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Three essays on the high school to community college STEM pathway
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Three essays on the high school to community college STEM pathway
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THREE ESSAYS ON THE HIGH SCHOOL TO COMMUNITY COLLEGE STEM
PATHWAY
A DISSERTATION
SUBMITTED TO THE FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE
DOCTOR OF PHILOSOPHY (URBAN EDUCATION POLICY)
Elizabeth So Yun Park
August 2019
ACKNOWLEDGMENTS
I would like to acknowledge the generous financial support provided by the USC Rossier
School of Education, the USC Graduate School, and the Haynes Foundation. With this support, I
was able to fully dedicate my time and energy towards completing this dissertation.
A heartfelt thank you goes out to my parents for supporting me throughout this Ph.D. I
came to the United States when I was four because my dad decided to pursue a Ph.D. in
Engineering in the United States. My childhood memory of his superb work ethic and whole
hearted dedication to push his dissertation to the finish line fueled my perseverance to finish
mine. If my dad fueled my perseverance, I learned how to persevere from my mom. She taught
me resilience by example – she successfully navigated through different community college and
university settings to improve her English and hustled through service and office jobs to make
ends meet. My parents taught me to see things through and do honest work. I know that my
resilience and drive stem from their teaching, support, optimism, and encouragement.
I am indebted to my faculty advisor, Tatiana Melguizo, and my dissertation committee
members, Morgan Polikoff, Adrianna Kezar, and T.J. McCarthy. I appreciated their willingness
to hear my unending stream of ideas and explorations. At some point, I decided that the amount
of feedback I received on a document was indicative of the amount of potential the reviewer saw
in my work. That said, I would like to say a special thank you to my dissertation committee for
providing me with thorough feedback on my ideas, outlines, and manuscripts over the years.
Thank you for holding me to high standards and for the tough love. In particular, I would like to
express my deep gratitude towards Tatiana for all of the helpful feedback and warm
encouragement along the way.
I would like to express my appreciation towards Laura Romero and Darnell Cole who
always asked me how I was doing not only as an academic but also as an individual. Thank you,
Laura, for helping me navigate any and all situations and thank you, Darnell, for your
willingness to listen to my ideas and progress.
There are many friends who supported me academically and emotionally at USC –
special shout out to Elizabeth Holcombe, Eddy Chi, Joanna Drivalas, Rebecca Gotlieb and the
rest of the “Cool Cohort,” Marissiko Wheaton, Jude Dizon, Federick Ngo, and many others.
Most notably, I would like to extend a big thank you to Federick Ngo for his mentorship and
willingness to give me candid advice whenever I needed it. In addition, a special thank you goes
out to Elizabeth Holcombe for her invaluable friendship. You all made my graduate school years
both intellectually stimulating and enjoyable.
Last but not least, I would like to say a sincere thank you to my soontobe husband, Ted
Kang. Thank you for always showing interest in my research and remaining highly engaged
throughout the years. Your support helped me overcome difficult times and nudged me to strive
for the best. Thank you for being my biggest critic and my biggest champion.
ABSTRACT
Science, Technology, Engineering, and Mathematics (STEM) related jobs are the fastest
growing jobs in the knowledge economy. However, a significant proportion of college students
with the intent to pursue STEM fields, or STEMaspiring students, exit the pathway. Moreover,
women and underrepresented minorities (URM) are more likely to switch to nonSTEM fields
and are less likely to pursue STEM majors in college than their White and male peers. While
community colleges serve diverse student populations and therefore have potential to diversify
the STEM talent pool, there exists scant empirical evidence examining community college as a
viable STEM pathway.
Addressing this gap, this dissertation consists of three related studies examining structural
barriers and explanations behind differential STEM participation in community college. Two of
the three studies investigate the role of math remediation, a common barrier for community
college students, and the third study examines the gender gap in STEM persistence at community
colleges. All three studies use linked high school and community college transcript data,
demographic data, and math and English placement test data of community college students who
graduated from a large, urban school district in California.
The first study investigates the extent to which students experienced math misalignment
in the transition from high school to community college. Math misalignment occurs when
community college students are placed lower than expected in math given their prior high school
coursetaking history and record of achievement. This study finds that many STEMaspiring
students – despite taking advanced high school math – placed in developmental math in college.
Subsequently, students who experienced math misalignment were less likely to attempt and
complete the course requirements necessary for their STEM degree.
The second study examines the effect of developmental math placement on STEM
participation. In addition, this study examines whether developmental math disproportionately
affects women, URMs, students who took advanced high school math and science courses
(“STEMoriented students”), and STEMaspiring students. The results indicate that students who
missed the cutoff and placed lower into developmental math were less likely to attempt
transferable STEM courses compared to students who placed directly in transferlevel math.
Women, URMs, STEMoriented, and STEMaspiring students were also negatively affected by
lower placement, indicating that developmental math is a structural barrier in the STEM
pathway.
The third study examines whether a STEM gender gap exists at community colleges and
subsequently investigates comparative advantage, a potential mechanism driving this gap.
Comparative advantage is the notion that students pursue future study based on early feedback of
their relative strength in course subjects. Results indicate no evidence of a STEM gender gap
among academically prepared students studying Physical Science/Engineering (PS/E). However,
there exists a persistent STEM gender gap among academically underprepared PS/E students
who initially placed in low levels of developmental math and English. Furthermore, comparative
advantage in STEM exacerbated this gap as academically underprepared PS/E men outpaced
academically underprepared PS/E women in completing transferable science courses.
Collectively, these three essays inspect potential barriers and explanations driving
students’ STEM participation and persistence at community colleges. This dissertation illustrates
specific ways in which community colleges can support STEMaspiring students, particularly
those from minoritized backgrounds, through various transitional points from high school on to
community college.
TABLE OF CONTENTS
Introduction ................................................................................................................................... 1
Research Problem .................................................................................................................... 3
Defining STEM ....................................................................................................................... 5
Research Questions and Three Papers ..................................................................................... 6
Essay I. The Role of Math Misalignment in the Community College STEM Pathway ... 6
Essay II. The Effect of Developmental Math on STEM Participation in Community
College: Variation by Race, Gender, Achievement, and Aspiration ................................ 7
Essay III. Comparative Advantage in STEM and the STEM Gender Gap in Community
College .............................................................................................................................. 8
Organization .......................................................................................................................... 10
References ............................................................................................................................. 11
Essay I. The Role of Math Misalignment in the Community College STEM Pathway........ 15
Prior Literature ...................................................................................................................... 19
Math Misalignment ........................................................................................................ 20
Implications for STEM ................................................................................................... 22
Data and Context ................................................................................................................... 23
Key Variables ........................................................................................................................ 23
Method ................................................................................................................................... 27
Identification ................................................................................................................... 28
STEM Outcome Measures ............................................................................................. 29
Missing Values ............................................................................................................... 30
Results ................................................................................................................................... 31
Descriptive Statistics ...................................................................................................... 31
Math Misalignment and STEM Outcomes ..................................................................... 31
Results for STEMAspiring Students ............................................................................. 32
Graphical Representation of the Findings ...................................................................... 33
Sensitivity Analyses .............................................................................................................. 34
Discussion .............................................................................................................................. 35
Policy Implication .................................................................................................................. 37
Future Research ..................................................................................................................... 39
References ............................................................................................................................. 42
Tables ..................................................................................................................................... 50
Figures ................................................................................................................................... 55
Appendix ............................................................................................................................... 56
Essay II. The Effect of Developmental Math on STEM Participation in Community
College: Variation by Race, Gender, Achievement, and Aspiration ...................................... 65
Conceptual Framework .......................................................................................................... 69
Math Remediation in STEM Pathways ................................................................................. 72
Math Assessment and Placement Policy in LUCCD ............................................................. 74
Data and Sample .................................................................................................................... 74
Empirical Strategy ................................................................................................................. 76
Regression Discontinuity ................................................................................................ 76
RD Validity .................................................................................................................... 79
Subgroup Analysis .......................................................................................................... 80
Outcomes ........................................................................................................................ 81
NonEnrollment .............................................................................................................. 82
Results ................................................................................................................................... 83
Main Estimation Results ................................................................................................. 84
Subgroup Results: Women and URMs ........................................................................... 85
Subgroup Results: STEM Orientation and Aspiration ................................................... 87
Sensitivity Analyses .............................................................................................................. 88
Limitations ............................................................................................................................. 90
Discussion .............................................................................................................................. 91
Conclusion ............................................................................................................................. 94
References ............................................................................................................................. 96
Tables ................................................................................................................................... 104
Figures ................................................................................................................................. 116
Appendix ............................................................................................................................. 120
Essay III. Comparative Advantage in STEM and the STEM Gender Gap in Community
College ........................................................................................................................................ 131
Conceptual Framework ........................................................................................................ 135
Empirical Literature ............................................................................................................. 137
Prior Preparation in Math and Science ......................................................................... 137
Comparative Advantage in STEM ............................................................................... 138
First Year of Community College ................................................................................ 140
Hypothesis ........................................................................................................................... 141
Data and Sample .................................................................................................................. 142
Empirical Strategy ............................................................................................................... 144
Nearest Neighbor Matching without Replacement ...................................................... 148
Results ................................................................................................................................. 149
Comparison with LUSD Graduates and California High School Graduates ............... 149
Pre and PostMatching Balance .................................................................................. 150
Graphical Representation of the Findings .................................................................... 154
Sensitivity Analyses ............................................................................................................ 155
Discussion ............................................................................................................................ 155
Policy implication ................................................................................................................ 158
Conclusion ........................................................................................................................... 160
Reference ............................................................................................................................. 163
Tables ................................................................................................................................... 173
Figures ................................................................................................................................. 180
Appendix ............................................................................................................................. 183
Conclusion ................................................................................................................................. 193
Common Themes ................................................................................................................. 194
Implications for Policy and Practice .................................................................................... 195
Future Research ................................................................................................................... 196
References ........................................................................................................................... 199
LIST OF TABLES
Tables from Essay I. The Role of Math Misalignment in the Community College STEM
Pathway
Table 1. Definitions of Misalignment Based on the Highest High School Math Course, HS
GPA, and Math Placement
Table 2. Sample Statistics
Table 3. High SchoolbyCollege Fixed Effects Estimation of Math Misalignment on STEM
Outcomes
Table 4. Interaction Estimation of Math Misalignment and STEM Aspiration on Passing
Math Requirement for AA
Table 5. Interaction Estimation of Math Misalignment and STEM Aspiration on STEM
Outcomes
Table A.1 Crosswalk of Major Name, Classification of Instructional Program (CIP) Code,
and the Taxonomy of Program (TOP) Code by STEM Majors (Life Science and Physical
Science/Engineering)
Table A.2. Description of Missing Values
Table A.3. High SchoolbyCollege Fixed Effects Estimation of Math Misalignment using
Last High School Math Course
Table A.4. Interaction Estimation of Math Misalignment using Last High School Math
Course and STEM Aspiration on STEM Outcomes
Table A.5 High SchoolbyCollege Fixed Effects Estimation of Math Misalignment using
Math Enrollment
Table A.6. Interaction Estimation of Math Misalignment using Math Enrollment and STEM
Aspiration on STEM Outcomes
Table A.7. High SchoolbyCollege Fixed Effects Estimation of Math Misalignment using
Highest High School Math Course Passed with A or B
Table A.8. Interaction Estimation of Math Misalignment using Highest High School Math
Passed with A or B and STEM Aspiration on STEM Outcome
Table A.9. Sharp Regression Discontinuity Estimates around the Intermediate
Algebra/TransferLevel Math Cutoff
Tables from Essay II. The Effect of Developmental Math on STEM Participation in
Community College: Variation by Race, Gender, Achievement, and Aspiration
Table 1. Demographic Breakdown of LUCCD Students, 20052008
Table 2. Test of Baseline Equivalence around Levels of Cutoff, +/ 0.75 SD Bandwidth
Table 3. The Effects of Developmental Math Placement on Math Progression and STEM
Participation
Table 4. Differential Effect of Developmental Math Placement on Math Progression and
STEM Participation for Female Students
Table 5. Differential Effect of Developmental Math Placement on Math Progression and
STEM Participation for URM Students
Table 6. Differential Effect of Developmental Math Placement on Math Progression and
STEM Participation for STEMOriented Students
Table 7. Differential Effect of Developmental Math Placement on Math Progression and
STEM Participation for STEMAspiring Students
Table 8. Effect of Developmental Math Placement on STEM Participation among Enrollees
Table A.1. Differential Effect of Developmental Math Placement on Math Progression and
STEM Participation for Female Enrollees
Table A.2 Differential Effect of Developmental Math Placement on Math Progression and
STEM Participation for URM Enrollees
Table A.3. Robustness of Main RD Estimates across Minimum and Maximum Bandwidth
Table A.4. Robustness of STEMAspiring Interaction Estimates across Minimum and
Maximum Bandwidth for those around the AR/PA and PA/EA Cutoffs
Table A.5. Robustness of STEMAspiring Interaction Estimates across Minimum and
Maximum Bandwidth for those around the EA/IA and IA/TLM Cutoffs
Tables from Essay III. Comparative Advantage in STEM and the STEM Gender Gap in
Community College
Table 1. Comparison of California Graduates, LUSD Graduates, and the LUSDLUCCD
Sample, 201213
Table 2. Pre and PostMatching Balance of PS/EAspiring Students
Table 3. Pre and PostMatching Balance of LSAspiring Students
Table 4. Gender Gap in STEM Persistence, Four Matched Samples
Table 5. Relationship between Comparative Advantage and STEM Persistence, Four
Matched Samples
Table 6. Differential Effect of Comparative Advantage and Gender on STEM Persistence,
Matched PS/E Sample
Table 7. Differential Effect of Comparative Advantage and Gender on STEM Persistence,
Matched LS Sample
Table A.1. Crosswalk of major name, Classification of Instructional Program (CIP) code,
and the Taxonomy of Program (TOP) code by Life Science and Physical
Science/Engineering
Table A.2. Robustness of the STEM Gender Gap across Different Estimation Procedures
Table A.3. Robustness of the Relationship between Comparative Advantage and STEM
Persistence across Different Estimation Procedures
Table A.4. Robustness of the Differential Effect of Comparative Advantage and Gender
across Different Estimation Procedures in the PS/EAspiring Sample
Table A.5. Robustness of the Differential Effect of Comparative Advantage and Gender
across Different Estimation Procedures in the LSAspiring Sample
LIST OF FIGURES
Figures from Essay I. The Role of Math Misalignment in the Community College STEM
Pathway
Figure 1. Interaction Plot of Transferable STEM Units Attempted and Completed Adjusted
Means by STEMAspiration
Figures from Essay II. The Effect of Developmental Math on STEM Participation in
Community College: Variation by Race, Gender, Achievement, and Aspiration
Figure 1. Math Enrollment Rates by Math Placement
Figure 2. Discontinuity in the Density of the Running Variables across Four Placement
Cutoffs
Figure 3. Fraction of Students Enrolled in College after Math Assessment
Figure 4. Discontinuity at the Intermediate Algebra/Transferlevel Math Cutoff on
Developmental Math Progression and STEM Participation
Figure A.1. Measures of Math Progression and STEM Participation around the
Arithmetic/PreAlgebra Cutoff with Local Linear Regression Fit on Each Side
Figure A.2. Measures of Math Progression and STEM Participation around the Pre
Algebra/Elementary Algebra Cutoff with Local Linear Regression Fit on Each Side
Figure A.3. Measures of Math Progression and STEM Participation around the Elementary
Algebra/Intermediate Algebra Cutoff with Local Linear Regression Fit on Each Side
Figures from Essay III. Comparative Advantage in STEM and the STEM Gender Gap in
Community College
Figure 1. The High School to Community College STEM Pathway
Figure 2. Adjusted Marginal Means for Academically Prepared PS/EAspiring Men and
Women
Figure 3. Adjusted Marginal Means for Academically Underprepared PS/EAspiring Men
and Women
Figure A.1. Common Support of Four Samples Pre and PostMatching
Figure A.2. Adjusted Marginal Means for Academically Prepared LSAspiring Men and
Women
Figure A.3. Adjusted Marginal Means for Academically Underprepared LSAspiring Men
and Women
1
Introduction
Increasing the size of the Science, Technology, Engineering, and Mathematics (STEM)
capable workforce is an ongoing consideration among policymakers, practitioners, and
researchers alike. There are several reasons fueling this attention. For one, STEMrelated jobs
are the fastest growing jobs in the knowledge economy (Vilorio, 2014). The Bureau of Labor
Statistics estimated that the total number of STEM occupations will grow to nine million
between 2012 to 2022, an increase of one million occupations from 2012 employment levels
(Vilorio, 2014). Additionally, these jobs typically require some postsecondary education while
the number of jobs for high school graduates continues to decline (Carnevale, Strohl, Cheah, &
Ridley, 2017). These trends disproportionately affect underrepresented minorities (URMs) as a
higher proportion of these individuals are concentrated in occupations that are at high risk of
automation (e.g., cashiers, drivers, administrative assistants) (Muro, Liu, Whiton, & Kulkarni,
2017).
Despite the projected growth in STEMrelated jobs, several reports point out that few
students – particularly women and URMs – persist as STEM majors and graduate with the skills
to meet this demand (Carnevale, Smith, & Melton, 2011; PCAST, 2012). Therefore, stakeholders
argue for the need to expand upon and diversify the relatively small and homogenous STEM
workforce as a way to preserve the nation’s economic vitality (National Science Board [NSB],
2018). Furthermore, ensuring that more women and URMs pursue and persist in STEM fields
advances not only national economic priorities, but also economic and social opportunities for
underrepresented students.
More recently, community colleges are garnering attention for their potential role in
diversifying the STEM talent pool (e.g., Bahr et al., 2017; Wang, 2013a; Wang, 2015). As
2
institutions with relatively low tuition rates and missions to serve the community, these colleges
educate a large population of firstgeneration, lowincome, and URMs aspiring to pursue STEM
fields (Van Noy & Zeidenberg, 2017). As such, community colleges are poised to play a key role
in building a STEM workforce that reflects the diversity of the U.S. population.
In three related studies, this dissertation presents new evidence on factors that bolster or
undermine STEM interest among students making the transition from high school to community
college. The transition from high school to college is a malleable time in students’ educational
trajectory (Johnson et al., 2007; National Science Foundation, 2017). Students report feeling
uncertain and even lost during the first year in college (Hurtado et al., 2007) and attrition from
the STEM pathway occurs more during the first year relative to later years (Chen & Soldner,
2013). Indeed, several interventions focused on college retention target early college years (e.g.,
Angrist, Autor, Hudson, & Pallais, 2014; Melguizo et al., 2018). For these reasons, this study
focuses on factors that affect STEM participation and persistence during the transition from high
school to community college.
Each study examines one aspect that may impede STEMaspiring community college
students from participating and persisting in STEM fields. In the first two papers, my coauthors
and I examine whether developmental (i.e., remedial) math affects students’ likelihood of STEM
participation in community college. In the third paper, I examine the extent to which there exists
a STEM gender gap in Life Sciences (LS) and Physical Sciences and Engineering (PS/E), and
subsequently investigate a potential mechanism driving this gap called comparative advantage.
As promoting and sustaining STEM interests are on the forefront of scholarly and educational
policy agendas, this dissertation consists of three essays on sustaining STEM interest among
community college students.
3
Research Problem
Several trends show that a significant proportion of college students with the intent to
pursue STEM fields, or STEMaspiring students, exit the pathway. First, fewer than 40% of
STEMaspiring students complete a degree in STEM (Carnevale et al., 2011; PCAST, 2012).
Second, many STEMaspiring students eventually switch to nonSTEM degrees while fewer
nonSTEM students switch into STEM fields (Chen & Soldner, 2013; National Center for
Education Statistics [NCES], 2017). Third, STEM attrition and attainment rates become more
pronounced along racial and gender lines. For example, STEMaspiring Black students and
women are more likely to switch to nonSTEM fields than their White and male peers (Chen &
Soldner, 2013). Given these trends, I focus on student populations aspiring to major in STEM
and, in particular, female and URM students aspiring to enter STEM fields.
