took
trigonometry, and so on. That the highest math course taken significantly
predicted total and remedial math completion ratios suggests that LACCD
academic counselors work closely with the surrounding K-12 school districts to
reinforce the importance of taking advanced math courses before college. While
some high school students “follow the path of least resistance” (Southem
Regional Education Board, 2000, p. 13) and take only the minimum number of
math courses necessary to graduate, research has shown the highest level of math
studied in high school to have the strongest influence on degree completion
(Adelman, 1999b) and that the odds of a student completing a bachelor’s degree
more than doubled when he or she completed a math course beyond algebra 2
(Adelman, 1999b).
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Students who always complete their homework assignments tend to have
higher total and remedial math completion ratios. Mathematics is cumulative in
nature and therefore it requires constant practice, usually through working on
homework exercises. Consequently, putting off or waiting until the last minute to
begin practicing does not lend itself well to success in math especially if one were
to fall behind. The LACCD math faculty should frequently stress the importance
of keeping up with and completing homework assignments. Even so, completing
daily homework assignments can be challenging for part-time students who must
work (Hagedom, Siadat, Nora, & Pascarella, 1997). Indeed for students in this
study, working tended to hinder total and remedial math achievement. Almost
71% of the students surveyed were employed and for many of these students,
working takes precedence over college studies. It may be useful for LACCD math
faculty to consider this when assigning homework. For example rather than
assigning twenty or thirty exercises for practice every night, or more if the class
does not meet daily, the faculty member might pick out the most important and/
or interesting problems for weekly assignments and class discussions. Lengthy
exercise sets that stress routine calculations and skill building might be better left
for weekend assignments.
Students with higher GPAs tended to have higher transfer level math
completion ratios. It may be that students with higher grade point averages tend to
be more aware of how they are performing academically and have become adept
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105
at help-seeking behaviors when their performance becomes substandard. Many of
these students will likely do well no matter what classes they take. For other
students, especially urban community college students, trying to maintain a
satisfactory GPA may be a constant struggle for a variety of reasons. These
students should be encouraged to participate in study groups, to visit tutoring
centers and counseling centers, and to seek out approachable faculty for guidance
and assistance. It might prove useful to study the characteristics of a sample of
LACCD students with higher GPAs. The results of such a study might aid in the
development of positive learning and study strategies for all urban community
college students.
The finding that remedial math courses was a negative predictor of total
and transfer level math completion ratios was unexpected and warrants further
investigation by the LACCD. This finding contradicts previous research results
that found remedial math courses to be predictive of achievement in subsequent
math courses (Penny and White, 1998; Waycaster, 2001). An examination of the
college catalogues for each of the LACCD schools revealed that prerequisite
courses passed with a letter grade of at least a C or appropriate placement test
scores were necessary to enroll in intermediate algebra courses or higher, an
indication that the right measures are in place to promote students’ success. It may
be however that a number of students who attempted transfer level math courses
needed remediation but passed some of their early remedial math courses with a
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106
grade of a low C or even a D, they “just got by”. “Just getting by” however may
not be a viable plan for students who need to satisfy remedial math requirements
before they can take transfer level math. It is curious that these students might
have believed they would be successful in more difficult math courses and further
investigation is suggested to discover if and why they might have reasoned so.
Clues to their motivations may aid faculty and counselors in creating and
implementing strategies early on to help remedial math students do more than just
get by. It is also recommended that the mathematics faculty communicate early on
with students in danger of failing that tutoring and/or extra help during office
hours would be in their best interests. That said, an inspection of the nine LACCD
college catalogues turned up no information that the nine colleges participate in
efforts to formally inform students of their progress at some point during the
semester. District administrators and faculty should work together to see that all
students are formally provided with mid-semester progress reports, whether by
mail or electronically. Such reports would ensure that faculty members were
intimately aware of their students’ progress and students would be informed early
enough to take appropriate measures.
To be sure there were a number of LACCD students who took remedial
math courses and who were completely successful in their transfer level math
courses. Of the students who took transfer level mathematics (N = 747), 451 were
completely successful, that is, they passed all of the transfer level math courses
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107
they attempted. Unfortunately any descriptive analyses are complicated by the
fact that not every student surveyed identified themselves by gender, ethnicity, or
age. For example if we disregard those students who did not identify themselves
by gender, then the number of students is reduced from 451 to 261. Nevertheless
these remaining 261 students are described in Table 25.