Extant empirical literature mainly focuses on STEMaspiring students enrolled at four
year universities and less attention has been placed on community college students. Specifically,
scholars have focused on highachieving minority students attending fouryear institutions
(Crisp, Nora, & Taggart, 2009; Melguizo & Wolniak, 2012) or precollege factors like high
school math and science preparation that affects STEM entry at universities (Gottfried, &
Bozick, 2016; Maltese & Tai, 2011; Wang, 2013b; Tai, Liu, Maltese, & Fan, 2006). In contrast,
STEMaspiring community college students have received far less attention. More recently, a
handful of scholars have examined STEM coursetaking patterns and STEM pathways at
community colleges (Bahr et al., 2017; Wang, 2016); but more empirical research is needed to
unpack the factors that contribute to successful STEM participation among women and URMs at
community colleges.
4
In this dissertation, I focus on community colleges because these institutions educate
nearly half of the U.S. population (American Association of Community Colleges, 2015). Recent
statistics show that while the number of Associate’s degrees conferred increased by 75% from
2000 to 2016 (NCES, 2018), less than 5% of the 201516 Associate’s degrees conferred were in
STEM. Notably, community colleges are located in almost every community, have lower tuition
costs, and are open access institutions that provide educational opportunity to many first
generation and/or lowincome students and students of color. While jobs that require at least a
bachelor’s degree in STEM are concentrated in a handful of technology industrydriven
metropolitan areas, jobs that require subbaccalaureate degrees in STEM are sprawled in every
large metropolitan area (Rothwell, 2013). Therefore, students equipped with relevant STEM
skills are less likely to be unemployed and more likely to meet the hiring demands of the local
economy. In particular, I examine students attending California community colleges. California
has the largest community college system in the nation and enrolls about 25% of all community
college students across the country (California Community College Chancellor’s Office, 2013).
Research demonstrates that women surpass men in degree attainment but fewer women
complete a degree in STEM (NCES, 2018). The latest national data available suggest that over
half of all degree holders are women. Specifically, in 201516, while 61% of all Associate’s
degrees conferred were to women, only 23% of women obtained an Associate’s degree in STEM
(NCES, 2018).
1
The gender disparity in STEM degree attainment is especially prominent when
examining STEM subfields like Physical Science and Engineering.
There is also untapped STEM potential among racial and ethnic minorities historically
underrepresented in STEM, such as those who identify as African American, Latinx, American
Indian, and Pacific Islander. Recent statistics show that URMs are less likely to pursue STEM
5
fields than White students. Specifically, in 201516, 11% of Blacks and 16% of Hispanics
attained an Associate’s degree in STEM compared to 61% of White students. Importantly, these
students may be “lost Einsteins” – those who might have made a difference in highly impactful
innovations but were denied opportunities due to educational inequality (Bell et al., 2017, pg. 5).
Following inventors’ lives from childhood to adulthood, Bell et al. (2017) found that White
children were three times more likely to invent and hold patents than Black children and only
18% of inventors were women (Bell et al., 2017). Therefore, statistics and empirical research
point to the need to engage diverse, underserved communities in STEMfocused education.
Defining STEM
Before describing the three essays, I clarify the definition of STEM I use throughout this
research. There is no commonly accepted definition of STEM that specifies the disciplines that
should be included. On the one hand, the Bureau of Labor Statistics defines STEM to include the
following disciplines: science, engineering, mathematics, and information technology. On the
other hand, the National Science Foundation includes the aforementioned disciplines as well as
some social sciences like psychology and economics. In this dissertation, I define STEM as a
combination of both science and engineering and technical fields, guided by previous studies on
community college STEM pathways (Wang, 2016; Van Noy & Zeidenberg, 2017). I include the
commonly considered STEM disciplines like science, engineering, mathematics, and information
technology but do not include social sciences. I also categorize the following program of study as
STEM: medical assistants, technicians, mechanics, agricultural science, and health sciences. I do
so for two reasons – first, community college students majoring in these fields take a significant
number of math and science courses (Bahr et al., 2017; Wang, 2016) and second, students in
6
these technical programs attain workrelevant skills and knowledge (Van Noy & Zeidenberg,
2017).
To execute this definition, I use a crosswalk of the Taxonomy of Program codes and the
Classification of Instructional Programs codes published by the California Community College
Chancellor’s Office (2004) and Wang’s (2016) study to classify different majors as STEM or
nonSTEM. Using data on students’ intended program of study obtained from their college
application, I categorize students’ intended program of study into STEM and nonSTEM fields.
Thus, STEMaspiring students are students whose majors fit under this dissertations’ definition
of STEM.
Research Questions and Three Papers
This dissertation contributes to the emerging body of research on STEMaspiring
students at community colleges by focusing on the following overarching research questions.
1. To what extent does the misalignment in math standards between high schools and
community colleges affect math attainment and STEM participation in community
college?
2. Given that a large proportion of community college students place in developmental
(remedial) math, does developmental math help students persist in STEM?
3. Are URM and female students more likely to exit from the STEM pathway due to
math remediation?
4. Is there a STEM gender gap at community colleges and what is driving this gap?
Essay I. The Role of Math Misalignment in the Community College STEM Pathway
This study examines a particular experience during the transition from high school to
college called math misalignment. Math misalignment is when students are placed lower in math
7
than expected given their prior high school coursetaking history and record of achievement
(Melguizo & Ngo, 2018). Using a high schoolbycollege fixed effects estimation approach, this
study identifies students with similar skills and backgrounds, from the same high school and
college, who due to placement testing results are placed in different math courses. This research
can be summarized by the following two research questions: (1) Is math misalignment related to
students’ college math attainment and STEM outcomes? (2) Do these relationships
disproportionately affect STEMaspiring students (i.e., students who intend to major in a STEM
field)? Results indicate that math misalignment especially hindered STEMaspiring students –
students with an interest in majoring in STEM – from pursuing STEM pathways. Specifically,
while on average STEMaspiring students attempted and completed more STEM courses than
nonSTEMaspiring students, they were less likely to attempt and complete these courses if they
experienced varying degrees of math misalignment.
Essay II. The Effect of Developmental Math on STEM Participation in Community
College: Variation by Race, Gender, Achievement, and Aspiration
This study examines whether assignment to a developmental math course affects the
likelihood of STEM participation in community college. In this community college district,
students can place into one of five math levels depending on how they score on the math
placement test and these math levels are arithmetic (AR), prealgebra (PA), elementary algebra
(EA), intermediate algebra (IA), and transferlevel math (TLM). Importantly, students do not
know the cutscore that determines their math placement. Thus, capitalizing on the system of
placement cutoffs used to assign students to these math courses, this study uses a regression
discontinuity (RD) design to determine the impact of these course assignments on STEM
outcomes. Specifically, we conduct separate RD analyses for students around the arithmetic/pre
8
algebra (AR/PA), prealgebra/elementary algebra (PA/EA), elementary algebra/intermediate
algebra (EA/IA) and intermediate algebra/transferlevel math (IA/TLM) cutoffs. Then, using
students’ high school transcript records we conduct a series of subgroup analyses and examine
STEM outcomes of URMs, women, students with significant high school math and science
preparation (“STEMoriented” students), and STEMaspiring students. The results show that
lower math placement may be marginally beneficial for students placed in the lowest level of
math (i.e., arithmetic). These students were more likely to take math prerequisites like
elementary or intermediate algebra than their higherplaced peers. Despite the potential benefits
to early math progression among those around the AR/PA cutoff, we do not find evidence that
lower placement ushered more women and URMs into STEM pathways. For the most part,
however, there were generally no positive effects and, in some cases, a clear detriment to math
remediation. Notably, lower placement was more of a deterrent in early math progression for
STEMaspiring and STEMoriented students than their peers who placed above. The findings of
the study show that developmental math introduced a structural barrier during early math
progression (Wang, 2015) and was a barrier for students, especially those at the margin of
transferlevel math.
Essay III. Comparative Advantage in STEM and the STEM Gender Gap in Community
College
Recent studies indicate that women surpass men in degree attainment, but there remains a
persistent gender gap in the attainment of STEM degrees (i.e., “STEM gender gap”). This trend
becomes especially pronounced within subfields like Physical Science and Engineering (PS/E);
thus, calling into attention the need to examine the STEM gender gap in college. While the
STEM gender gap at fouryear universities has received more attention in the literature, fewer
9
studies examined the STEM gender gap at community colleges. Therefore, this study first
examines whether a STEM gender gap exists at community colleges, disaggregated by initial
levels of academic preparation and STEM subfields, and subsequently investigates a potential
mechanism driving this gap called comparative advantage in STEM. Comparative advantage in
STEM is the notion that students pursue future study based on their relative strength in STEM
courses compared to nonSTEM courses. This research can be summarized by the following
three research questions: (1) Is there a STEM gender gap by LS and PS/E subfields and by
initial level of academic preparation in community college? (2) Does comparative advantage in
STEM during the first year of community college predict persistence in STEM? (3) Does the
STEM gender gap in LS and PS/E narrow as students demonstrate comparative advantage in
STEM during their first year of community college? To ensure that STEMaspiring men and
women are observationally equivalent across an array of coursetaking and demographic
indicators, this study employs propensity score matching method. Results indicate no evidence of
a STEM gender gap among academically prepared male and female community college students
aspiring to pursue PS/E fields. However, this study finds a gender gap in the attempt and
completion of science courses among PS/Easpiring men and women initially identified as
academically underprepared. Furthermore, comparative advantage in STEM exacerbated this gap
as academically underprepared men with a comparative advantage in STEM outpaced women in
attempting and completing transferable science units. In other words, despite displaying
comparable comparative advantage in STEM, academically underprepared PS/Easpiring women
attempted fewer STEM courses than their academically underprepared male peers. The findings
imply that academically underprepared female students internalize their comparative advantage
in STEM differently than male students.
10
Organization
The three essays will be presented in the following three chapters. All three studies use
data on graduates from a large, urban school district (LUSD) who attended one of the community
colleges in a large urban community college district (LUCCD) in California. Each study can be
read as a standalone research study. In chapter five, I conclude with common themes across the
three papers and discuss implications for policy, practice, and future research.
Endnotes
1
A similar pattern is also evident at the Bachelor’s level. In 201516, while 57% of all Bachelor’s degrees conferred
were to women, only 36% of women obtained a Bachelor’s degree in a STEM field (NCES, 2018).
11
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Bahr, P. R., Jackson, G., McNaughtan, J., Oster, M., & Gross, J. (2017). Unrealized potential:
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Crisp, G., Nora, A., & Taggart, A. (2009). Student characteristics, precollege, college, and
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Dowd, A.C., Malcom, L.E. & Bensimon, E.M. (2009). Benchmarking the success of Latina and
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National Center for Education Statistics. (2018, March). The condition of education.
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15
Essay I. The Role of Math Misalignment in the Community College STEM Pathway
Abstract
Limited attention has been placed on the relationship between developmental math and STEM
outcomes in community college. Therefore, we examine one particular experience during the
transition from high school to college called math misalignment. Math misalignment occurs
when college students are placed lower in math given their highschool coursetaking history and
record of achievement. We find that a majority of students experienced math misalignment in
community college. Moreover, math misalignment especially hindered STEMaspiring students
from pursuing STEM pathways. Specifically, STEMaspiring students who experienced math
misalignment were less likely to attempt and complete STEM courses than STEMaspiring
students who were directly placed in transferlevel math. This study underscores the importance
of aligning academic standards across highschool and postsecondary institutions as a means of
improving STEM participation.
16
Increasing the number of students interested in Science, Technology, Engineering, and
Mathematics (STEM) fields continues to be a focus for many educators and policymakers alike
(American Association of State Colleges and Universities, 2018). Several reports project that
STEMrelated jobs will continue to grow (National Science Board, 2015; Vilorio, 2014),
1
and
graduates who major in STEM fields are less likely to be unemployed and are more likely to earn
higher wages than graduates with a nonSTEM degree (National Science Board, 2015). Despite
the growing demand for a STEMcapable workforce, reports and studies show that many
students, especially those from underrepresented backgrounds, are not graduating from college in
STEM fields (Carnevale, Smith, & Melton, 2011). Therefore, bolstering the STEM pipeline by
encouraging more students from underrepresented backgrounds to pursue STEM fields is at the
forefront of education policy agendas.
Being the point of entry to STEM fields for many underrepresented minorities (URMs),
2
community colleges provide educational opportunities to many URMs who aspire to enter STEM
fields (Dowd, Malcom, & Bensimon, 2009). This point is especially relevant in California, home
to 115 community colleges and serving a large population of URMs. Yet despite the important
role community colleges are poised to play in diversifying the STEM talent pool, few studies
have examined the community college STEM pathway and the relationship between
developmental math, a common experience at community colleges, and STEM outcomes. An
expansive study examining STEM participation across the California community colleges
focused on math coursetaking in STEM pathways, but it did not examine how developmental
math factored into these pathways (Bahr, Jackson, McNaughtan, Oster, & Gross, 2017).
Developmental math is an important juncture in STEM pathways as approximately 65% of first
time California community college enrollees start their college trajectory in developmental math
17
(Rodriguez, Johnson, Mejia, & Brooks, 2017). Although there is significant research on
developmental/ remedial math on academic outcomes like degree attainment and transfer (see
Valentine, Konstantopoulous, & GoldrickRab, 2018, for review), just a few studies have
examined whether developmental math affects students’ STEM participation (Hagedorn &
DuBray, 2010).
Motivated by the theory that students develop STEM momentum in K12 schooling and
that this momentum waxes or wanes in early college (Wang, 2015, 2017a), we examine one
particular experience during the transition from high school to college called math misalignment.
Math misalignment occurs when college students are placed lower in math than expected given
their prior high school coursetaking history and is a consequence of misaligned academic
readiness benchmarks between high school and community college (Melguizo & Ngo, 2018).
For instance, students who took advanced high school math courses – courses that are algebra 2
and above – may place into developmental math as opposed to transferlevel math (i.e., math
courses above algebra 2) in college and experience math misalignment. Since math is an integral
component of STEM pathways in community college (Bahr, et al., 2017), math misalignment
may halt students’ STEM momentum and is therefore a relevant experience for understanding
differences in STEM outcomes.
We are able to pinpoint experiences of math misalignment by analyzing rich, linked high
school to community college transcript data that captures alignment in studentlevel math course
taking between sectors. We first document the extent to which math misalignment is a barrier for
students in STEM pathways. We do so by comparing students who experienced aligned
transition with students who experienced math misalignment. Then, we conduct additional
analyses to examine whether math misalignment halts students’ STEM momentum among
18
STEMaspiring students who indicated clear STEM interest on their community college
enrollment form. The research asks two research questions:
(1) Is math misalignment related to students’ college math attainment and STEM outcomes?
(2) Do these relationships disproportionately affect STEMaspiring students (i.e., students
who intend to major in a STEM field)?
In answering these questions, this study makes several important contributions. First,
experiences of math in high school and math coursetaking in college significantly factor into
STEM momentum and aspirations (Crisp et al., 2009; Wang, 2013a, 2015). However, scholars
have yet to focus specifically on math misalignment in the community college STEM pathway, a
relatively common experience (Melguizo & Ngo, 2018).
In addition, our study makes a methodological contribution by outlining the use of high
schoolbycollege fixed effects. This method accounts for the fact that not all students from a
particular high school attend the same community college. Therefore, by including these controls
we eliminate the unobserved highschoolbycollege level variation (Andrews, Schank, &
Upward, 2006). Unlike prior studies that controlled for selection bias using high school fixed
effects, we use high schoolbycollege fixed effects to control for nonrandom sorting of students
in high schools and in community colleges. Specifically, we identify students with similar skills
and backgrounds from the same high school and attending the same college, but due to
placement testing results are placed in different math courses. Therefore, we account for any
additional unobserved factors due to attending the same high school and college.
To preview our results, we find that a large proportion of students who completed
advanced high school math placed in developmental math in community college. Specifically,
5598% of the students experienced math misalignment, depending on the definition of advanced
19
high school math. Moreover, students who experienced math misalignment were less likely to
pass the math requirement for an Associate’s degree and attempted and completed fewer
transferable STEM courses. In particular, we find that math misalignment especially hindered
STEMaspiring students from pursuing STEM fields.
The following section describes prior literature and the study and policy context. We
proceed to discuss the data and the key variables of the study. Next, we present the method used
to answer our research questions. We then present our findings and conclude with policy
implications.
Prior Literature
Conceptually, our study builds upon the literature on STEM aspirations, preparation, and
momentum and their relationship to STEM outcomes. Several studies found that a key factor in
ushering students into STEM fields is students’ STEM aspirations (Maltese & Tai, 2011; Tai,
Liu, Maltese, & Fan, 2006; Wang, 2013a, 2013b). Students’ STEM aspirations are regarded as a
key driving force behind actions that are conducive to persisting in STEM (Lent, 2003; Maltese
& Tai, 2011). In developing students’ aspirations, studies highlight the importance of high school
math and science exposure and building students’ selfefficacy through evidence of early
achievement in STEM subjects (Wang, 2013a, 2013b). Subsequently, students’ aspirations and
preparation feed into building students’ STEM momentum.
The concept of STEM momentum provides a framework for examining who enters and
attrits from STEM pathways during the transition to college. STEM momentum is defined as
“academic behaviors and efforts students exhibit in early STEM coursework that propel them
forward towards persistence and success in STEM fields of study” (Wang, 2015, p. 377).
According to this concept, students sustain STEM momentum, which is composed of and
20
affected by individual and environmental characteristics, from high school to postsecondary
education along three specific domains: the curricular domain, the motivational domain, and the
teaching and learning domain (Wang, 2017a). In this study, we focus on the curricular domain of
STEM momentum, and specifically, the opportunity for students to maintain forward momentum
in coursework and progress through an educational sequence. This model also emphasizes
experiences that produce friction to STEM momentum, such as when students face financial
barriers, unclear pathways, and inadequate advising. We focus on one potential barrier to STEM
momentum: the lack of clear pathways aligned with students’ intent, as evidenced by math
misalignment.
In addition to molding aspirations and feeding into the momentum, STEM high school
performance measures are also regarded as demonstrations of academic readiness. Academic
readiness is “the preparation required to enroll in college and persist to graduation without need
for remediation” (Duncheon, 2015, p. 10). Academic readiness is often operationalized by
indicators like HS GPA, prior coursetaking, freshman GPA, and the avoidance of remedial work
(Klasik & Strayhorn, 2018; Porter & Polikoff, 2012). We focus on the mismatch between HS
GPA and advanced math coursetaking (i.e., two benchmarks of readiness in high school), and
community college math placement (i.e., a benchmark of readiness in college), as they relate to
promoting or halting students’ momentum in STEM pathways.
Math Misalignment
Math misalignment may be particularly relevant for understanding postsecondary STEM
attainment because, as described above, math coursetaking experiences are integral to STEM
momentum. In contrast to examining just the influence of high school math coursetaking on
postsecondary STEM participation (e.g., Goodman, 2017), or remedial coursetaking and
21
majoring in STEM fields in college (e.g., Crisp et al., 2009), math misalignment characterizes
students’ math placement as a more nuanced experience by linking college math placement to
high school performance measures. This nuance is important because, in theory, students who
are deemed “collegeready” by high school benchmarks should not need remediation in
community college; they should progress forward in their math coursetaking.
Yet postsecondary remediation is commonplace (Mejia et al., 2016; Rodriguez, Mejia, &
Johnson, 2016). In fact, community college students often report being surprised by their
remedial course assignments (DeilAmen, 2010; Venezia, Bracco, & Nodine, 2010). This
experience may largely be the consequence of mismatch in readiness standards across sectors
and colleges (Melguizo & Ngo, 2018). Case in point, a survey of colleges revealed that colleges’
math cut scores for the ACCUPLACER placement test ranged from 25 to 96 depending on the
campus, suggesting that students are placed in different levels conditional on where they attend
(Rodriguez et al., 2016). In addition, researchers have documented a number of problems with
the overreliance on placement tests. For example, studies estimate that a sizeable percentage of
students  as many as onequarter of math students  may be placed in error into lowerlevel
courses and that misplacement is detrimental to students’ academic success (Ngo, Chi, & Park,
2018; ScottClayton et al., 2014).
As such, several states now mandate the use of multiple measures like high school
records in determining students’ college placement (ScottClayton, 2018). In Florida, students
are placed into remediation only if they have not received a high school diploma (Hu et al.,
2015). Likewise, students in Tennessee are referred to remediation in college if they score below
a threshold in ACT, a test administered during high school (Kane et al., 2018). Similar to these
states, California community colleges are now required to place students using measures like
22
high school math coursetaking records and high school GPA. Prior to 2017, all California
community colleges used some form of placement test to assess students’ math level, though the
specific matriculation policy varied by campus (Melguizo, Kosiewicz, Prather, & Bos 2014;
Rodriguez et al., 2016). However, in 2017, California passed Assembly Bill (AB) 705 that
requires colleges to use high school measures in lieu of placement tests to place students into
developmental courses (Burks, 2017; Rodriguez et al., 2018).
Implications for STEM
As research suggests math is an important juncture in all STEM fields (Bahr et al., 2017),
the experience of being placed in a misaligned math course may contribute to differences in
STEM outcomes. Indeed, there are a number of studies linking math coursetaking to STEM
participation and attainment. For example, studies show that students who took advanced math
coursework are less likely to drop out, more likely to persist in college (Adelman, 2006), and
more likely to pursue STEM fields (Goodman, 2017).
Although a large proportion of students begin their community college journey in
developmental math, there is less research examining how developmental math factors into
STEM pathways in community college. Since the majority of the students begin their college
journey in developmental math, whether math misalignment serves as a diversion or counter
momentum friction from pursuing and persisting in STEM pathways is an important,
unanswered question that this study aims to investigate. As Wang (2017a) pointed out,
community college students face considerable countermomentum friction that erode at the
STEM momentum accumulated in high school. We identify math misalignment as one counter
momentum friction that may be particularly consequential for STEMaspiring students. Overall,
our goals are to identify the consequences of math misalignment and examine the implications of
23
this misalignment for a population of STEMaspiring high school students making the transition
to community college.
Data and Context
The data used in this study are linked longitudinal transcript data obtained through
partnerships with a Large Urban School District (LUSD) and a Large Urban Community College
District (LUCCD) in the same metropolitan area in California. This rich longitudinal data include
students’ complete high school and community college transcript data, demographic information,
and placement test score information and outcomes through 2016. The sample consists of 45,807
LUSD students who enrolled in one of the LUCCD colleges during 20092014 and within three
years of graduation. We excluded students who are concurrent high school students and students
with no known high school coursetaking and math placement information. From our initial
number of 45,807 students, we identified 8,822 (19%) STEMaspiring students.
The LUSD is a diverse school district that educates over 600,000 students each year
where over 80% are categorized as socioeconomically disadvantaged, over 80% are students of
color, and 28% are categorized as English Learners. LUCCD is one of the largest community
college districts in the nation, enrolling over 225,000 students each year. Being the local
community college district, about 4045% of LUSD graduates enroll in the LUCCD each year.
3
Serving a large population of minoritized students, these two districts are relevant spaces for the
analyses on diversifying the STEM talent pool.
4
Key Variables
Before describing the methods, we explain below how we operationalize the main
explanatory variables: STEMaspiring and math misalignment.
24
STEMAspiring. STEMaspiring students are LUSD graduates who indicated that they
intend to major in one of the STEM fields in their college application. The LUCCD transcript
data include the name of the major as well as the corresponding Taxonomy of Program (TOP)
code. The TOP code represents numerical codes used at the state level to align local programs
into similar program categories. The U.S. Department of Education classifies different majors
and programs using the Classification of Instructional Programs (CIP) code. We use a crosswalk
of TOP codes and CIP codes published by the California Community College Chancellor’s
Office (2004) and Wang’s (2016) study on community college STEM pathways to classify
different majors as STEM or nonSTEM. Appendix Table A.1 shows the crosswalk of the name
of the program at the college, the TOP codes, and the 2digit CIP codes implemented in this
study.
Definitions of Math Misalignment. We disaggregate students’ math placement levels by
prior math coursetaking history. We make the distinction between remediation and
misalignment because indicators of remediation are predominantly based on college standards
and do not incorporate high school math proficiency in a meaningful way. For example, a
remediationbased analysis might consider all students placed in intermediate algebra (algebra 2
equivalent) as having the same academic preparation and level of readiness for college
mathematics. However, a misalignmentbased analysis would distinguish students who placed in
remediation by evidence of prior achievement in high school math (Melguizo & Ngo, 2018).
Table 1 displays our three definitions of math alignment. In the first three rows, we
define math misalignment based solely on coursetaking in high school. The second definition of
misalignment is based on overall grades (GPA), and the third incorporates both grades and math
coursetaking. According to the first definition, students experience math misalignment if they
25
took algebra 2, precalculus, or calculus in high school and placed in intermediate algebra
(algebra 2 equivalent) or below in college. In other words, students do not experience math
misalignment if they took high school algebra 2 or higher and placed in transferlevel math in
college. Since students completing algebra 2, precalculus, or calculus in high school are
expected to progress to transferlevel math in college, we separate these analyses by highest level
of math completed. Transferlevel math courses are collegelevel math course that are accepted
by the University of California (UC) and the California State University (CSU).
The second and third definitions are derived from the rules developed for a recent
legislation passed in California, AB 705, that mandates the use of high school records to place
community college students (Research and Planning Group [RP Group], 2018). We conduct an
exercise using these additional definitions in order to gain insight into how such rules might
affect students in STEM pathways under AB 705.
5
In particular, the third definition, which
draws from a combination of coursetaking and GPA, is relevant for STEMaspiring students
attending a California community college. According to AB 705, students who intend to major in
STEM must either have at least a 3.4 HS GPA or at least a 2.6 HS GPA and have enrolled in
calculus in order to directly place in transferlevel math without additional math support. We
examine the STEM outcomes of students meeting these criteria to see how the proposed
definitions might influence community college STEM participation.
It is important to note that while we derive the last two definitions based on the new
policy, the use of HS GPA and coursetaking are part of a broad set of multiple measures that
were already used by many colleges before AB 705 (Ngo & Kwon, 2015). The difference with
the passage of AB 705 is that colleges will now determine placement mainly using multiple
measures instead of regarding multiple measures as supplemental indicators. Nonetheless, these
26
benchmarks outline criteria by which students should be able to progress in math between high
school and college, and therefore offer policyrelevant ways of defining misalignment.
To examine groups of students who met each math misalignment definition, we create
five separate subsamples that fit under these definitions as shown in Table 1. The first definition
includes 20,600 students who took algebra 2, 9,195 students who took precalculus, and 1,632
students who took calculus. The second definition includes 7,331 students with at least 3.0 HS
GPA and finally, the third definition includes 3,183 students who have at least a 3.4 HS GPA or
at least a 2.6 HS GPA and took calculus. Since students could be placed far below transferlevel
math, the “aligned” course, the misalignment indicator is not dichotomous but a degree.
Table 1 displays the distribution of math placement among all students and STEM
aspiring students. We crosstabulate students’ highest high school math course with college math
placement. Table 1 indicates that, irrespective of the math misalignment definition, less than
50% of the students experienced alignment, with students experiencing increased severity of
misalignment the farther they are from taking calculus (i.e., algebra 2). The grey cells highlight
the most common placement within each row. For example, the most common math placement
among students who took algebra 2 was prealgebra (52%). On the other hand, among students
who took precalculus or with at least a 3.0 HS GPA, the most common math placement was
intermediate algebra (algebra 2 equivalent). The most common math placement among students
who took high school calculus was transferlevel math (45%). Depending on the definition, 55
98% of the students experienced misalignment.
While the specific percentages differ, the pattern that we see in all students is also
apparent in the STEMaspiring sample. Specifically, very few STEMaspiring students (3%)
placed in transferlevel math if algebra 2 was their highest math enrollment in high school. In
27
fact, half of all STEMaspiring students whose highest high school math was algebra 2 placed in
the lowest math level in college (prealgebra and below). Even when we examine STEM
aspiring students with at least a 3.0 HS GPA or who took high school precalculus, most placed
into intermediate algebra (algebra 2 equivalent) or below in college.
Method
To answer our two research questions, we estimate the following regressions with high
schoolbycollege and year fixed effects:
!
"#$%
= '
(
+ ∑ '
+
, ,
"#$%,+
.
+/0
+ 1′3+ 4
#$
+ 5
%
+ 6
"#$%
(1)
!
"#$%
= '
(
+ ∑ '
+
,,
"#$%,+
.
+/0
+ '
7
89:;
"$#%
+ ∑ '
+
,,
"#$%,+
∗89:;
"$#%
=
+/>
+ 1′3+ 4
#$
+
5
%
+ 6
"#$%
(2)
where, !
"#$%
represents STEM outcomes (detailed below) for student i who graduated from high
school s attending college c in cohort t. The variable , ,
"#$%,+
is a series of dummy variables
referring to the degree of math misalignment based on the three definitions under Table 1, with
alignment as the omitted/base category. 1 is a set of control variables including: gender, race,
special education status, whether the student lives within the district zone, whether or not
students intend to transfer or complete an Associate’s degree, English learner status, and
citizenship status. Importantly, we also include academic background variables that can account
for differences in academic preparation among aligned and misaligned students. These variables
include whether they took an honors or AP course, HS GPA, math and science state standardized
test scores,
6
and taking AP math and science courses. 4
#$
refers to high schoolbycollege fixed
effects and 5
%
refers to year (i.e., cohort) dummies.
In equation 1, we estimate the relationship between each degree of math misalignment
and STEM outcomes for all students in the sample. In equation 2, we include an interaction
28
between the math misalignment variable and a dichotomous indicator of STEM aspiration,
89:;
"$#%
. These interactions allow us to identify whether the experience of misalignment
differentially affects students in STEM pathways.
Identification
Most STEMrelated studies on the transition from high school to college estimated
regression or logistic regression without school fixed effects (e.g., RiegleCrumb & King, 2010;
RiegleCrumb et al., 2012; Tai et al., 2006; Wang, 2013a). However, students’ STEMcourse
taking patterns and their subsequent likelihood of STEM participation in college differ
depending on the high school students attend (Gottfried & Bozick, 2016). For example, some
high schools may put a premium on STEM education and that may impact students’ aspirations
to pursue STEM fields. Schools are not randomly assigned and thus the notion that the school
level measures are independent of student level factors is a strong assumption. Also, students
attending the same schools may have correlated errors (unobserved similar characteristics);
therefore, it is preferable to compare students who come from the same high school.
However, there are two methodological complexities unique to this study. The first
consideration is that students who graduated from the same high school can attend different
LUCCD colleges. Thus, there may be unobserved correlation due to attending the same college
and also due to attending the same high school. In other words, the withinhighschool estimation
(i.e., high school fixed effects) does not entirely correct for selection bias due to nonrandom
sorting among students from the same high school into different colleges (e.g., Andrews, Schank,
& Upward, 2006; RabeHesketh & Skrondal, 2012). This issue can be addressed by including
highschoolbycollege fixed effects. The highschoolbycollege fixed effects removes any high
schoolbycollege level variation. By doing so, students in one college who come from the same
29
high school are compared with others who also fit that criteria. Therefore, we use highschool
bycollege fixed effects as our analytical approach because community colleges draw students
from a range of high schools and vice versa.
Additionally, we include year (i.e., cohort) dummies to remove any correlation due to
being part of the same cohort. For example, it could be that students in one cohort are more
motivated than others or that some students who were part of a cohort of high school graduates
during the Great Recession may have entered higher education at a higher rate than the later
cohorts. Therefore, the highschoolbycollege fixed effects with cohort dummies is the preferred
estimation. All analyses include high schoolbycollege cluster robust standard errors (Bertrand,
Duflo, & Mullainathan, 2004). In short, we estimate the relationship between math misalignment
and STEM outcomes for students in the same feeder pathways.
STEM Outcome Measures
Our outcomes of interest are passing the math requirements for an Associate’s degree
(e.g., passing algebra 2 equivalent) and the number of transferable STEM units students
attempted and completed. To create the transferable STEM units attempted and completed
measures, we first exported out all possible course names listed in the enrollment records. Then
we referenced the college websites and course catalogs to check whether each course name and
course number combinations count as transferable math or science courses. Next, we devised a
set of rules that lists the math and science courses that count for transfer and flag the appropriate
course name in the data. Transferable units are defined as units that are accepted in the UC or the
CSU.
The number of transferable STEM units attempted and completed are indicative of the
extent to which students have persevered in STEM courses. Previous studies have examined
30
whether or not students declared a STEM major at the start of college (Crisp et al., 2009;
Gottfried & Bozick, 2016; RiegleCrumb & King, 2010) and other studies have studied
bachelor’s degree attainment or transfer (Wang, 2015; Wang, Sun, Lee, & Wagner, 2017b).
While bachelor’s degree attainment and majoring in STEM fields are important milestones,
outcomes like accumulating enough transferable STEM credits for transfer are important
intermediary milestones in the community college setting. A recent report by a research arm of
the California Community College Chancellor’s Office pointed out that not all students who
transferred did so with an Associate’s degree and among students with enough credits to transfer,
a significant number of students did not complete an Associate’s degree (RP Group, 2017).
Therefore, this study focuses on intermediary outcomes like passing the math requirement for
attaining an A.A., as well as accumulating enough transferable STEM units necessary for STEM
transfer.
Missing Values
There are different amounts of missing values depending on the covariate. Most of the
covariates have minor missing values and the missing values are assumed to be random coding
error (see Table A.2 for more information on missing data). Thus, we flag missing values with an
extra indicator identifying which observations on that variable have missing values (Allison,
2002).
7
For high school GPA, we impute missing values with the mean value. Given the small
number of missing values on HS GPA (n=65) we found that the results are nearly identical to
ones without imputing for missing values.
31
Results
Descriptive Statistics
Table 2 below shows how the sample of LUSDLUCCD students (column 1) compares to
STEMaspiring students (column 2) along various demographic and coursetaking measures.
There are several interesting trends evident in Table 2. Over 75% of students in either sample are
URMs, with the majority being Latina/o students. In the larger LUSDLUCCD sample, 12%
have special education designations, but fewer percentage (i.e., 10%) of STEMaspiring students
are identified as special education.
Students’ high school coursetaking measures also paint a nuanced picture of the two
samples. Notably, STEMaspiring students, on average, have stronger academic preparation than
the full LUSDLUCCD sample, having taken more math and science courses, earning higher HS
GPAs, and receiving higher scores on the math and science state standardized tests. Therefore,
STEMaspiring students perform better on high school measures compared to the full sample of
LUSDLUCCD students.
Math Misalignment and STEM Outcomes
In Table 3, we display the relationship between the degree of math misalignment on
passing intermediate algebra and attempting and completing transferable STEM units for
students in the same high school to community college feeder pathways.
We find that community college students who experienced varying degrees of math
misalignment were less likely to pass the math requirement for an Associate’s degree and
attempted and completed fewer transferable STEM courses than those who experienced
alignment. These relationships held irrespective of the alignment criteria. Among those who
completed algebra 2, students who placed in intermediate algebra (algebra 2 equivalent) were 37
32
percentage points less likely to complete intermediate algebra and attempted and completed six
fewer STEM units compared to students who placed directly in transferlevel math. Exhibiting
stronger high school math preparation did not buffer against the experience of misalignment.
Among those who completed calculus, students who experienced math misalignment were 24
percentage points less likely to complete the math requirement for an Associate’s degree and
were also associated with attempting and completing six fewer STEM units compared to students
who placed directly in transferlevel math.
Students who experienced severe misalignment were much less likely to pass the math
requirement for an Associate’s degree, and attempted and completed fewer transferable STEM
courses than students who experienced alignment. Among students who completed calculus, if
they placed in prealgebra or below, they were 45 percentage points less likely to pass
intermediate algebra and attempted and completed 10 to 11 fewer STEM units compared to
students who placed directly in transferlevel math.
In short, the experience of math misalignment is strongly and negatively associated with
STEM outcomes for all entering community college students. Next, we also investigate whether
these results differ if students display STEM aspiration.
Results for STEMAspiring Students
Table 4 examines whether the degree of misalignment on math attainment is moderated
by STEM aspiration and Table 5 examines whether the degree of misalignment on STEM
outcomes is moderated by STEM aspiration. Again, these are students who indicated a STEM
major on their college enrollment form. Table 4 shows that there is a significant interaction effect
mainly for students who took algebra 2 or precalculus as their highest high school math or had
at least a 3.0 HS GPA. Specifically, Table 4 indicates that math misalignment is associated with
33
a decreased likelihood of passing the math requirement for an Associate’s degree. Yet, STEM
aspiring students who experienced math misalignment were more likely to pass this requirement
than similar nonSTEMaspiring peers (see columns 1, 2, & 4). The general insignificant results
when examining students who took calculus or had a HS GPA of 3.4 or above suggest that
STEMaspiring students were just as likely to pass their math requirements for a degree as their
nonSTEMaspiring peers.
Despite this positive result, the results on transferable STEM units attempted and
completed paint a different picture. As shown in Table 5, STEMaspiring students, on average,
attempted significantly more STEM courses than nonSTEMaspiring students. However,
STEMaspiring students were disproportionately less likely to attempt and complete transferable
STEM units than their STEMaspiring peers who experienced alignment, evidenced by the
statistically significant negative interaction terms. This finding held across all misalignment
definitions. For example, as shown in Table 5, column 5, STEMaspiring students who
experienced alignment attempted about 14 more STEM units as STEMaspiring peers who were
misaligned three levels below (i.e., 7.936.09). Thus, STEMaspiring students who experienced
severe math misalignment were much less likely to attempt and complete transferable STEM
courses than similar STEMaspiring students who experienced alignment.
Graphical Representation of the Findings
Next, we present graphical representation of the findings under one of the multiple
measure criteria most relevant to STEMaspiring students according to AB 705: indication of
graduating with at least a 3.4 HS GPA or having taken calculus. Figure 1, below, shows the
results for STEMaspiring students on the number of STEM courses attempted and completed.
34
Figure 1 shows that STEMaspiring students, on average, attempted and completed more
transferable STEM courses than nonSTEMaspiring students. However, the steeper downward
slopes for STEMaspiring students indicate that these students were more negatively affected by
the experience of misalignment. Corresponding to the results in Table 5, the graph shows that
STEMaspiring students who experienced alignment attempted six to fourteen more transferable
STEM units compared to STEMaspiring students who experienced varying degrees of math
misalignment.
Sensitivity Analyses
We conduct four sensitivity analyses to check whether the results are sensitive to how
math misalignment is specified. First, we respecify the multiple measure indicators based on
students’ last high school math course instead of students’ highest high school math course since
some students may not take any math course during the last year of high school or may take an
easier math course during 12
th
grade compared to 11
th
grade. Second, we examine math
enrollment instead of placement and use the same estimation strategy because students may not
comply with their math placement, may decide to not enroll at all, or delay their enrollment after
receiving their math placement results. Third, we restrict our main specification – using highest
high school math – to students who received an A or a B in their course grades.
Lastly, even though our fixed effects estimation approach included a number of variables
to account for academic preparation and included state standardized high school test scores, it
may be that misaligned and aligned students are systematically different in their testing ability.
We therefore conduct a sharp regression discontinuity (RD) analysis in which we examine a
subset of students around a narrow bandwidth of placing into intermediate algebra versus
transferlevel math. We exploit the deterministic change in the probability of placing lower or
35
above close to the placement test score cutoff given that students do not know the cutscore that
determines their placement. Therefore, students close to the cutoff are equivalent in expectation.
However, we note that the RD estimates here do not capture the full gradient of misalignment
but rather represent the result of a testbased placement policy around a narrow bandwidth.
Appendix Tables A.3 and A.4 show the results examining the mismatch between
students’ last math course and math placement. Appendix Tables A.5 and A.6 show the results
examining the mismatch between students’ highest high school math course and math
enrollment. Appendix Tables A.7 and A.8 show the results examining the mismatch between
students’ highest high school math course passed with an A or a B and math placement. Finally,
Appendix Table A.9 shows the regression discontinuity results of students close to the
intermediate algebra versus transferlevel math cutoff.
All of the main results are robust and qualitatively similar to the various specifications of
misalignment. Irrespective of how we redefine misalignment, students who experienced math
misalignment were less likely to complete the math requirement for an Associate’s degree and
were less likely to attempt and complete transferable STEM courses. Corroborating our main
results, the math misalignment penalty was larger for STEMaspiring students than nonSTEM
aspiring students. This helps to confirm our hypothesis that math misalignment is a consequential
experience in the STEM pathway particularly for STEMaspiring students.