Table 25
Number of Students Completely Successful in Transfer Math bv Gender and
Ethnicity
Male Female Total
Asian 28 34 62
African-American 12 26 38
Hispanic 48 86 134
White 16 11 27
Total 104 157 261
Of the 451 students who were completely successful in transfer math, 102 of them
took level 2 remedial math courses, 31 took level 1 remedial math courses, and 27
took level 0 remedial math courses. Of the 102 who took level 2 math courses,
twenty-two of them took level 1 remedial math courses. It would appear that
remedial math courses were of some benefit to these students. Perhaps a separate
study with a qualitative component would assist LACCD administrators and
faculty in discovering common characteristics of these 451 students associated
with their achievement in math, especially for those who traveled the remedial
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108
pathway to transfer level success. The results of such a study may aid faculty in
developing appropriate curricula valuable for all students, especially students in
need of remedial math.
Achievement-related expectancies and academic self-concept failed to
make significant contributions to the models for total, transfer, and remedial math
completion ratios. These results differ from previous research that found
achievement-related expectancies and academic self-concept to be predictors of
achievement in various four-year college math courses (House, 1995b, 1995c,
1995d, 2000). This may be due to the different populations studied. Urban
community colleges have largely diverse student bodies whereas four-year
colleges and university student populations tend to be more traditional. For
example traditional four-year college students tend to enroll immediately after
earning the high school diploma, they often depend on their families for academic
encouragement and financial support, and if they work at all during the school
year it is likely to be only part-time (NCES, 2002). These students are therefore
unencumbered by the outside influences that urban community college students
are forced to contend with on a daily basis consequently research comparisons
between both populations are problematic and must be made with great care.
Furthermore, the scale for achievement-related expectancies was composed of
two items from the survey instrument, namely expectations of getting a bachelor’s
degree and expectations of transferring to a four-year college, however many
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109
community college students have no such goals. To be sure many community
college students intend to take only one or two courses without pursuing a degree
(Bean & Metzner, 1985) yet that one or two courses meets their particular
educational goals (Alfrey, 1997). Finally the scale for academic self-concept was
composed of items from the survey that had to do with attitudes such as, “I expect
to earn good grades” and “I keep trying even when I’m frustrated”. It may be that
many urban community college students are not so much motivated by attitudes
such as “I can” as they are by attitudes such as “I must”. Consider that African-
Americans and Hispanics living in urban areas are four times more likely to be
unemployed, to live in poverty, and to live in poor housing (Cisneros, 1996). It
seems reasonable to suggest that performing well in college, rather than an end
unto itself, can be a means for escaping poverty and unemployment.
The second research question sought to determine if the predictive
relationship between cognitive and non-cognitive variables and success in
mathematics was similar for all groups of students in terms of gender and
ethnicity however when Pedhazur’s (1982) method was used to check for gender
and ethnicity interactions between the independent variables, neither reached
significance thus no further regression analyses on gender or ethnicity separately
were necessary. Even so a two-way ANOVA was performed twice to determine if
there were differences in math completion ratios by gender and ethnicity, once for
transfer level and again for remedial level. In either case there was no significant
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110
interaction between gender and ethnicity. Also, in either case there was no
significant main effect for gender. Females did not achieve significantly different
completion ratios than males at the transfer or remedial level. While it can not be
concluded that the gender gap in math achievement no longer exists for LACCD
students, these results are encouraging in light of findings in previous research
that the gap persists. The same can not be said of differences between ethnic
groups. In the case of transfer level completion ratios, Asian students had
significantly higher completion ratios than Hispanic students. In the case of
remedial level completion ratios, white students had significantly higher
completion ratios than Hispanic students and African-American students. Both
results echo the disparity in math achievement found between different ethnic
groups at earlier ages where according to the NAEP 2000 (U. S. Department of
Education, 2001c) assessment of mathematics achievement of fourth, eighth, and
twelfth grade students across the nation, white and Asian/Pacific Islander students
scored higher on average than African-American and Hispanic students. It is
curious that none of the nine LACCD campuses have a Mathematics,
Engineering, and Science Achievement program (MESA). The MESA program is
administered through the University of California and provides math, engineering
and science academic enrichment to educationally underprepared community
college students, especially students belonging to minority groups
underrepresented in the sciences, so that they can succeed academically and
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transfer to four-year colleges or universities as math-based majors (California
MESA, 2004). It may be that the LACCD lacks the resources necessary to
implement such a program. If that is the case then perhaps it would be useful for
LACCD administrators, faculty, students and other stakeholders to approach
industries in the Los Angeles area to identify sources of funding in order to
support a MESA program for at least one of the nine colleges. It is also
recommended that LACCD math faculty seriously consider the different learning
styles of Hispanic and African-American students. For example Sanchez (2000)
found that Hispanic students preferred concrete examples over theories and
hypotheses, working in groups and sharing ideas over competing with others for
grades, and a desire to participate in classroom activities. Fullilove and Treisman
(1990) sought to determine the factors that explained differences in the
performances of African-American and Chinese-American students enrolled in
first-year calculus at the University of California, Berkeley. The researchers found
that African-American students were more likely to study alone whereas Chinese-
American students were more likely to study together and to combine their social
time with study time. The results showed that the Chinese students excelled in
calculus whereas the African-American students failed. With these important
ideas in mind, it is recommended that the LACCD math faculty consider allowing
time for students to work together on classroom activities and require group
projects outside of class that stress real-world problem solving. Indeed these
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112
recommendations are similar to those recommended by the American
Mathematical Association of Two-Year Colleges (1999), namely that
mathematics should be taught in the context of real-world situations and that
effective mathematics instruction should include the active participation of
students working together on in-depth projects. Such methods may benefit
minority students more so than the traditional method of college math instruction
of lecturing only.