Discussion
Using a linked dataset of students’ high school and community college records, we
identified the experience of math misalignment using three different definitions and explored the
relationship between math misalignment and college STEM outcomes. We also focused our
analysis on STEMaspiring students who entered community college with an intent to major in a
36
STEM field. We found a significant mismatch between students’ high school math achievement
and community college math placement; 5598% of the students experienced math misalignment
depending on the definition. In addition, we found that students who experienced math
misalignment were less likely to pass the math requirement for an Associate’s degree and
attempted and completed fewer transferable STEM courses. Moreover, misaligned STEM
aspiring students were much less likely to attempt and complete transferrable STEM courses
than STEMaspiring students who experienced alignment.
This study adds new evidence to the existing literature on developmental education,
namely, that it is a context that creates experiences of math misalignment, which in turn has
negative implications for academic achievement. The math misalignment penalty was especially
salient for STEMaspiring students who were more deterred from key STEM milestones than
their peers. In this regard, math misalignment hindered the very students with the greatest STEM
interest. Given that a typical STEM course is about three to five units, the magnitude of the
results translates to attempting and completing two to three fewer transferable STEM courses
due to math misalignment. Studies note that students who begin their STEM education at
community colleges are most successful in transferring to a fouryear university if they
accumulate significant STEM credits during the first year of college (Wang, 2015). In fact, the
most common coursetaking pattern of students who successfully transfer is accumulating at
least three transferable STEM units during their firstterm in community college (Wang, 2016).
In light of these findings, the misalignment penalty is akin to “starting off on the wrong foot” –
STEMaspiring students who experienced math misalignment faced the burden of rectifying a
bad start.
37
An explanation behind why math misalignment disproportionately affected STEM
aspiring students may be that STEMaspiring students who placed lower than they expected
received conflicting messages about their academic ability to perform well in STEM subjects.
Studies indicate that students enter college with an inaccurate assessment of their ability to
perform in math and science courses (Stinebrickner & Stinebrickner, 2013). It may be that
students received one message about their level of academic preparedness in high school and a
different message from their math placement results in college. Particularly for STEMaspiring
students who took advanced high school math like precalculus or calculus, placing in pre
algebra or below in college sends conflicting signal about their fit and potential to succeed in
STEM courses.
For these reasons, unexpectedly finding one’s self in a math course that is at a lower level
than expected based on high school preparation may have significant psychic costs.
Stinebrickner and Stinebrickner (2011, 2013) showed that early feedback in college in the form
of grades led students to evaluate their abilities and potential, and this had implications for
choosing STEM majors (2013) and the college dropout decision (2011). We see math
misalignment as a form of early feedback that may affect students’ academic progress in college
and their STEM participation in particular. Therefore, STEMaspiring students who experienced
math misalignment and placed into lower levels of math may have lost the STEM momentum
that they developed in high school.
Policy Implication
Several states across the nation have enacted legislation that emphasizes the use of
multiple measures such as high school grades, a paradigm shift from the testbased placement
scheme (Ross, 2014). The shift towards using multiple measures means that community colleges
38
must now place students using measures like high school GPA (HS GPA) and prior coursework
instead of relying on placement test scores (Burks, 2017). Indeed, California is one of the states
refocusing their assessment and placement policies from placement tests to multiple measures,
with statewide implementation slated for fall 2019 (Rodriguez et al., 2018). In anticipation of
this policy rollout, the present study concludes that aligning academic readiness standards by
incorporating high school benchmarks may help reduce math misalignment and increase STEM
participation in community colleges.
Specifically, the results suggest that if math misalignment were reduced, then students
entering community colleges with STEM aspirations would likely complete more transferable
STEM courses, and presumably, increase their likelihood of STEM degree attainment. Given the
importance of consistent messaging during the transition from high school to college, one policy
recommendation is to give students a better sense of their math preparation while in high school.
One option may be to expand on dual enrollment as a lowcost way of allowing students to
understand college course expectations while still in high school (Karp et al., 2007). Tennessee
community colleges, for example, partnered with local high schools to offer dual enrollment
options for high school seniors who scored below a threshold on the ACT math (Kane et al.,
2018). The dual enrollment option provides students with a better assessment of their academic
preparation by gauging students’ math level according to college benchmarks. In addition, it may
reduce misalignment in math coursetaking and allow students to bypass costly and redundant
developmental education in community college.
Another recommendation is to actively encourage intersector alignment between high
schools and community colleges (Melguizo & Ngo, 2018). For example, the California State
Universities started to form partnerships with local high schools and to incentivize students to
39
take math courses during the summer before their freshmen year as a way to prepare students for
collegelevel coursework (Kurlaender, Lusher, & Case, 2017). Similarly, community colleges
may want to include local feeder high schools in the process of revamping their math sequence
and their assessment and placement process. For one, colleges can partner with local high
schools to inform students about how their high school records will affect their college
trajectory. Increased intersector curricular alignment may help remove any unnecessary counter
momentum friction in the transition from high school to college.
Future Research
Our study provides directions for future research. First, this study focused on only one
aspect of STEM momentum: curriculum and sequence progression. However, there are
additional facets that makeup students’ STEM momentum including, but not limited to,
aspirations, motivations, beliefs, pedagogy and teaching (Wang, 2013a; 2017a). When we
describe math misalignment as an experience, we surmise that students may have received a
discouraging signal of their math abilities from misaligned math placement. However, the math
misalignment experience may be part of a suite of math experiences both within and outside of
the math classroom. For instance, it may be that students who placed in lowerlevel math may
also have experienced more skillanddrill math instructional approaches than students in upper
level math (Cox, 2015; Grubb, & Gabriner, 2013). Recent studies suggest the importance of
active learning in boosting students’ STEM persistence in community college (Wang et al.,
2017b). While we identify math misalignment as an important structural experience, we are
unable to link math misalignment to teaching and learning that occurs inside the classroom and is
an important caveat to our description of students’ math misalignment experiences. A study with
a focus on whether and how math misalignment alters students’ aspirations as well as a look
40
inside developmental math classroom pedagogical practices would complement the findings of
this study.
In addition, this study also suggests an equity concern given that the majority of the
students in this study are URMs. Over 75% of the students in our sample are URMs, many of
whom are STEMaspiring. However, many of these students were placed in remediation despite
taking advanced math in high school and thus experienced math misalignment. This finding
corresponds to studies that found URMs have a higher likelihood of experiencing conflicting
math expectations in high school and in college (Fong & Melguizo, 2017; Melguizo & Ngo,
2018; Klasik & Strayhorn, 2018; Rodriguez, 2018). As increasing the number of URMs who
enter STEM fields is a national imperative (National Science Board, 2015), our findings suggest
that the overreliance on the placement test may have especially hindered STEMaspiring URMs
from pursuing STEM pathways. Future studies should examine racial and gender gaps in STEM
achievement and explore ways to reduce STEM inequities in community college.
41
Notes
1
These authors specified that this growth is mostly driven by occupations related to computer and information
systems.
2
The racialethnic composition of underrepresented minorities in this study are Black, Hispanic, and Native
American students as identifiable in the current data. Bahr et al.’s 2017 study on the STEM pathways in California
Community Colleges also defined underrepresented minorities as Blacks, Hispanics, and Native Americans. Like
the U.S. Census’ definition of Hispanics, we define Hispanics as “a person of Cuban, Mexican, Puerto Rican, South
or Central American or other Spanish culture or origin regardless of race.” It is also important to note that Asian is a
broad categorization that encompasses many different ethnicities, including Asian groups that are also
underrepresented in STEM. However, the current data do not allow for disaggregating Asians.
3
This information is obtained from the National Student Clearinghouse summary report.
4
Aligning with the California state graduation requirements, LUSD students are required to complete at least three
years of math and two years of science courses to obtain a high school diploma (California Department of
Education, 2018). At LUCCD, students are required to pass intermediate algebra (algebra 2 equivalent) with a C or
higher in order to obtain an Associate’s degree. However, in order to transfer to a California State University (CSU)
or a University of California (UC) in one of the STEM majors, students must complete 60 semester units or 90
quarter units. This information was obtained through the assist.org website. The specific criteria vary depending on
the major. For example, to transfer with a Biology major, students need 40 majorspecific units and in Biochemistry,
students need 44 majorspecific units.
5
These parameters resulted from a suit of validation studies conducted by the research arm of the Chancellor’s
Office (Research and Planning Group, 2018). The Chancellor’s Office provided this set of default placement rules if
colleges wish to bypass their own AB 705 validation efforts.
6
Prior to 2014, all students in grades 9 through 11 were required to take the math and science CST if they attend a
California public school. The state set five performance level on the CST based on a range of cut scores, and they
are: advanced, proficient, basic, below basic, and far below basic. In 201415, California implemented a new testing
scheme aligned to the Common Core State Standards. The data used in this study cuts off at 2014. We include
students’ CST scores in math and science as well covariates capturing the math and science course taken in 10
th
and
11
th
because the CST tests students take directly corresponds to their course.
7
All missing values except HS GPAs are imputed with a zero and included with the extra dummy indicator in all
specifications.
42
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50
Tables
Table 1
Definitions of Misalignment Based on the Highest High School Math Course, HS GPA, and
Math Placement
Note. Each row is a subsample based on the placement criteria and STEMaspiration. The row percentages add to
100%. The grey cells indicate the highest percentage within each row. Transfer = alignment, Int. Alg. = intermediate
algebra (algebra 2 equivalent), Elem. Alg. = elementary algebra, PreAlg. and Below = prealgebra and below.
High School Math Experience
Transfer Int. Alg. Elem Alg.
PreAlg. and
Below N
Panel A. All LUSDLUCCD Students
Highest HS Math = Algebra 2 2% 19% 28% 52% 20600
Highest HS Math = PreCalculus 13% 34% 23% 30% 9195
Highest HS Math = Calculus 45% 33% 9% 13% 1637
HS GPA ≥ 3.0 18% 32% 21% 29% 7331
HS GPA ≥3.4 OR HS GPA ≥2.6 and took Calculus 31% 34% 14% 21% 3183
Panel B. STEMAspiring Students
Highest HS Math = Algebra 2 3% 20% 27% 50% 3,697
Highest HS Math = PreCalculus 16% 34% 21% 29% 2,273
Highest HS Math = Calculus 51% 29% 7% 13% 611
HS GPA ≥ 3.0 25% 31% 17% 27% 1,921
HS GPA ≥3.4 OR HS GPA ≥2.6 and took Calculus 40% 32% 9% 19% 1,010
Math Placement in College
51
Table 2
Sample Statistics
Note. Students who entered college between 20092014 and who are not concurrent high school students are
included in these samples. Also, students who have not taken any math course in high school and do not have math
placement information are not included in the sample.
1
All students in the 20092014 cohort
2
Students in the 20092014 cohort who indicated that they would like to pursue a STEM major (Life Science or
Physical Science/Engineering).
3
Students who declined to state, or unknown race.
4
Indicator of students’ educational goals at the start of college.
Mean or SD Mean or SD
Demographic and Academic Indicators
Female 51% 55%
Asian 7% 11%
Black 9% 8%
Hispanic 71% 68%
White 7% 7%
Other
3
6% 6%
Special education 12% 10%
English learner categorization 14% 12%
Honors or AP 7% 11%
Years of AG Math 2.82 0.94 2.92 0.94
Years of AG Science 2.17 0.93 2.29 0.94
11th Grade Math CST Score 273.92 48.25 283.07 53.22
11th Grade Science CST Score 303.33 41.69 311.68 44.84
Cumulative HS GPA 2.37 0.63 2.47 0.65
Number of nonAP advanced math 2.16 1.99 2.59 2.16
Number of AP math or science 0.23 0.83 0.39 1.12
Placed in Transfer Level Math 5% 9%
Transfer or AA Intent
4
61% 63%
STEMAspiring 19% 
N 45,807 8822
(1) (2)
LUSDLUCCD
Students
1
STEMAspiring
Students
2
52
Table 3
High SchoolbyCollege Fixed Effects Estimation of Math Misalignment on STEM Outcomes
Note. All estimation includes the following covariates: gender, race, whether or not the student lives within the school district, students' primary language,
whether or not the student is a U.S. citizen, ELL status, SPED status, transfer or AA intent, whether or not students took AP or honors courses in high school, HS
GPA, 11th grade math and science CST scores, the different types of 11th grade math and science course students took, years of math and science AG courses
taken, whether or not students took at advanced math (geometry or above) in high school, the number of AP math or science courses taken, high schoolby
college and year fixed effects. Standard errors are clustered at the high schoolbycollege level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Highest HS Math =
Algebra 2
Highest HS Math =
PreCalculus
Highest HS Math =
Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR
HS GPA ≥2.6 and
took Calculus
Panel A. Passing Math Requirement for AA
Misaligned One Level Below/Placed in IA 0.37*** 0.22*** 0.24*** 0.16*** 0.14***
(0.02) (0.01) (0.03) (0.02) (0.02)
Misaligned Two Levels Below/Placed in EA 0.47*** 0.34*** 0.40*** 0.28*** 0.29***
(0.02) (0.02) (0.06) (0.02) (0.04)
Misaligned Three Levels Below/Placed in PreAlg. & Below 0.55*** 0.44*** 0.45*** 0.43*** 0.44***
(0.02) (0.02) (0.05) (0.03) (0.04)
Panel B. Transferable STEM Units Attempted
Misaligned One Level Below/Placed in IA 6.42*** 5.49*** 5.97*** 5.62*** 4.59***
(0.96) (0.81) (1.72) (0.88) (1.27)
Misaligned Two Levels Below/Placed in EA 8.23*** 8.14*** 11.57*** 8.69*** 10.22***
(0.99) (0.84) (2.30) (0.82) (1.37)
Misaligned Three Levels Below/Placed in PreAlg. & Below 9.17*** 8.95*** 11.09*** 10.27*** 11.03***
(0.95) (0.85) (2.62) (0.88) (1.48)
Panel C. Transferable STEM Units Completed
Misaligned One Level Below/Placed in IA 5.94*** 5.39*** 5.94*** 5.53*** 4.67***
(0.85) (0.72) (1.56) (0.81) (1.16)
Misaligned Two Levels Below/Placed in EA 7.57*** 7.67*** 11.24*** 8.17*** 9.64***
(0.85) (0.74) (2.02) (0.76) (1.24)
Misaligned Three Levels Below/Placed in PreAlg. & Below 8.46*** 8.42*** 10.79*** 9.77*** 10.55***
(0.83) (0.78) (2.48) (0.84) (1.37)
Number of High School by College Clusters 679 448 217 422 290
Number of Students 20600 9195 1637 7331 3183
53
Table 4
Interaction Estimation of Math Misalignment and STEM Aspiration on Passing Math Requirement for AA
Note. STEMaspiring refers to students who declared a STEM major in their college application. All estimation includes the following covariates: gender, race,
whether the student lives within the school district, students' primary language, whether the student is a U.S. citizen, ELL status, SPED status, transfer or AA
intent, whether students took AP or honors courses in high school, HS GPA, 11th grade math and science CST scores, the different types of 11th grade math and
science course students took, years of math and science courses taken, whether students took at advanced math (geometry or above) in high school, the number
of AP math or science courses taken, and high schoolbycollege and year fixed effects. Standard errors are clustered at the high schoolbycollege level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Passing Math Requirement for AA
Highest HS Math =
Algebra 2
Highest HS Math =
PreCalculus
Highest HS Math =
Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR
HS GPA ≥2.6 and
took Calculus
STEMAspiring 0.06** 0.01 0.03** 0.02 0.01
(0.02) (0.01) (0.01) (0.01) (0.01)
Misaligned One Level Below 0.41*** 0.25*** 0.28*** 0.18*** 0.18***
(0.02) (0.01) (0.03) (0.02) (0.02)
Misaligned Two Levels Below 0.50*** 0.36*** 0.38*** 0.31*** 0.32***
(0.02) (0.02) (0.07) (0.03) (0.04)
Misaligned Three Levels Below 0.58*** 0.47*** 0.51*** 0.46*** 0.50***
(0.02) (0.02) (0.05) (0.03) (0.04)
Misaligned One Level Below X STEMAspiring 0.19*** 0.11*** 0.10* 0.09*** 0.12***
(0.03) (0.02) (0.04) (0.02) (0.03)
Misaligned Two Levels Below X STEMAspiring 0.16*** 0.10*** 0.07 0.12*** 0.08
(0.02) (0.03) (0.09) (0.03) (0.06)
Misaligned Three Levels Below X STEMAspiring 0.11*** 0.12*** 0.21*** 0.15*** 0.21***
(0.02) (0.03) (0.06) (0.03) (0.04)
Number of High School by College Clusters 679 448 217 422 290
Number of Students 20600 9195 1637 7331 3183
54
Table 5
Interaction Estimation of Math Misalignment and STEM Aspiration on STEM Outcomes
Note. STEMaspiring refers to students who declared a STEM major in their college application.
All estimation includes the following covariates: gender, race, whether the student lives within the school district,
students' primary language, whether the student is a U.S. citizen, ELL status, SPED status, transfer or AA intent,
whether students took AP or honors courses in high school, HS GPA, 11th grade math and science CST scores, the
different types of 11th grade math and science course students took, years of math and science courses taken,
whether students took at advanced math (geometry or above) in high school, the number of AP math or science
courses taken, and high schoolbycollege and year fixed effects. Standard errors are clustered at the high schoolby
college level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Highest HS Math =
Algebra 2
Highest HS Math =
PreCalculus
Highest HS Math =
Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR
HS GPA ≥2.6 and
took Calculus
Panel A. Transferable STEM Units Attempted
STEMAspiring 13.87*** 15.88*** 16.80*** 17.64*** 18.28***
(1.94) (1.55) (1.93) (1.17) (1.37)
Misaligned One Level Below 4.64*** 3.04*** 4.28** 2.87*** 2.15
(0.93) (0.75) (1.61) (0.77) (1.21)
Misaligned Two Levels Below 5.85*** 5.19*** 7.62** 5.31*** 7.05***
(0.92) (0.86) (2.36) (0.79) (1.27)
Misaligned Three Levels Below 6.42*** 5.82*** 8.04** 6.95*** 7.93***
(0.92) (0.88) (2.54) (0.84) (1.45)
Misaligned One Level Below X STEMAspiring 5.25* 5.79*** 1.96 6.29*** 4.29*
(2.15) (1.63) (3.19) (1.27) (1.86)
Misaligned Two Levels Below X STEMAspiring 7.88*** 7.43*** 9.11** 9.10*** 5.85
(1.93) (1.65) (3.51) (1.67) (3.06)
Misaligned Three Levels Below X STEMAspiring 9.61*** 7.87*** 2.59 8.55*** 6.09***
(2.04) (1.71) (2.94) (1.32) (1.81)
Panel B. Transferable STEM Units Completed
STEMAspiring 12.20*** 13.39*** 15.02*** 15.87*** 16.71***
(1.76) (1.45) (1.81) (1.06) (1.21)
Misaligned One Level Below 4.22*** 3.21*** 4.26** 2.90*** 2.13
(0.83) (0.68) (1.51) (0.71) (1.11)
Misaligned Two Levels Below 5.36*** 5.15*** 7.64*** 5.01*** 6.56***
(0.80) (0.77) (2.05) (0.74) (1.13)
Misaligned Three Levels Below 5.93*** 5.71*** 8.03** 6.61*** 7.55***
(0.80) (0.83) (2.50) (0.79) (1.36)
Misaligned One Level Below X STEMAspiring 5.37** 5.30*** 2.26 6.22*** 4.88**
(1.93) (1.56) (2.98) (1.17) (1.70)
Misaligned Two Levels Below X STEMAspiring 7.55*** 6.38*** 8.33* 8.66*** 5.99*
(1.74) (1.55) (3.27) (1.55) (2.91)
Misaligned Three Levels Below X STEMAspiring 9.11*** 6.93*** 2.43 8.40*** 6.08***
(1.84) (1.63) (3.22) (1.27) (1.71)
Number of High School by College Clusters 679 448 217 422 290
Number of Students 20600 9195 1637 7331 3183
55
Figures
Figure 1
Interaction Plot of Transferable STEM Units Attempted and Completed Adjusted Means by
STEMAspiration
Note. STEMaspiring refers to students who declared a STEM major in their college application. NonSTEM
Aspiring refers to all other students (both undecided and nonSTEM).
0
5
10
15
20
25
30
35
40
Aligned 1 LBT 2 LBT 3 LBT
Transferable STEM Units Attempted
NonSTEM
Aspiring
STEM
Aspiring
0
5
10
15
20
25
30
35
40
Aligned 1 LBT 2 LBT 3 LBT
Transferable STEM Units Completed
NonSTEM
Aspiring
STEM
Aspiring
56
Appendix
Table A.1
Crosswalk of Major Name, Classification of Instructional Program (CIP) Code, and the
Taxonomy of Program (TOP) Code by STEM Majors (Life Science and Physical
Science/Engineering)
Life Science Physical Science/Engineering
Major 2digit CIP
Code
3 or 4digit
TOP Code
Major 2digit CIP
Code
3 or 4digit
TOP Code
Agricultural
Sciences
01 101, 102 Computer and
Information
Sciences
11 116, 119, 614,
In between
701799
Natural Sciences
and Conservation
03 114, 115,
301, 302,
399
Engineering 14 901, 934
Biological and
Biomedical
Sciences
26 401, 402,
403, 407,
410
a
Engineering
Technologies,
Technicians
15 924, 934, 935,
943, 946, 953,
956, 957, 961,
999
Medical
Assistant
b
51 120, 121,
122, 123,
124, 125,
126, 129,
136, 1201,
1251, 1260,
1261
Mathematics and
Statistics
27 1701, 1799
Physical Science 40 1901, 1919,
1930, 1999
Science
Technologies,
Technicians
a
41 1920
Mechanic, Repair
Technologies,
Technicians
a
47 943, 953, 947,
948, 949, 950,
962,
Biological and
Physical Science
and Mathematics
30 4902, 990
Note. This categorization borrows from Wang’s categorization in the 2016 study titled “Coursetaking patterns of
community college students beginning in STEM: Using data mining techniques to reveal viable STEM transfer
pathways.” Biological and Physical Science and Mathematics is included in this study but was not included in
Wang’s 2016 study.
a
This indicates that the majors is flagged as “likely terminal” meaning students who pursue these majors do not
usually transfer to a fouryear university.
b
This is to note that the major was not included in Wang’s study but is included in this study as medical assistants
take a significant number of STEM courses.
57
Table A.2
Description of Missing Values
Variable Missing Rationale Solution
Female 0 N/A N/A
Asian 0 N/A N/A
Black 0 N/A N/A
Hispanic 0 N/A N/A
White 0 N/A N/A
Other 0 N/A N/A
Special education 0 N/A N/A
English learner categorization 46 Will assume random missing Dummy code
Honors or AP 76 Will assume random missing Dummy code
Years of AG Math 0 N/A N/A
Years of AG Science 0 N/A N/A
11th Grade Math CST Score 20,819
For grades 811, the test depends upon the particular math
course in which the student is enrolled. Grades 911 took
summative math CST; Include a control variable for the math
course taken in 11th grade. Dummy code
11th Grade Science CST Score 19,699
The science test depends on the course in which students are
enrolled; Include a control variable for the science course
taken in 11th grade. Dummy code
Cumulative HS GPA 65 Will assume random missing
Dummy code; 8
cases replaced
with the mean
Number of nonAP advanced math 0 N/A N/A
Number of AP math or science 0 N/A N/A
58
Table A.3
High SchoolbyCollege Fixed Effects Estimation of Math Misalignment using Last High School Math Course
Note. All estimation includes the following covariates: gender, race, whether or not the student lives within the school district, students' primary language,
whether or not the student is a U.S. citizen, ELL status, SPED status, transfer or AA intent, whether or not students took AP or honors courses in high school, HS
GPA, 11th grade math and science CST scores, the different types of 11th grade math and science course students took, years of math and science AG courses
taken, whether or not students took at advanced math (geometry or above) in high school, the number of AP math or science courses taken, high schoolby
college and year fixed effects. Standard errors are clustered at the high schoolbycollege level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Last HS Math =
Algebra 2
Last HS Math = Pre
Calculus
Last HS Math =
Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR HS
GPA ≥2.6 and took
Calculus
Panel A. Passing Math Requirement for AA
Misaligned One Level Below/Placed in IA 0.36*** 0.22*** 0.26*** 0.16*** 0.14***
(0.02) (0.01) (0.03) (0.02) (0.02)
Misaligned Two Levels Below/Placed in EA 0.46*** 0.33*** 0.42*** 0.28*** 0.30***
(0.02) (0.02) (0.06) (0.02) (0.04)
Misaligned Three Levels Below/Placed in PreAlg. & Below 0.55*** 0.44*** 0.46*** 0.43*** 0.45***
(0.03) (0.02) (0.05) (0.03) (0.04)
Panel B. Transferable STEM Units Attempted
Misaligned One Level Below/Placed in IA 6.34*** 5.48*** 5.80** 5.62*** 4.44***
(1.01) (0.85) (1.75) (0.88) (1.24)
Misaligned Two Levels Below/Placed in EA 8.07*** 8.14*** 10.60*** 8.69*** 9.92***
(1.04) (0.83) (2.34) (0.82) (1.37)
Misaligned Three Levels Below/Placed in PreAlg. & Below 9.20*** 8.90*** 10.96*** 10.27*** 10.95***
(1.02) (0.84) (2.72) (0.88) (1.51)
Panel C. Transferable STEM Units Completed
Misaligned One Level Below/Placed in IA 5.92*** 5.34*** 6.01*** 5.53*** 4.56***
(0.88) (0.75) (1.59) (0.81) (1.14)
Misaligned Two Levels Below/Placed in EA 7.51*** 7.64*** 10.69*** 8.17*** 9.39***
(0.90) (0.73) (2.05) (0.76) (1.24)
Misaligned Three Levels Below/Placed in PreAlg. & Below 8.54*** 8.34*** 10.87*** 9.77*** 10.51***
(0.89) (0.77) (2.56) (0.84) (1.40)
Number of High School by College Clusters 653 446 211 422 287
Number of Students 18522 9158 1528 7331 3119
59
Table A.4
Interaction Estimation of Math Misalignment using Last High School Math Course and STEM
Aspiration on STEM Outcomes
Note. STEMaspiring refers to students who declared a STEM major in their college application.
All estimation includes the following covariates: gender, race, whether the student lives within the school district,
students' primary language, whether the student is a U.S. citizen, ELL status, SPED status, transfer or AA intent,
whether students took AP or honors courses in high school, HS GPA, 11th grade math and science CST scores, the
different types of 11th grade math and science course students took, years of math and science courses taken,
whether students took at advanced math (geometry or above) in high school, the number of AP math or science
courses taken, and high schoolbycollege and year fixed effects. Standard errors are clustered at the high schoolby
college level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Last HS Math =
Algebra 2
Last HS Math = Pre
Calculus
Last HS Math =
Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR HS
GPA ≥2.6 and took
Calculus
Panel A. Passing Math Requirement for AA
STEMAspiring 0.06** 0.01 0.03** 0.02 0.01
(0.02) (0.01) (0.01) (0.01) (0.01)
Misaligned One Level Below 0.40*** 0.25*** 0.30*** 0.18*** 0.18***
(0.02) (0.01) (0.03) (0.02) (0.02)
Misaligned Two Levels Below 0.50*** 0.36*** 0.40*** 0.31*** 0.32***
(0.03) (0.02) (0.07) (0.03) (0.04)
Misaligned Three Levels Below 0.58*** 0.47*** 0.51*** 0.46*** 0.50***
(0.03) (0.02) (0.05) (0.03) (0.04)
Misaligned One Level Below X STEMAspiring 0.19*** 0.11*** 0.10* 0.09*** 0.12***
(0.03) (0.02) (0.04) (0.02) (0.03)
Misaligned Two Levels Below X STEMAspiring 0.17*** 0.11*** 0.06 0.12*** 0.08
(0.03) (0.03) (0.09) (0.03) (0.06)
Misaligned Three Levels Below X STEMAspiring 0.11*** 0.13*** 0.20** 0.15*** 0.21***
(0.02) (0.03) (0.07) (0.03) (0.04)
Panel B. Transferable STEM Units Attempted
STEMAspiring 13.30*** 15.71*** 17.19*** 17.64*** 18.22***
(2.01) (1.45) (1.94) (1.17) (1.38)
Misaligned One Level Below 4.86*** 2.97*** 3.92* 2.87*** 1.99
(1.02) (0.76) (1.71) (0.77) (1.24)
Misaligned Two Levels Below 5.97*** 5.16*** 6.80** 5.31*** 6.86***
(1.02) (0.82) (2.48) (0.79) (1.33)
Misaligned Three Levels Below 6.72*** 5.75*** 7.49** 6.95*** 7.80***
(1.03) (0.86) (2.68) (0.84) (1.48)
Misaligned One Level Below X STEMAspiring 4.47* 5.63*** 2.46 6.29*** 4.21*
(2.27) (1.55) (3.35) (1.27) (1.85)
Misaligned Two Levels Below X STEMAspiring 7.32*** 7.07*** 8.90* 9.10*** 5.66
(1.97) (1.59) (3.70) (1.67) (3.06)
Misaligned Three Levels Below X STEMAspiring 9.02*** 7.50*** 3.46 8.55*** 6.26***
(2.14) (1.64) (2.80) (1.32) (1.83)
Panel C. Transferable STEM Units Completed
STEMAspiring 11.64*** 13.32*** 15.29*** 15.87*** 16.65***
(1.83) (1.34) (1.81) (1.06) (1.23)
Misaligned One Level Below 4.48*** 3.10*** 4.12* 2.90*** 2.02
(0.90) (0.68) (1.60) (0.71) (1.15)
Misaligned Two Levels Below 5.56*** 5.05*** 7.26*** 5.01*** 6.42***
(0.90) (0.74) (2.13) (0.74) (1.18)
Misaligned Three Levels Below 6.26*** 5.59*** 7.76** 6.61*** 7.47***
(0.89) (0.81) (2.59) (0.79) (1.40)
Misaligned One Level Below X STEMAspiring 4.60* 5.20*** 2.80 6.22*** 4.82**
(2.03) (1.48) (3.10) (1.17) (1.69)
Misaligned Two Levels Below X STEMAspiring 6.99*** 6.19*** 8.06* 8.66*** 5.78*
(1.80) (1.48) (3.43) (1.55) (2.91)
Misaligned Three Levels Below X STEMAspiring 8.54*** 6.69*** 3.13 8.40*** 6.25***
(1.95) (1.57) (2.98) (1.27) (1.72)
Number of High School by College Clusters 653 446 211 422 287
Number of Students 18522 9158 1528 7331 3119
60
Table A.5
High SchoolbyCollege Fixed Effects Estimation of Math Misalignment using Math Enrollment
Note.
All estimation includes the following covariates: gender, race, whether or not the student lives within the school district, students' primary language, whether or
not the student is a U.S. citizen, ELL status, SPED status, transfer or AA intent, whether or not students took AP or honors courses in high school, HS GPA, 11th
grade math and science CST scores, the different types of 11th grade math and science course students took, years of math and science AG courses taken,
whether or not students took at advanced math (geometry or above) in high school, the number of AP math or science courses taken, high schoolbycollege and
year fixed effects. Standard errors are clustered at the high schoolbycollege level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Highest HS Math =
Algebra 2
Highest HS Math = Pre
Calculus
Highest HS Math =
Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR HS
GPA ≥2.6 and took
Calculus
Panel A. Passing Math Requirement for AA
Misaligned One Level Below/Placed in IA 0.17*** 0.09*** 0.09*** 0.05** 0.04
(0.02) (0.02) (0.02) (0.02) (0.02)
Misaligned Two Levels Below/Placed in EA 0.32*** 0.24*** 0.27*** 0.20*** 0.21***
(0.02) (0.02) (0.03) (0.02) (0.03)
Misaligned Three Levels Below/Placed in PreAlg. & Below 0.41*** 0.34*** 0.30*** 0.34*** 0.35***
(0.02) (0.02) (0.06) (0.03) (0.04)
Panel B. Transferable STEM Units Attempted
Misaligned One Level Below/Placed in IA 4.68*** 4.98*** 4.59* 5.75*** 4.58***
(0.72) (0.84) (2.07) (0.94) (1.33)
Misaligned Two Levels Below/Placed in EA 6.92*** 7.45*** 9.10*** 8.00*** 8.68***
(0.75) (0.78) (2.27) (0.91) (1.40)
Misaligned Three Levels Below/Placed in PreAlg. & Below 8.32*** 8.73*** 11.19*** 10.28*** 11.51***
(0.74) (0.87) (2.93) (0.95) (1.76)
Panel C. Transferable STEM Units Completed
Misaligned One Level Below/Placed in IA 4.32*** 5.01*** 4.01* 5.55*** 4.35***
(0.66) (0.79) (1.90) (0.89) (1.26)
Misaligned Two Levels Below/Placed in EA 6.30*** 7.19*** 8.30*** 7.59*** 8.05***
(0.68) (0.76) (1.93) (0.84) (1.28)
Misaligned Three Levels Below/Placed in PreAlg. & Below 7.61*** 8.33*** 10.45*** 9.70*** 10.67***
(0.67) (0.85) (2.90) (0.91) (1.66)
Number of High School by College Clusters 631 423 196 394 268
Number of Students 17026 8036 1425 6460 2809
61
Table A.6
Interaction Estimation of Math Misalignment using Math Enrollment and STEM Aspiration on
STEM Outcomes
Note. STEMaspiring refers to students who declared a STEM major in their college application.
All estimation includes the following covariates: gender, race, whether the student lives within the school district,
students' primary language, whether the student is a U.S. citizen, ELL status, SPED status, transfer or AA intent,
whether students took AP or honors courses in high school, HS GPA, 11th grade math and science CST scores, the
different types of 11th grade math and science course students took, years of math and science courses taken,
whether students took at advanced math (geometry or above) in high school, the number of AP math or science
courses taken, and high schoolbycollege and year fixed effects. Standard errors are clustered at the high schoolby
college level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Highest HS Math =
Algebra 2
Highest HS Math = Pre
Calculus
Highest HS Math =
Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR HS
GPA ≥2.6 and took
Calculus
Panel A. Passing Math Requirement for AA
STEMAspiring 0.04 0.01 0.06* 0.02 0.03
(0.04) (0.01) (0.02) (0.01) (0.02)
Misaligned One Level Below 0.20*** 0.11*** 0.11*** 0.07*** 0.06*
(0.02) (0.02) (0.03) (0.02) (0.03)
Misaligned Two Levels Below 0.35*** 0.27*** 0.24*** 0.23*** 0.23***
(0.02) (0.03) (0.04) (0.03) (0.03)
Misaligned Three Levels Below 0.43*** 0.36*** 0.26*** 0.38*** 0.38***
(0.02) (0.03) (0.07) (0.03) (0.05)
Misaligned One Level Below X STEMAspiring 0.14*** 0.04 0.04 0.04 0.04
(0.04) (0.02) (0.05) (0.02) (0.03)
Misaligned Two Levels Below X STEMAspiring 0.12** 0.09*** 0.09 0.09*** 0.04
(0.04) (0.02) (0.06) (0.03) (0.04)
Misaligned Three Levels Below X STEMAspiring 0.08* 0.09** 0.14 0.13*** 0.13*
(0.04) (0.03) (0.13) (0.04) (0.06)
Panel B. Transferable STEM Units Attempted
STEMAspiring 11.97*** 16.06*** 15.12*** 16.25*** 16.59***
(1.77) (1.41) (1.86) (1.39) (1.51)
Misaligned One Level Below 3.25*** 2.58*** 4.21 3.35*** 2.79*
(0.70) (0.76) (2.17) (0.97) (1.39)
Misaligned Two Levels Below 5.24*** 4.80*** 6.92** 5.75*** 7.31***
(0.69) (0.78) (2.29) (0.85) (1.37)
Misaligned Three Levels Below 5.92*** 5.25*** 9.10*** 6.98*** 9.14***
(0.69) (0.86) (2.69) (0.95) (1.56)
Misaligned One Level Below X STEMAspiring 4.11* 6.02*** 0.16 5.50*** 3.12
(1.92) (1.50) (3.69) (1.51) (1.97)
Misaligned Two Levels Below X STEMAspiring 5.06** 6.99*** 4.69 5.96*** 3.37
(1.81) (1.59) (2.81) (1.58) (2.41)
Misaligned Three Levels Below X STEMAspiring 8.19*** 9.76*** 2.21 9.46*** 6.34**
(1.85) (1.56) (4.68) (1.47) (2.23)
Panel C. Transferable STEM Units Completed
STEMAspiring 10.65*** 13.64*** 13.28*** 14.79*** 14.97***
(1.69) (1.33) (1.74) (1.25) (1.35)
Misaligned One Level Below 2.79*** 2.86*** 3.66 3.08*** 2.35
(0.59) (0.69) (2.02) (0.90) (1.28)
Misaligned Two Levels Below 4.66*** 4.87*** 6.50** 5.31*** 6.62***
(0.57) (0.73) (1.97) (0.80) (1.22)
Misaligned Three Levels Below 5.36*** 5.25*** 8.62*** 6.49*** 8.45***
(0.55) (0.83) (2.57) (0.90) (1.44)
Misaligned One Level Below X STEMAspiring 4.83** 5.51*** 0.21 5.98*** 4.00*
(1.77) (1.44) (3.45) (1.38) (1.80)
Misaligned Two Levels Below X STEMAspiring 5.20** 6.15*** 3.83 6.12*** 3.48
(1.74) (1.52) (2.47) (1.46) (2.19)
Misaligned Three Levels Below X STEMAspiring 7.91*** 8.79*** 1.93 9.28*** 5.77**
(1.79) (1.50) (4.43) (1.37) (2.16)
Number of High School by College Clusters 631 423 196 394 268
Number of Students 17023 8036 1425 6460 2809
62
Table A.7
High SchoolbyCollege Fixed Effects Estimation of Math Misalignment using Highest High School Math Course Passed with A or B
Note. All estimation includes the following covariates: gender, race, whether or not the student lives within the school district, students' primary language,
whether or not the student is a U.S. citizen, ELL status, SPED status, transfer or AA intent, whether or not students took AP or honors courses in high school, HS
GPA, 11th grade math and science CST scores, the different types of 11th grade math and science course students took, years of math and science AG courses
taken, whether or not students took at advanced math (geometry or above) in high school, the number of AP math or science courses taken, high schoolby
college and year fixed effects. Standard errors are clustered at the high schoolbycollege level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Highest HS Math A/B
= Algebra 2
Highest HS Math A/B
= PreCalculus
Highest HS Math A/B
= Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR HS
GPA ≥2.6 and took
Calculus
Panel A. Passing Math Requirement for AA
Misaligned One Level Below/Placed in IA 0.28*** 0.17*** 0.27*** 0.16*** 0.13***
(0.01) (0.02) (0.04) (0.02) (0.02)
Misaligned Two Levels Below/Placed in EA 0.38*** 0.31*** 0.44*** 0.28*** 0.31***
(0.02) (0.03) (0.06) (0.02) (0.04)
Misaligned Three Levels Below/Placed in PreAlg. & Below 0.48*** 0.40*** 0.43*** 0.43*** 0.46***
(0.02) (0.03) (0.11) (0.03) (0.04)
Panel B. Transferable STEM Units Attempted
Misaligned One Level Below/Placed in IA 5.79*** 6.33*** 7.60* 5.65*** 5.05***
(0.84) (1.23) (3.30) (0.88) (1.44)
Misaligned Two Levels Below/Placed in EA 7.85*** 10.39*** 12.94** 8.86*** 11.61***
(0.83) (1.17) (3.99) (0.81) (1.55)
Misaligned Three Levels Below/Placed in PreAlg. & Below 8.75*** 10.42*** 12.85** 10.30*** 12.73***
(0.89) (1.18) (4.91) (0.90) (1.78)
Panel C. Transferable STEM Units Completed
Misaligned One Level Below/Placed in IA 5.73*** 6.04*** 7.46* 5.56*** 5.12***
(0.78) (1.04) (2.91) (0.82) (1.36)
Misaligned Two Levels Below/Placed in EA 7.59*** 9.65*** 12.03*** 8.31*** 10.69***
(0.79) (1.04) (3.32) (0.77) (1.41)
Misaligned Three Levels Below/Placed in PreAlg. & Below 8.36*** 9.77*** 12.49** 9.79*** 12.03***
(0.83) (1.08) (4.51) (0.86) (1.65)
Number of High School by College Clusters 480 330 143 413 265
Number of Students 8975 4040 666 7116 2508
63
Table A.8
Interaction Estimation of Math Misalignment using Highest High School Math Passed with A or
B and STEM Aspiration on STEM Outcomes
Note. STEMaspiring refers to students who declared a STEM major in their college application.