Conclusion
The primary purpose of this dissertation was to determine whether cognitive and
non-cognitive variables had any predictive value for urban community college
students’ success in mathematics. The results of this study showed that cognitive
items that included English placement scores, the highest math course taken, and
college GPA significantly predicted achievement in mathematics for urban
community college students whereas having taken remedial math courses and
being employed were negative predictors. Always completing homework
assignments was the only non-cognitive item to significantly predict math
achievement (overall math and transfer level math). These results add to the small
body of research that has shown cognitive and non-cognitive variables to be
positively associated with various four-year college math and science courses.
This is especially noteworthy as a literature search failed to produce any studies
that simultaneously examined cognitive and non-cognitive variables as predictors
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113
of achievement in mathematics for students enrolled in community colleges.
While House (1993a, 1993b, 1993c, 1993d, 1994, 1995a, 1995b, 1995c, 1995d,
2000) found non-cognitive variables such as academic self-concept and
achievement-related expectancies to be predictors of achievement in various four-
year college courses, this study showed otherwise. It has been suggested here that
achievement-related expectancies and academic self-concept are non-cognitive
variables that are perhaps inappropriate when attempting to measure academic
outcomes for urban community college students. Another study with the same
scope and magnitude as the TRUCCS project and conducted at other urban
community college districts might serve to confirm or refute that claim.
Recommendations
The following recommendations evolved from the findings:
1. The LACCD math instructors may wish to consider supplementing
homework assignments that stress routine calculations with
problems that ask students to search for meaning and
understanding. Such problems may allow students to elaborate new
information with previous knowledge leading to a deeper
understanding of new material.
2. The LACCD math faculty should frequently stress the importance
of completing homework assignments. Further, they may want to
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114
consider leaving lengthy assignments for weekends, to
accommodate students who must work, while assigning interesting
and challenging problems for daily assignments. Such assignments
might include small group projects or problems that stress real-
world applications.
3. The LACCD mathematics faculty should consider designating
English 21 English Fundamentals or the equivalent as a
prerequisite to basic remedial math courses. It may be that poor
performance in remedial math courses is due to poor English skills
rather than the mathematical content of the courses.
4. The LACCD academic counselors should work closely with the
surrounding K-12 school districts to emphasize the importance of
taking advanced math courses before college.
5. The LACCD should formally provide students with mid-semester
progress reports to keep them informed of their progress.
6. The LACCD administrators, faculty, students, and other
stakeholders should work closely to determine the feasibility of
developing a MESA program. By providing enrichment in math,
engineering, and science, the MESA program would prepare
LACCD students to transfer to four-year colleges or universities as
math-based majors.
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115
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Asset Metadata
Creator
Gervasi, Jeffrey Michael
(author)
Core Title
Community college students and achievement in mathematics: Predictors of success
School
Rossier School of Education
Degree
Doctor of Education
Degree Program
Education
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
education, community college,Education, higher,Education, Mathematics,OAI-PMH Harvest
Language
English
Contributor
Digitized by ProQuest
(provenance)
Advisor
Hagedorn, Linda Serra (
committee chair
), Newman, Fran (
committee member
), Sundt, Melora (
committee member
)
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c16-518379
Unique identifier
UC11335817
Identifier
3140474.pdf (filename),usctheses-c16-518379 (legacy record id)
Legacy Identifier
3140474.pdf
Dmrecord
518379
Document Type
Dissertation
Rights
Gervasi, Jeffrey Michael
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 au...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA
Tags
education, community college
Education, Mathematics