All estimation includes the following covariates: gender, race, whether the student lives within the school district,
students' primary language, whether the student is a U.S. citizen, ELL status, SPED status, transfer or AA intent,
whether students took AP or honors courses in high school, HS GPA, 11th grade math and science CST scores, the
different types of 11th grade math and science course students took, years of math and science courses taken,
whether students took at advanced math (geometry or above) in high school, the number of AP math or science
courses taken, and high schoolbycollege and year fixed effects. Standard errors are clustered at the high schoolby
college level.
* p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5)
Highest HS Math A/B
= Algebra 2
Highest HS Math A/B
= PreCalculus
Highest HS Math A/B
= Calculus HS GPA ≥ 3.0
HS GPA ≥3.4 OR HS
GPA ≥2.6 and took
Calculus
Panel A. Passing Math Requirement for AA
STEMAspiring 0.04* 0.00 0.02 0.01 0.00
(0.02) (0.01) (0.02) (0.01) (0.01)
Misaligned One Level Below 0.31*** 0.20*** 0.30*** 0.18*** 0.17***
(0.01) (0.03) (0.05) (0.02) (0.02)
Misaligned Two Levels Below 0.43*** 0.33*** 0.52*** 0.32*** 0.35***
(0.02) (0.04) (0.08) (0.03) (0.04)
Misaligned Three Levels Below 0.51*** 0.44*** 0.50*** 0.46*** 0.51***
(0.02) (0.03) (0.11) (0.03) (0.04)
Misaligned One Level Below X STEMAspiring 0.15*** 0.09*** 0.08 0.09*** 0.14***
(0.03) (0.03) (0.08) (0.02) (0.03)
Misaligned Two Levels Below X STEMAspiring 0.19*** 0.08 0.24 0.12*** 0.14*
(0.03) (0.05) (0.15) (0.03) (0.06)
Misaligned Three Levels Below X STEMAspiring 0.12*** 0.14*** 0.33*** 0.14*** 0.23***
(0.02) (0.04) (0.08) (0.03) (0.05)
Panel B. Transferable STEM Units Attempted
STEMAspiring 15.69*** 16.32*** 15.14*** 17.64*** 17.72***
(1.79) (1.80) (3.73) (1.19) (1.68)
Misaligned One Level Below 3.59*** 3.72*** 6.02 2.90*** 2.72
(0.85) (1.08) (3.18) (0.78) (1.45)
Misaligned Two Levels Below 5.04*** 7.07*** 12.20** 5.43*** 8.72***
(0.91) (1.19) (4.37) (0.83) (1.44)
Misaligned Three Levels Below 5.48*** 7.87*** 9.34* 6.95*** 9.54***
(0.95) (1.25) (4.72) (0.87) (1.71)
Misaligned One Level Below X STEMAspiring 5.11* 6.11** 0.27 6.28*** 3.38
(2.05) (2.15) (7.27) (1.29) (2.25)
Misaligned Two Levels Below X STEMAspiring 7.70*** 7.47*** 0.20 9.18*** 4.73
(1.94) (2.12) (6.97) (1.76) (3.45)
Misaligned Three Levels Below X STEMAspiring 9.91*** 4.95* 5.86 8.52*** 6.07**
(1.87) (2.23) (5.88) (1.39) (2.27)
Panel C. Transferable STEM Units Completed
STEMAspiring 13.70*** 14.41*** 12.81*** 15.86*** 16.02***
(1.73) (1.65) (3.49) (1.08) (1.56)
Misaligned One Level Below 3.61*** 3.64*** 5.80* 2.94*** 2.72
(0.80) (0.95) (2.78) (0.73) (1.38)
Misaligned Two Levels Below 5.00*** 6.56*** 11.75** 5.10*** 7.98***
(0.84) (1.07) (3.88) (0.77) (1.35)
Misaligned Three Levels Below 5.38*** 7.46*** 9.65* 6.62*** 9.06***
(0.88) (1.16) (4.44) (0.82) (1.61)
Misaligned One Level Below X STEMAspiring 5.30** 5.73** 0.70 6.17*** 3.99
(1.94) (1.96) (6.56) (1.19) (2.07)
Misaligned Two Levels Below X STEMAspiring 7.28*** 7.28*** 1.32 8.72*** 4.59
(1.84) (1.95) (6.17) (1.63) (3.21)
Misaligned Three Levels Below X STEMAspiring 9.18*** 4.55* 4.27 8.32*** 5.78**
(1.77) (2.14) (5.45) (1.33) (2.22)
Number of High School by College Clusters 480 330 143 413 265
Number of Students 8975 4040 666 7116 2508
Table A.9
Sharp Regression Discontinuity Estimates around the Intermediate Algebra/TransferLevel Math Cutoff
(1) (2) (3)
Passing Math
Requirement for AA
Transferable STEM
Units Attempted
Transferable STEM
Units Completed
Panel A. All Students
Missing the cutoff and placing into
intermediate algebra 0.313** 8.656** 8.989**
(0.054) (3.026) (2.797)
N 548 548 548
Panel B. STEMAspiring Students
Missing the cutoff and placing into
intermediate algebra 0.180* 13.265* 14.069*
(0.087) (6.670) (6.121)
N 157 157 157
Note. Local linear regression estimated for students around the intermediate algebra/transferlevel cutoff. Students attending two campuses were excluded from
the regression discontinuity analysis because those campuses administered a different placement test during the timeframe of this study. The bandwidth is +/ 1
standard deviations around the test score cutoff. Standard error in parentheses.
* p<0.05, ** p<0.01, *** p<0.001
Essay II. The Effect of Developmental Math on STEM Participation in Community
College: Variation by Race, Gender, Achievement, and Aspiration
Abstract
Improving math skills may help college students be more successful in STEM courses,
but whether remedial/ developmental math education increases STEM participation is unknown.
We use regression discontinuity design to examine the impact of placing into developmental
math on STEM participation in community college. We also conduct subgroup analyses to
determine if these relationships differ for underrepresented minorities (URMs), women, STEM
oriented, and STEMaspiring students. The results show that lower math placement may be
marginally beneficial for women and URMs placed in the lowest levels of math. However, lower
placement was more of a deterrent in early math progression for STEMaspiring and STEM
oriented students than their peers who placed above. These results suggest that lower math
placement delayed progress in the STEM pathway, particularly for those most poised to enter
STEM fields.
66
Retaining college students in Science, Technology, Engineering, and Mathematics
(STEM) fields can increase STEM degree production and bolster competitiveness in the U.S.
workforce (President’s Council of Advisors on Science and Technology, 2012). As such,
attrition from STEM pathways and inequality in STEM participation and attainment have
motivated ample scholarship on ways to fortify the STEM pipeline. Researchers have
importantly focused on such topics as financial incentives for STEM majors (Evans, 2017),
developing student interest and engagement in STEM topics through academic exposure (Crisp,
Nora, & Taggart, 2009), advising and early college interactions and momentum (Wang, 2013a,
Wang, 2015), fostering math and science identities (Sax et al., 2015), and on creating welcoming
academic environments (Good, Rattan, & Dweck, 2012).
There has surprisingly been less focus on structural barriers to STEM participation such
as math prerequisites and postsecondary math remediation. Research has documented how
students build STEM momentum and STEM selfefficacy as they take science and math courses
in high school (Gottfried & Bozick, 2016; Wang, 2013b, 2015). However, this momentum may
fade as students, particularly those in the nation’s community colleges, encounter
remedial/developmental math coursework and math prerequisites required for entry into STEM
fields. This may be particularly acute for students of color, who attend community colleges at
higher rates and are therefore more subject to remediation than academically equivalent peers at
fouryear institutions (Attewell et al., 2006).
Further, most studies of postsecondary math remediation have focused on generic
outcomes such as gatekeeper course completion, dropout, yeartoyear persistence, credit
accumulation, and degree attainment (e.g., Bettinger & Long, 2009; Clotfelter et al., 2014; Lesik,
2006). Some have examined learning gains (ScottClayton & Rodriguez, 2015) and wages
67
(Martorell & McFarlin, 2011), but there is scant research examining the impact of math
remediation on STEM participation. These connections are important to consider because
evidence suggests that math remediation may be more of a diversion rather than a gateway to
enrollment in STEM courses (Bryk & Treisman, 2010).
This study investigates whether assignment to a developmental/remedial math course
affects the likelihood of STEM participation in community college. We do so using data from a
large urban community college district (LUCCD) in California that serves about 250,000
students each year, the vast majority of whom are students of color. With access to demographic
information, assessment and placement results, and course enrollment records, we link math
course placement to enrollment in STEM courses for roughly ten years after initial community
college enrollment. Specifically, we capitalize on the system of placement cutoffs used to assign
students to various math courses in the developmental math sequence and use a regression
discontinuity (RD) design to determine the impact of these course assignments. If students
scoring just below the placement cutoff differ from their peers scoring just above with respect to
their subsequent STEM participation, then this can be interpreted as a consequence of
developmental math placement.
We also conduct subgroup analyses to determine if there are differences in the
relationship between developmental math placement and STEM participation for
underrepresented minorities (URMs) and women. Previous studies showed that female and URM
students are less likely to take advanced STEM courses in community college (Bahr et al., 2017),
more susceptible to attriting from STEM pathways (Chen & Soldner, 2013), and more likely to
populate lower levels of developmental math (Fong & Melguizo, 2016). However, studies have
not yet determined the causal link between math remediation and advanced STEM coursetaking
68
among women and URMs. This is an important analysis because placement in lowerlevel math
may perpetuate negative stereotypes about female and URM students’ “fit” in STEM fields
(BenZeev et al., 2017; Walton, Logel, Peach, Spencer, & Zanna, 2015) and subsequently more
strongly deter them from STEM pathways relative to their White, Asian, and/or male peers. This
study can therefore provide new evidence on how math remediation impacts underrepresented
students’ entry into STEM pathways. Investigating this link is timely given the ongoing need to
diversify the STEM talent pool (National Science Foundation, 2017).
A unique contribution of our study is that we use students’ high school transcripts and
community college application data to examine how those with an orientation towards STEM
and those with STEM aspirations are impacted by math remediation. Specifically, we identify
two nonmutually exclusive student groups who are STEMoriented and STEMaspiring. We
classify students who likely developed considerable STEM selfefficacy and momentum by
passing advanced math and science courses in high school as STEMoriented students, and
students who intend to pursue a STEM major on their community college application as STEM
aspiring students. Consequently, these students may be more likely to take STEM courses in
college. We conduct subgroup analyses for STEMoriented and STEMaspiring students to
determine whether math remediation impacts these students’ STEM participation.
We find that developmental math was not beneficial for students at the cusp of placing
into transferlevel math. Compared to students who placed directly into transferlevel math,
students who placed lower into intermediate algebra were less likely to take advanced STEM
courses both in the short and longrun. In addition, students who missed the cutoff and placed
lower into elementary algebra were less likely to accumulate STEM credits relative to students
who placed above into intermediate algebra. However, for students who placed in arithmetic and
69
prealgebra – the two lowest levels of the developmental math sequence – there is suggestive
evidence that lower placement helped students attempt the math requirement for an Associate’s
degree and possibly increased STEM participation in the shortterm. Despite this evidence, lower
placement into arithmetic or prealgebra did not increase STEM participation in the long run.
Our subgroup analyses revealed interesting differences in math progression and STEM
participation for women and URMs. Lower placement into arithmetic or prealgebra appeared to
be helpful for the least academically prepared women and URM, increasing the likelihood that
they persisted in the math sequence and took upperlevel STEM courses. In contrast, for students
aspiring to pursue STEM or with advanced STEM coursetaking records, lower placement was a
significant deterrent in early math progression.
In the following section, we describe the conceptual framework undergirding the study
and the community college policy context. We then discuss our sharp RD strategy and explain
why this method is appropriate. Finally, we present results and conclude with policy
implications.
Conceptual Framework
We draw on a combination of social cognitive career theory (SCCT), the theory of STEM
momentum, and the theory of stereotype threat for our conceptual framework. A theory rooted in
Bandura’s (1986) socialcognitive theory, SCCT examines the interaction of the self and the
environment in influencing thoughts, beliefs, emotion, and behavior within the context of career
development (Lent et al., 2003; Lent, Brown, & Hackett, 1994; Lent, Lopez, & Bieschke, 1991).
The SCCT hypothesizes that individuals become interested in and eventually pursue a career
based on three interlinked social cognitive processes: selfefficacy, outcome expectation, and
goals (i.e., aspirations). Specifically, the SCCT suggests that individuals aspire to enter STEM
70
fields if they feel efficacious in STEM subjects and hold beliefs that pursuing STEM will
produce valued outcomes (i.e., outcome expectations). Subsequently, the model supposes that
students with the goal of pursuing STEM, whom we call STEMaspiring students, will take
courses and make educational decisions that align with their goals.
Among various theorized sources of STEM selfefficacy, research documents that prior
achievement in math and science courses is amongst the biggest (Britner & Pajares, 2006; Lent,
Lopez, Bieschke 1991). Therefore, displaying mastery in STEM subjects, or having a STEM
orientation, is linked to STEM success through increased levels of STEM selfefficacy (Britner
& Pajares, 2006). Despite the relevance of STEMorientation in predicting future achievement in
STEM subjects, the SCCT does not explicitly factor in STEMorientation as a source of self
efficacy. Noting the relevance of STEMorientation in the SCCT model, Wang (2013b) included
high school math and science achievement indicators as predictors of STEM aspirations.
Although the SCCT acknowledges that supports and barriers influence career
development in general terms, the theory does not define what supports and barriers mean–
factors that are pertinent in the community college context. Moreover, the theory does not
adequately capture the continuous, cumulative nature of educational progress. Therefore, we also
draw on Wang’s (2015, 2017) model of STEM momentum for community college students
which specifies the possible barriers that community college students face and underscores the
temporal nature of students’ development of career aspirations. Wang’s model defines STEM
momentum as the level of achievement and academic effort expended during the early stages of
students’ college trajectory and evidence of progressing in STEM pathways at a good pace.
Based on this model, community colleges provide access to STEM careers by cultivating
students’ STEM momentum early in college (Wang, 2015).
71
At the same time, community college students may face countermomentum friction due
to several factors. Students may be overwhelmed by the range of possible curricular pathways,
be uninspired by decontextualized instruction, receive inadequate advising, experience financial
barriers, and/or find themselves in developmental courses (Wang, 2017). While the momentum
theory identifies the structural factors that promote or halt students’ momentum, it does not
specify the aspirational and motivational linkages related to STEM outcomes. Therefore, the
STEM momentum theory and the SCCT complement each other– the STEM momentum theory
details structural forces while the SCCT details motivational processes.
Both models allude to the importance of students’ race and gender identities in affecting
STEM aspiration, orientation, and participation, but these theories do not explicitly acknowledge
these characteristics. Research shows that few women and URMs major in STEM, and among
those who do, they are more likely to leave STEM pathways than their White, Asian, or male
peers (Chen & Soldner, 2013). Thus, personal characteristics like race and gender may be
important moderating variables that influence the link between selfefficacy, outcome
expectations, and goals during the experiences of math remediation.
The stereotype threat literature (Steele, 1997; Steele & Aronson, 1995) sheds some light
on why students with marginalized identities are less likely to pursue STEM fields. The idea
behind stereotype threat is that there exists a prevailing bias that women and URMs are not
“STEM material” in American society, and STEMoriented or STEMaspiring women and
URMs tend to underperform due to anxiety induced by these stereotypes. As such, placement in
remediation might especially exacerbate anxiety and feelings of inadequacy among female and
URM students, and subsequently impact STEM participation.
72
We draw from these three theories to ground our research design. Specifically, this study
posits that students developed their STEM goals based on their judgments of their ability to
perform well in STEM subjects (i.e., selfefficacy) and their belief that pursuing STEM is linked
to valued outcomes (i.e. outcome expectations). We note that students’ selfefficacy is based on
their cumulative exposure and achievement in math and science subjects from high school (i.e.,
STEMorientation). Taken together, SCCT specifies the motivational linkages and mechanisms
driving STEM participation, while momentum theory underscores that STEM participation
occurs within structural constraints and may be a byproduct of students’ cumulative effort in
math and science subjects. College math remediation may be one source of countermomentum
friction and, as such, a detriment to STEM participation. Given the literature on stereotype
vulnerabilities, particularly in STEM contexts, we pay attention to the dynamics of race and
gender in these relationships.
Math Remediation in STEM Pathways
The conceptual link between college math remediation and STEM outcomes in
community college should not be surprising since there are a number of studies linking math
performance to STEM participation and attainment. For example, studies show that students with
a strong foundational training in math are less likely to drop out, more likely to persist in college
(Adelman, 2006), and more likely to pursue STEM fields (Goodman, 2017). Some studies
looked specifically at the correlation between STEM coursestaking in high school and declaring
a STEM major in college (Gottfried & Bozick, 2016; Wang, 2013a, 2013b), and other studies
examined the relationship between college coursetaking, majoring in STEM fields, and
bachelor’s degree attainment in STEM (Wang, 2015). In each study, math was a key factor in
STEM participation.
73
Developmental math is a particular concern in STEM pathways since it is a gatekeeper
course for most community college students. Several studies, many of which employed
regression discontinuity designs, found that developmental math placement led to a decreased
likelihood of remaining enrolled in community college and virtually no effect on degree
attainment and labor market outcomes (Martorell & McFarlin, 2011; ScottClayton & Rodriguez,
2015). Other studies found that the impact of remediation can vary by institutional context
(Melguizo et al., 2016) and by students’ level of academic preparation (Boatman & Long, 2018;
ScottClayton & Rodriguez, 2015). Overall, a metaanalysis of RD studies showed that placing
into developmental education has a negative, statistically significant, and substantively large
effect on the probability of passing the collegelevel course in which remediation was needed,
college credits earned, and attainment (Valentine et al., 2017).
Although a majority of students begin their college journey in developmental math, there
lacks empirical evidence on whether developmental math serves as a diversion from pursuing
and persisting in STEM. Developmental math is an important juncture in STEM pathways as
approximately 65% of firsttime California community college enrollees start their college
trajectory in developmental math, and high proportion of these students are from minoritized
backgrounds (Rodriguez, Johnson, Mejia, & Brooks, 2017). In a recent study, Bahr et al. (2017)
found that California community college students in STEM pathways who started off in the
lowest nondevelopmental course (college algebra) were much less likely to advance to the next
level than those who began one level higher (trigonometry). Although that study provided a
useful curricular map of STEM pathways in community college, the authors excluded students
who placed in developmental math. Thus, the effect of math remediation in STEM pathways is
an underexplored area of research.
74
Math Assessment and Placement Policy in LUCCD
Prior to 2018, most colleges in California used a placement test to assign students to
developmental or collegelevel courses and supplemented the test score with points from various
additional measures, also known as “multiple measures” (Melguizo, Kosiewicz, Prather & Bos,
2014; Ngo & Kwon, 2015; Rodriguez et al., 2016). This meant that most students took the
placement test before enrolling in math and English. At the large urban community college
district (LUCCD) that is the context for our study, the four developmental math levels listed in
order are: arithmetic (AR), prealgebra (PA), elementary algebra (EA), and intermediate algebra
(IA). Transferlevel math (TLM) follows this and has IA as a prerequisite. Students could decide
to enroll in the level in which they placed, or any lower level, but were not allowed to enroll in
the level above unless they completed a process to challenge their results or retested at a later
time.
1
Data and Sample
The data used in this study are linked longitudinal transcript data obtained through
partnerships with LUCCD and a large urban school district (LUSD) in the same metropolitan
area. The LUCCD enrolls about 250,000 students each year, a significant portion of whom are
lowincome, and/or firstgeneration college students. We construct a unique studentlevel dataset
that includes high school as well as community college coursetaking information, placement test
score results, and demographic data for each student found in both systems.
We focus on the sample of LUSD students who enrolled in a LUCCD college within
three years of high school graduation during 20052008 and who were not concurrent high
school students. Therefore, we focus on a subset of all LUCCD community college students and
identify them as LUSDLUCCD students. We are able to track these students’ community
75
college outcomes through 2016, thus observing outcomes for 11 years for the first cohort and 8
years for the last cohort.
Our initial sample includes 30,209 LUSDLUCCD students who took the math placement
test but for our analyses we focus on 11,354 students who took the math assessment at one of
four LUCCD colleges – colleges A, B, C, and D – between 20052008. We chose these four
community colleges because they administered the same math placement test, allowing us to
pool students who attended different colleges, and before placement policy changes were
enacted. Among these 11,354 students, 2,425 placed in AR/PA, 5,113 placed in PA/EA, 4,574
placed in EA/IA, and 919 placed in IA/TLM.
Table 1 examines the generalizability of our analytical samples relative to all LUSD
LUCCD students. Specifically, Table 1 compares the demographic breakdown of all LUSD
LUCCD students with students from colleges ABCD as well as with students by levels of
developmental math placement. First, we observe that the characteristics of ABCD students are
similar to LUSDLUCCD students. Specifically, about half of the students are women, over 80%
of students are URMs, and a little over a third of the students intend to transfer.
However, the demographic breakdown of students around the cutoffs differ depending on
the math remediation level. For one, fewer URMs and women populated the IA/TLM levels than
the AR/PA levels. Also, perhaps unsurprisingly, more students who placed in IA/TLM displayed
STEM orientation and transfer intent than students who placed in AR/PA. Finally, more students
who placed in IA/TLM took the math assessment and enrolled in college compared to students
who placed in AR/PA (96% vs. 85%). These sample statistics suggest that students who placed
in upper levels displayed stronger academic preparation, were more interested in STEM, and
enrolled in college at higher rates than students who placed in lower levels.
76
Empirical Strategy
Regression Discontinuity
To establish a causal relationship between developmental assignment on STEM
outcomes, we would need to randomly assign students to placement levels. For instance, if we
randomly assigned students to intermediate algebra (treatment) or transferlevel math (control),
we can estimate the causal effect of treatment on outcomes. The argument is that students, by
virtue of random assignment, are equal in expectations at the outset; thus, any subsequent effects
are attributable to the treatment (Rubin, 1974). We would like to estimate the effect of treatment
on STEM participation for student i (Yi(1)) compared to the same student i’s outcomes if s/he
didn’t receive the treatment (Yi(0)). Because we do not observe both outcomes for student i we
estimate the average treatment effect (ATE): E[Y(1)Y(0)]=E[Y(1)]E[Y(0)]. Absent random
assignment, quasiexperimental methods such as a RD design can establish causality if treatment
assignment is determined by a rule that cannot be manipulated.
We use a RD in which assignment to treatment is determined by a predictor, or running
variable (Imbens & Lemieux, 2008; Lee & Lemieux, 2010). Specifically, if there is a policy or
some administrative decision that creates a discontinuity at some threshold of the predictor, those
who fall slightly below or slightly above the threshold are as good as randomly assigned. The
predictor in this study is the math placement test score. Students who just miss the placement
cutoff are typically assigned to varying levels of developmental math whereas students who
score higher than the cutoff are placed one level above. Because there are four cutscores that
determine placement into AR, PA, EA, IA, and TLM, we run four separate RD analyses for
students around the AR/PA, PA/EA, EA/IA, and IA/TLM cutscores.
77
Critical to the internal validity of this study design, students did not know the cutscores
that determine placement. Further, if administrators systematically thought that students who
scored just below the cutoff had higher math ability and exempted those students, the placement
exam score itself may be correlated with STEM participation. In another scenario, there would
be selection bias around the cutoff if students who were more motivated, better testtakers,
and/or were more meticulous were systematically clustered above the placement cutoff. These
scenarios are unlikely because students took a computeradaptive test that automatically adjusted
depending on how each student responded to previous questions. Because students did not know
the criteria that determined which math level they would place, there should not be any selection
around the threshold. In effect, students who just missed the cutoff and placed lower and those
who just exceeded the cutoff and placed above are similar in expectation.
Given the decentralized nature of the California’s community college system, each
college enacted different cutscores that determined where their students should be placed in the
developmental math sequence. Even among colleges that administered the same placement test,
there was a range of cutscores used to place students into the four developmental math levels
and transferlevel math. For example, students would need to receive a score of 60.5 or higher to
place in IA at one college while at another college, students would need a score of 80 or higher.
2
In order to pool together the students from four colleges, we standardize the four cut
scores to each have a common zero. To calculate a common zero, we subtract the college
specific mean from the college specific cutscore and divide by the college specific standard
deviation. This results in a common zero across all four colleges. Then, we subtract each campus
specific standardized placement test score from a common zero, thereby centering the pooled
placement test scores. We do this for all the cutscores that determine the five math placement
78
levels. Using this method, we are able to pool the colleges together and increase the sample size
and generalizability of this study.
We estimate a local linear regression separately for each of the four cutoffs using the
meansquared error optimal bandwidth recommended by Calonico, Cattaneo, and Titiunik (2014,
2017).
3
We find that at the AR/PA cutoff the optimal bandwidth ranges from 0.6 to 1 standard
deviation (SD). For sample consistency, we take the midpoint of these two options and estimate
around +/ 0.86 SD around the AR/PA cutoff. For the remaining three cutoffs (PA/EA, EA/IA,
IA/TLM), we examine bandwidths ranging from +/ 0.61 to 0.65 SD. Because observations that
are far away from the cutoff may impact parametric estimates, local linear regression estimator
relaxes the assumptions about the functional form away from the cutoff (Calonico, Cattaneo, &
Titiunik, 2014, 2017; Imbens & Kalyanaraman, 2012).
The RD model is presented in the following equation:
!
"#$
= '
(
(*+,.)+'
1
(2+32)+'
4
(*+,.∗2+32)+6
$
+7
#
+8
"#$
where !
"#$
refers to developmental math progression and STEM participation for student i in
semester t at college c. '
(
is the effect of placing one level below into AR, PA, EA, or IA on
outcomes. '
1
captures the relationship between the pooled running variable and the outcome of
interest. '
4
allows the regression slope to differ to the left and the right of the treatment
threshold. Next, we include college fixed effects, 6
$
, to account for variation among the four
colleges (e.g., collegespecific policy, differential sorting to colleges). Finally, because the
cohort of students who take the math placement test in the spring term may differ from the
cohort of students who take the test in the fall, we include assessment term fixed effects, 7
#
.
Figure 1 shows that the percentage of students who complied with their placement levels
across the four centered pooled placement test scores in standard deviation units. Specifically,
79
Figure 1 shows that students who placed in lower levels of developmental math were less likely
to enroll in these courses relative to students who directly placed in upper levels. The fraction of
students who enrolled in upperlevel math sharply increased as scores pass the threshold,
indicating the appropriateness of a sharp RD.
RD Validity
We check to see that students’ placement status is quasirandomly assigned close to the
cutoff. If we observed a discontinuity, we would be worried that students near the threshold
behaved differently in unobserved ways. First, we estimate whether the density of the running
variable is smooth using the kernel density estimator along four pooled cutscores (Cattaneo,
Jansson, & Ma, 2018). Similarly, Figure 2 estimates the McCrary (2008) density test and shows
that there is no visible jump around the threshold along all four placement cutoffs. None of the
estimated discontinuities are statistically significant.
In addition, Table 2 displays the comparison of sample means across a range of baseline
characteristics along the four cutoffs. There are noticeable differences in means when comparing
students who placed below to students who placed above irrespective of the placement level.
First, more female and URM students populated lower placement levels relative to upper levels.
Second, more STEMoriented and STEMaspiring students populated upper levels. Third,
students who placed above enrolled at a higher rate than those who missed the cutoff and placed
one level below except for those around the AR/PA cutoff. We test for continuity in these
variables across the RD thresholds by substituting each variable as the outcome in the RD
equation described above. At a +/0.75 SD unit bandwidth, we generally do not find meaningful
differences around the cutoffs. Overall, students who placed lower, on average, were similar with
80
respect to race, gender, STEM orientation, and STEM aspiration as students who placed above at
each cutoff.
Subgroup Analysis
There are reasons to hypothesize that remediation may affect women and URMs
differently when examining STEM participation. Research shows that female and URM students
are more susceptible to attriting from STEM pathways than their nonURM and male peers
(Chen & Soldner, 2013). Also, missing the cutoff and placing in lower levels of developmental
math may inadvertently send a signal to women and URMs that they are not equipped to pursue
STEM. Therefore, math remediation may especially discourage women and URMs from
pursuing and persisting in STEM fields.
In contrast, we hypothesize that STEMaspiring and STEMoriented students may take
more STEM courses relative to their peers despite lower placement. These students developed
STEM momentum in high school by taking advanced math and science courses or started college
with a clear interest in STEM. We surmise that STEMoriented and STEMaspiring students may
be more likely to persist in STEM pathways than their peers without an interest or background in
STEM. The equation below shows how we assess subgroup differences in STEM participation.
!
"#$
= '
(
(*+,.)+'
1
(39*:;9<)+'
4
(*+,.∗39*:;9<)+'
=
(2+32)+'
>
(2+32∗
*+,.)+'
?
(39*:;9<∗2+32)+'
@
(*+,.∗39*:;9<∗2+32)+6
$
+7
#
+8
"#$
(2)
where, as before, !
"#$
refers to developmental math progression and STEM participation for
student i in semester t at college c. We interact each of the main terms in (1) with a dichotomous
indicator we derived for each subgroup (i.e., women, URM, STEMoriented, or STEMaspiring).
'
4
captures whether the effect of lower math placement on outcomes differs by subgroup.
Similar to equation (1), we include college fixed effects, 6
$
and assessment term fixed effects, 7
#
.
81
Our subgroup analyses on STEMaspiring and STEMoriented students are not causal.
We can only identify STEMoriented and STEMaspiring students among those who enrolled in
community college as opposed to all students who took the math placement test. In the data
available, we do not observe students’ high school records and initial major if they did not
officially enroll but have available all students’ demographic and math placement information.
Therefore, unlike our women and URMs subgroup analyses, our analyses pertaining to STEM
orientation and STEM aspiration are not causal estimates as the identification of these students
hinges on whether they ever enrolled.
Outcomes
The momentum literature underscores the importance of initial academic course load and
effort expended in pursuing academic outcomes (Attwell, Hiel, & Reisel, 2012; Wang, 2015,
2017). Drawing from this definition, we examine early progression through the developmental
math sequence. Specifically, we examine the following indicators of early math progression: (1)
taking elementary algebra, the math requirement for an Associate’s degree at the time; (2) taking
intermediate algebra, a common prerequisite for advanced math and science courses; and (3)
taking transferlevel math, a course required for transfer. Next we examine shortterm STEM
participation: (4) Time in quarters before taking first STEM course; (5) total transferable STEM
credits attempted in three years; and (6) total transferable STEM credits completed in three
years.
In addition, we examine the following measures of STEM participation in the longrun
and they are: (7) the number of transferable STEM credits attempted and (8) completed overall;
and (9) attempting at least 18 transferable STEM credits. We examine whether students
attempted at least 18 transferable STEM credits because students who aim to transfer as a junior
82
with a STEM major need at least 18 semester STEM credits. Notably, the STEM participation
outcomes are longterm effects of math placement as we observe student outcomes up to 11
years since initial enrollment.
4
Because the data allow us to observe students’ outcomes long
term, we interpret our results of math placement on longterm STEM participation as the overall
likelihood of participating in STEM coursework.
5
Examining STEM participation rather than summative measures like degree attainment
and/or transfer rates is especially informative in the community college setting. Several studies
document gains in the labor market from taking just a few community college courses (Bahr,
2014; Dadgar & Trimble, 2015; Hodara & Xu, 2016). In particular, accumulating STEM credits
is a proxy for learning relevant skills for success in the knowledge economy and warrants
attention irrespective of whether students graduate with a STEM degree. Indeed, several reports
underscore the growing importance of a STEMfocused education even if students decide not to
work in a STEM field (National Science Board, 2015, 2018). By examining markers that indicate
steady progress in STEM pathways, this study also stresses that obtaining a STEMfocused
college education is indicative of academic success.
NonEnrollment
Not all students who took the math placement test subsequently enrolled in a college
course within three years of their high school graduation. For the nonenrollees, we do not
observe their outcomes. To explore this concern, we first examine to see whether placement
affects students’ decision to enroll in college. Figure 2, below indicates that remedial assignment
did not affect students’ college enrollment rate at the margin. Indeed, recent studies also suggest
that developmental placement does not discourage enrollment in community college (Martorell,
McFarlin, & Xue, 2014).
83
In order to preserve our initial causal identification, we recode these nonenrollee’s
outcomes from missing to zeros (ScottClayton & Rodriguez, 2015). For example, the zero in
one of our outcomes, ever enrolling in a transferlevel math course, includes students who
enrolled in college but never took a transferlevel math course, those who dropped out, those
who withdrew, or those who delayed their enrollment altogether beyond the timeframe of our
data. The benefit to using this approach is that we are able to preserve our initial identification
and estimate a causal intent to treat effect. The downside to this approach is that our estimate
may be downward biased. We elaborate on the potential selection bias associated with
differential takeup of remedial assignment and how this may affect our estimates in the
sensitivity section.
Results
We start by inspecting graphical displays of the discontinuities on the outcomes across all
four cutoffs. We visually explore the effect of lower placement on early math progression and
STEM participation. We first create the mean value of each dependent variable within 0.250.30
standard deviation units as the prespecified bin and fit a separate linear regression line at each
side of the normalized value of zero. Upon examining all of the graphs, we find the most visible
discontinuities around the IA/TLM cutoffs. Therefore, we display the scatter plots of the
IA/TLM cutoff here and include the scatter plots of the remaining math levels in Appendix
Figures A.1A.3. Figure 4, below, shows the relationship between placing lower into IA or above
into TLM on math progression and STEM outcomes.
By visual inspection, we see that students who placed in TLM attempted their first
transferable STEM course faster. Also, placing above appears to be associated with attempting
more transferable STEM courses in the shortterm and completing more transferable STEM
84
courses in the longterm. Finally, it appears that more students who placed in TLM attempted at
least 18 STEM credits, a requirement for transfer to a fouryear institution. Below we estimate
the magnitude of the jumps that we see in Figure 4.
Main Estimation Results
In Table 3 we estimate the magnitude of the discontinuities that we visually observe in
Figure 3. Examining the effect of lower placement on students’ progression through the
developmental math sequence, we see that lower placement helped those who were the least
prepared in math. Specifically, students who placed in AR were eight percentage points more
likely to have ever taken EA than students who placed in PA. Therefore, the AR/PA results
indicate that more students at the margin successfully progressed to EA due to lower placement.
Next, we observe a null to negative effect from lower placement when examining
developmental math cutoffs like PA/EA and EA/IA. We interpret both a null and a negative
effect to mean that students at the margin who placed lower may perform just as well or better if
placed higher. Examining the PA/EA cutoff, we find that students who placed below into PA
were just as likely to attempt upperlevel math courses as students who placed directly into EA.
Also, examining the EA/IA cutoff, we find fewer students who placed lower into EA took
prerequisite math courses like IA relative to students who placed directly into IA. Specifically,
placing into EA resulted in a 14 percentage points decreased likelihood of ever taking IA, a
common prerequisite for advanced STEM courses.
Finally, the cost from lower math placement is most evident among students around the
IA/TLM cutoff. Specifically, students who placed in IA were 19 percentage points less likely to
have ever taken TLM, 17 percentage points less likely to have attempted at least 18 transferable
STEM units, and on average, attempted 9.5 fewer transferable STEM units than students who
85
placed directly into TLM. These estimates corroborate the discontinuity we observe in Figure 3.
In fact, the negative coefficients suggest that placing lower into IA hindered students at the
margin from participating in STEM.
In summary, the results are mixed depending on the placement level, with positive effects
on early math progression among those who placed in the lowest end of the math sequence
(AR/PA) and clear negative effects among those who placed in the highest end of the math
sequence (IA/TLM). Below, we present interaction results by subgroups.
Subgroup Results: Women and URMs
Table 4 displays the differential effect of developmental math placement for women
relative to men across all four cutoffs. The results differ depending on the developmental math
level. Examining the lowest end of the developmental math sequence, AR/PA, the effect of
lower placement did not differ between men and women with respect to both math progression
and STEM participation. In contrast, at the PA/EA cutoff, we find evidence that lower placement
helped increase women’s STEM participation relative to men. Specifically, Table 4 indicates that
women who placed lower into PA attempted 6.7 (4.6+11.4) more transferable STEM credits
relative to women who placed higher into EA. In addition, women who placed lower into PA
completed five more transferable STEM credits relative to men who placed higher.
While we find evidence that lower placement may be beneficial when examining women
and men who placed in PA, we do not find evidence that they achieved differently at the upper
end of the math sequence. Specifically, women and men who placed lower into EA were just as
likely to participate in STEM as those who placed in IA. Similarly, students who placed in IA
were just as likely to attempt upperlevel math and STEM courses as those placed in TLM. Thus,
86
examining the upper end of the developmental math sequence, lower placement similarly
hindered students in early math progression and STEM participation.
Next, Table 5 displays the differential effect of developmental math placement for URMs
relative to their White and Asian peers across all four cutoffs. We find significant positive
interaction effects on math progression when examining the lowest developmental math levels,
AR/PA. Specifically, URM students who placed in AR were 14 percentage points (.39 + .53)
more likely to take EA but no more likely to take IA or TLM relative to URM students who
placed in PA. Despite the positive effect on early math progression, lower math placement did
not ultimately increase STEM participation in the short and longrun relative to URMs who
placed above.
Examining the remaining math levels, lower placement at each cutoff did not help URMs
successfully progress in math nor did it increase STEM participation. In fact, for URMs around
the EA/IA cutoff, students who placed lower into EA were eight percentage points less likely to
attempt 18 transferable STEM credits. Moreover, examining students around the IA/TLM cutoff,
URMs who placed in IA were 25 percentage points less likely to take transferlevel math than
URMs who placed directly in TLM.
Taken together, we find patterns consistent with the main results: developmental math
appears to be beneficial for students deemed the most academically underprepared and placed at
the lower end of the math sequence (AR/PA and PA/EA), particularly women and URM
students. We find evidence that women and URMs who placed lower were more likely to
attempt upperlevel math or transferable STEM courses relative to their samedemographic peers
placed above. At the upper end of the sequence (EA/IA and IA/TLM), we find evidence that
87
lower placement was a particular deterrent for URMs in attempting transferlevel math or
attempting transferable STEM courses.
Subgroup Results: STEM Orientation and Aspiration
Table 6 shows the differential effect of developmental math placement for STEM
oriented students – those who took advanced math and science courses in high school – relative
to their nonSTEMoriented peers across all four cutoffs. Among those who were least prepared
in math (i.e., those around AR/PA), we do not find evidence that lower placement deterred
STEMoriented students any more than their nonSTEMoriented counterparts or those placed in
the higherlevel courses. However, contrary to the results for women and URM students present
in the previous section, we observe a penalty for STEMoriented students around the PA/EA
cutoff. STEMoriented students who placed in PA were 18 percentage points less likely to
attempt EA, a math course necessary for an Associate’s degree. Examining STEMoriented
students around the EA/IA and IA/TLM cutoffs, we do not find evidence that lower placement
increased early math progression and STEM participation.
Table 7 shows the differential effect of developmental math placement for STEM
aspiring students across all four cutoffs. Notably, the significant positive coefficients for STEM
aspiration throughout Table 7 indicate that STEMaspiring students had higher average STEM
attainment than nonSTEMaspiring students and that they took courses aligning with their
educational goals. In addition, STEMaspiring students placed in PA versus EA were less likely
to be timedelayed, by about 3 quarters, before enrolling in a STEM course, perhaps
underscoring their motivation and interest in STEM fields.
Nevertheless, we also find evidence that lowerlevel math placement at the PA/EA cutoff
differentially affected STEMaspiring students’ persistence in the STEM pathway. STEM
88
aspiring students who placed lower into PA were significantly less likely to attempt upperlevel
math courses than their peers in EA. In sum, lower placement into AR or PA was more of a
deterrent in early math progression for STEMaspiring and STEMoriented students than their
peers who placed above.
Examining the interaction effect among those at the upper end of the sequence (EA/IA
and IA/TLM), we find no differences between STEMaspiring students and nonSTEM aspiring
students. The lack of significant interaction effects indicates that STEMaspiration did not
mitigate against the negative effects of remedial placement any more than those without an intent
to major in STEM.
Sensitivity Analyses
In this section we address the sensitivity of our analyses from replacing zeros for non
enrollment. It may be that any observed effect – or the lack thereof – on STEM outcomes is not
the result of remediation, but rather, due to student's decision to not enroll in STEM courses.
Similar to previous RD analyses, we recoded missing outcomes to zeros (see for example,
Martorell & McFarlin, 2011; ScottClayton & Rodriguez, 2015). However, this approach may
bias our results if developmental math placement affects the likelihood that the outcome is
missing. As shown in Table 2, most of the nonenrollees are concentrated among those at the
lower end of the developmental math sequence. There are fewer nonenrollees around the
IA/TLM cutoff compared to those around the AR/PA cutoff. By recoding the missing outcomes
to zero, we assume that the average outcomes of these students on STEM participation is zero.
6
Recoding missing outcomes to zero is essentially the worstcase scenario as it is highly
improbable that all of the nonenrollees would have performed poorly (Lee, 2009).
89
Given that we “impute” zeros in our main analyses, our estimates may well be downward
biased. There are two scenarios in which we may be presenting downward biased estimates. The
first scenario is that we may have underestimated the benefits to lower placement. Specifically,
we observe a positive effect from lower placement among those placed either in AR or PA.
Therefore, the true benefits to lower placement among those around the AR/PA cutoff may be
larger than what we present. The second scenario is that we may have underestimated the costs
to lower placement. We interpret null to negative results as both evidence that lower placement
diverted students from upperlevel math courses and from STEM pathways. Put differently, a
null effect suggests that remediation did not sufficiently develop students’ skills to affect their
likelihood of STEM participation.
We redo all of our analyses conditioning on the sample of enrollees. By doing so, we
assume that remediation does not affect the likelihood of dropping out. Table 8 below shows the
results without imputing zeros for missing outcomes. Conditioning on the sample of enrollees,
we find statistically insignificant relationships similar to the main results.
For the coefficients that are statistically significant, the direction and magnitude
correspond to our main results. For instance, the negative effects on STEM participation for
students at the IA/TLM cutoff are consistent. One notable difference between the main results
and Table 8 is the relationship between lower placement into AR and ever taking EA. In the
main table, we report that lower placement into AR led to eight percentage points increased
likelihood of ever taking EA. However, Table 8 indicates no statistically significant relationship.
Thus, the discrepancy places an upper bound on the positive effect found for students around the
AR/PA cutoff.
90
We also find that the positive interaction results that we report for women and URMs are
similar when conditioning on enrollees. Despite the fact that nonenrollees who placed lower
were more likely to be women and URMs and subsequently received a zero as their outcome the
results remained qualitatively similar. In effect, the gap in early math progression and STEM
participation between URMs and women relative to men and nonURMs remained comparable
examining all students as well as only enrollees. The full table of results can be found in the
Appendix Tables A.1 and A.2. As mentioned previously, the results for STEMoriented and
STEMaspiring students already conditioned on enrollment.
Finally, in Appendix Table A.3 to A.5, we examine how sensitive our results are to
different choices of bandwidth. Similar to other scholars (e.g., Castleman, Long, & Mabel,
2017), the main analysis is based on a midpoint from a range of bandwidths specified after
estimating developmental math progression and STEM participation outcomes. Here, we re
specify the meansquared error optimal bandwidth to the minimum and the maximum of the
bandwidth (ranging from 0.47 to 1.1) across all four cutoffs. In Appendix Tables A.3 to A.5, we
examine the sensitivity of the results by specifying the minimum and the maximum of the
bandwidth range. The direction and magnitude of the estimations are robust to different
specifications of the bandwidth. We present the most pertinent robustness results in the
appendix, and the rest are available upon request.
Limitations
The aforementioned bandwidth analyses help to address one key limitation of RD
estimates  they only apply to a narrow bandwidth around the treatment cutoff. Even though
consistency across bandwidths suggests that the results can be applied to more students around
the placement cutoffs, the results nevertheless only apply to students in these four colleges
91
during the time period of the study, and generalization should not be made to other contexts.
Thus, we estimate the intent to treat effect of the developmental assignment, generalizable to
those who scored near the cutoff. From a policy perspective, students who are on the margin of
being remediated are the student population who are most likely to be impacted by different
policy schemes as opposed to those who are farther away from the cutoffs (i.e., more
academically prepared or academically underprepared).
In addition, the STEM aspiration and orientation results are not causal. We could not
generate the high school STEM profiles of those students who took math placement tests but did
not subsequently enroll in a course. Therefore, future research should confirm the results we
found, particularly for STEMaspiring students.
Discussion
Bolstering the STEM pipeline, particularly for underrepresented students, has been on the
national education policy agenda for the last few decades. Community colleges are seen as a
linchpin in this effort to increase the number of diverse STEM graduates, but they are also faced
with the reality that many community college students are referred to developmental math. While
some regard developmental education as a way to prepare students for collegelevel courses
(Bettinger & Long, 2009), others show that it is a source of discouragement or diversion from
college progress (Martorell & McFarlin, 2011; ScottClayton & Rodriguez, 2015). In this study,
we examined whether structures like developmental education, which are supposed to equip
students to be successful in collegelevel STEM courses, precluded community colleges from
developing diverse students’ STEM talents. With access to student records and college
applications, we closely looked at those for whom experiences of math remediation may be most
consequential with respect to STEM participation – women, URMs, students who may be
92
STEMoriented, and those who have STEM aspiration. This study, therefore, provides new
evidence on the ongoing debate regarding the merits of developmental education.
The results show that lower math placement may be marginally beneficial for students
who placed in lowest levels of math (i.e., arithmetic and prealgebra) and this is especially the
case for women and URMs. These students were more likely to take math prerequisites like
elementary algebra than their higherplaced peers. Despite the potential benefits to early math
progression, we generally do not find evidence that lower placement ushered more women and
URMs into STEM pathways.
Aligning with what the theory suggests, STEMaspiring students on average attempted
more transferable STEM courses than their nonSTEMaspiring peers. Therefore, we found
evidence that STEMaspiring students made educational decisions that align with their STEM
related goals. However, we found that STEMaspiring and STEMoriented students were
disproportionately less likely to attempt upperlevel math courses due to lower placement than
their peers who did not express interest in STEM. Like research showing that feedback about
academic ability affects dropout decisions (Stinebrickner & Stinebrickner, 2012), it is possible
that feedback about STEM potential possibilities, here in the form of a math course placement,
might have deterred students from pursuing STEM fields. These results suggest that community
colleges should identify STEMoriented and STEMaspiring students (e.g., on community
college enrollment forms, high school records) and provide support early on in college as a
means to retaining them in the STEM pathway.
For students in the upper end of the developmental math sequence (i.e., elementary
algebra and above), there were no positive effects and, in some cases, a clear detriment to math
remediation. The cost to lower placement with respect to STEM participation was most evident
93
among those at the margin of intermediate algebra and transferlevel math. Students who just
missed the transferlevel math cutoff were significantly less likely to obtain a STEMfocused
education. Specifically, students who placed in remediation attempted nearly ten fewer
transferable STEM credits than students who directly placed in transferlevel math. Lower
placement into intermediate algebra similarly hindered female, URMs, STEMoriented, and
STEMaspiring students as their male, nonURM, nonSTEMoriented and nonSTEMaspiring
peers.
Importantly, the differences in STEM participation at the IA/TLM cutoff were observed
in both the short and longrun. Students placed in IA completed about 1.3 less STEM credits
after 3 years, but this grew to 5.9 units after 10 years. For these students, developmental math
was a structural hindrance to early math progression and STEM participation. That these students
did not “catch up” to students who had access to higherlevel math suggests that early STEM
momentum (Wang, 2015) matters for community college STEM participation, and that the
effects of lowerlevel math placement persist in the longer term.
The findings of the study show that developmental math does introduce a structural
source of countermomentum friction in early math progression (Wang, 2015), particularly for
those students at the margin of transferlevel math. By not attempting math prerequisites, these
students were significantly less likely to earn transferable STEM credits. This supports the
findings of Wang (2015) that community colleges should help cultivate diverse students’ early
STEM momentum in order to usher more students into STEM pathways.
Further, the results imply that eliminating developmental education in its entirety may
prevent academically underprepared students from receiving additional support at the detriment
to their academic success. In other words, providing students who are the least academically
94
prepared in math with targeted math support may help students, particularly women and URMs,
learn relevant math and STEM skills for success in the knowledge economy. At the same time,
the results also suggest that the current multitiered developmental math is too lengthy and is
generally ineffective for most students. Moreover, taking multiple developmental math courses is
both timeintensive and costly for community college students and these costs may offset any
possible benefits to a multitiered developmental sequence. As colleges implement policies to
tighten their developmental math offerings, this study underscores the need to provide targeted
support for community college students who are the least prepared in math while removing
barriers for the rest of the students.
Conclusion
Improving STEM participation in the nation’s community colleges, a system that is more
likely to serve students who are underrepresented in STEM fields, remains a national education
policy priority. Although some benefits were found for certain groups of students, overall, the
study showed that developmental math may produce frictions in the STEM pathway, even for
students with expressed STEM aspirations. Given initiatives across the nation to reform
developmental education, it is important to consider how changes to policy and practice may
impact both general community college outcomes and the promise of the community college
STEM pathway.
95
Endnotes
1
10% (n= 1,173) of students retested of which 29% (n=338) retested into a higher math level. Therefore, only
3% of the students who retested placed in a higher math level than their initial math course. Most students who
retested ended up placing into lower levels. Retesters have to retest if they don’t enroll within a semester or
within a year.
2
In recent years, California passed key legislation, Assembly Bill 705, that mandates the use of high school
measures in lieu of placement tests unless colleges provide evidence that the placement test is a more effective
instrument.
3
We also reestimated our results using Imbens and Kalyanaraman’s (2012) bandwidths and the results were
qualitatively similar.
4
In our sample of students, the average number of years enrolled is five with very few students (<5%) enrolled
by year 11.
5
We acknowledge that completion hinges on whether students attempt the course. Therefore, there is inherent
selection bias in examining completion outcomes because not all students may attempt and complete the
course. In the main analysis we code the outcome of students who did not attempt the course as zero to
preserve our initial causal identification strategy but remove students who did not attempt the course in the
sensitivity analysis.
6
The percentage of those in AR PA EA IA that are missing and that we recoded to zero are as follows: 15% of
students who placed in AR, 13 % of students who placed in PA, 9% of students who placed in EA, 7% of
students who placed in IA, and 2 % of students who placed in TLM.
96
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Tables
Table 1
Demographic Breakdown of LUCCD Students, 20052008
All LUSD
LUCCD
students
who took
the math
test
VMCS
students
with valid
math cut
scores
VMCS
students
around the
AR/PA
cutoff
VMCS
students
around the
PA/EA
cutoff
VMCS
students
around the
EA/IA cut
off
VMCS
students
around the
IA/TLM
cutoff
Female 53% 53% 56% 54% 50% 47%
URM 80% 81% 86% 86% 77% 55%
STEM Aspiration 16% 14% 13% 11% 17% 25%
STEM
Orientation 24% 25% 7% 20% 35% 59%
HS Diploma 94% 93% 90% 94% 95% 95%
Transfer Intent 38% 36% 29% 34% 40% 48%
US Citizen 80% 77% 81% 76% 77% 68%
Assessed and
Enrolled 89% 89% 85% 88% 92% 96%
30209 11354 2425 5113 4574 919
Note. LUSD = Large Urban School District; LUCCD = Large Urban Community College District; ABCD = students
attending one of the four colleges within this LUCCD; AR=arithmetic; PA=prealgebra; EA=elementary algebra;
IA=intermediate algebra; TLM=transferlevel math. The numbers only include students who were enrolled between
20052008 and who were not concurrent high school students.
105
Table 2
Test of Baseline Equivalence around Levels of Cutoff, +/ 0.75 SD Bandwidth
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. The coefficient estimates the likelihood of
observing a significant treatment effect across the list of demographic characteristics around +/0.75 SD bandwidth.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
AR PA RD Coeff. PA EA RD Coeff. EA IA RD Coeff. IA TLM RD Coeff.
Female 0.57 0.46 0.17 0.55 0.51 0.01 0.52 0.47 0.05 0.48 0.46 0.01
URM 0.86 0.84 0.03 0.89 0.81 0.03 0.82 0.70 0.03 0.61 0.51 0.05
STEM Aspiration 0.13 0.14 0.04 0.09 0.15 0.03 0.15 0.20 0.06+ 0.24 0.26 0.05
STEM Orientation 0.07 0.10 0.05 0.15 0.31 0.00 0.28 0.44 0.06 0.57 0.60 0.06
HS Diploma 0.92 0.82 0.08 0.93 0.95 0.01 0.95 0.95 0.02 0.95 0.94 0.04
Transfer Intent 0.29 0.31 0.02 0.33 0.36 0.03 0.38 0.43 0.01 0.43 0.51 0.02
US Citizen 0.81 0.80 0.04 0.78 0.71 0.04 0.78 0.76 0.02 0.64 0.71 0.06
Assessed and Enrolled 0.85 0.85 0.09 0.86 0.90 0.02 0.91 0.93 0.00 0.93 0.98 0.03
AR/PA CutOff PA/EA CutOff EA/IA CutOff IA/TLM CutOff
106
Table 3
The Effects of Developmental Math Placement on Math Progression and STEM Participation
AR/PA PA/EA EA/IA IA/TLM
Bandwidth +/ 0.86 Bandwidth +/ 0.65 Bandwidth +/ 0.67 Bandwidth +/ 0.61
Dependent Variable
RD
Coeff. SE
RD
Coeff. SE
RD
Coeff. SE
RD
Coeff. SE
Math Progression
Ever took EA 0.082* (0.012) 0.022 (0.036)
Ever took IA 0.049 (0.031) 0.051 (0.076) 0.143* (0.037)
Ever took TLM 0.024 (0.048) 0.044 (0.084) 0.055 (0.025) 0.189+ (0.023)
ShortTerm STEM Participation
Time in qtrs before taking first STEM course 1.104 (0.694) 0.104 (0.563) 0.039 (0.429) 0.122 (0.494)
Total transferable STEM credits attempted, 3
yrs 0.696 (0.324) 0.963* (0.108) 1.846+ (0.709) 2.595+ (0.250)
Total transferable STEM credits completed, 3
yrs 0.279 (0.403) 0.725* (0.112) 1.551* (0.328) 1.276* (0.053)
LongTerm STEM Participation
Total transferable STEM credits attempted 0.424 (1.401) 1.396 (1.241) 2.818 (1.435) 9.455* (0.662)
Total transferable STEM credits completed 0.699 (0.981) 1.175 (0.847) 2.711+ (0.971) 5.878* (0.309)
Took at least 18 transferable STEM credits 0.084 (0.037) 0.045 (0.017) 0.055 (0.035) 0.172+ (0.020)
N 646 1672 1745 408
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. The RD coefficient estimates a local linear
regression with campus and term fixed effects. The coefficient estimates the likelihood of observing a significant treatment effect on outcomes around the
specified bandwidth. Outcomes observed up to 2016 for 20052008 entering cohorts. All estimations include campus and term fixed effects. Standard errors are
in parentheses.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
107
Table 4
Differential Effect of Developmental Math Placement on Math Progression and STEM Participation for Female Students
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
Ever took
EA
Ever took
IA
Ever took
TLM
Time in
qtrs
before
taking
first
STEM
course
Total
transferable
STEM
units
attempted,
3 yrs
Total
transferable
STEM
units
completed,
3 yrs
Number of
transferable
STEM
units
attempted
Number of
transferable
STEM
units
completed
Took at
least 18
transferable
STEM
units
Placed into AR 0.023 0.065 0.081* 0.968+ 0.660+ 0.193 1.157 1.686 0.043
(0.050) (0.027) (0.012) (0.329) (0.159) (0.404) (1.267) (1.227) (0.054)
Female 0.087 0.114 0.118+ 0.409 0.197 0.283 0.871 1.178 0.025
(0.071) (0.043) (0.039) (0.579) (0.811) (0.751) (4.349) (3.151) (0.134)
Placed into AR x Female 0.221 0.242 0.227 0.355 0.001 0.921+ 1.509 2.052 0.086
(0.132) (0.114) (0.121) (1.401) (0.430) (0.226) (2.950) (2.982) (0.097)
Rsquared 0.049 0.046 0.035 0.026 0.015 0.031 0.031 0.040 0.031
Observations 646 646 646 646 646 646 646 646 646
Placed into PA 0.061 0.025 0.026 0.171 0.594 0.545 4.645+ 3.218* 0.110
(0.022) (0.070) (0.082) (1.117) (0.557) (0.738) (1.203) (0.493) (0.056)
Female 0.050 0.015 0.013 0.742 1.361 0.912 7.442+ 4.646* 0.195**
(0.035) (0.039) (0.044) (0.800) (0.625) (0.586) (1.859) (0.761) (0.012)
Placed into PA x Female 0.076+ 0.052 0.039 0.101 2.918+ 2.394 11.435*** 8.313* 0.290+
(0.025) (0.043) (0.031) (1.028) (0.806) (1.050) (0.202) (0.864) (0.087)
Rsquared 0.048 0.029 0.022 0.012 0.033 0.032 0.036 0.037 0.034
Observations 1672 1672 1672 1672 1672 1672 1672 1672 1672
Placed into EA
0.103+ 0.021 0.256 0.722 0.845 0.785 1.729 0.032
(0.043) (0.052) (0.728) (1.348) (0.709) (3.254) (2.487) (0.086)
108
Female
0.040 0.064 1.223* 1.722 1.204 2.490 1.158 0.109
(0.046) (0.039) (0.277) (1.698) (1.421) (4.183) (3.576) (0.122)
Placed into EA x Female
0.077 0.151 0.539 2.221 1.360 3.950 1.788 0.172
(0.052) (0.065) (0.997) (1.181) (0.668) (3.548) (3.060) (0.116)
Rsquared
0.046 0.024 0.012 0.023 0.025 0.025 0.030 0.022
Observations 1745 1745 1745 1745 1745 1745 1745 1745
Placed into IA
0.083+ 0.891 2.957 2.029 8.948 7.065 0.076
(0.007) (0.986) (2.966) (2.836) (3.165) (2.883) (0.037)
Female
0.075* 0.303* 2.613 0.989 8.751 2.900 0.314*
(0.002) (0.017) (1.318) (1.134) (7.163) (6.269) (0.023)
Placed into IA x Female
0.226 1.408 0.981 1.747 0.326 2.961 0.190
(0.055) (1.140) (7.540) (6.766) (5.895) (5.902) (0.039)
Rsquared
0.092 0.060 0.046 0.047 0.090 0.089 0.083
Observations 408 408 408 408 408 408 408
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. All estimations include campus and term
fixed effects. Standard errors are in parentheses.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
109
Table 5
Differential Effect of Developmental Math Placement on Math Progression and STEM Participation for URM Students
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
Ever took
EA
Ever took
IA
Ever took
TLM
Time in
qtrs
before
taking
first
STEM
course
Total
transferable
STEM
units
attempted,
3 yrs
Total
transferable
STEM
units
completed,
3 yrs
Number of
transferable
STEM
units
attempted
Number of
transferable
STEM
units
completed
Took at
least 18
transferable
STEM
units
Placed into AR 0.391* 0.318 0.339 0.519 0.182 0.749+ 4.521+ 3.716** 0.341**
(0.060) (0.132) (0.127) (0.292) (0.278) (0.253) (1.289) (0.348) (0.011)
URM 0.377* 0.277* 0.287+ 0.807 1.767 2.286 5.568 4.609 0.255*
(0.046) (0.064) (0.072) (0.370) (1.549) (1.300) (3.036) (2.255) (0.042)
Placed into AR x URM 0.532** 0.411 0.408 0.645 1.035 1.115* 4.595+ 3.314* 0.288**
(0.051) (0.150) (0.166) (1.108) (0.500) (0.234) (1.143) (0.682) (0.010)
Rsquared 0.057 0.046 0.036 0.025 0.023 0.027 0.033 0.030 0.037
Observations 646 646 646 646 646 646 646 646 646
Placed into PA 0.100* 0.067 0.077 0.705 1.759 1.302 1.358 0.218 0.054
(0.017) (0.118) (0.120) (1.833) (1.645) (1.444) (4.171) (4.334) (0.024)
URM 0.024 0.054 0.069 0.898 2.701 2.115 7.336+ 5.150 0.202**
(0.072) (0.071) (0.079) (1.746) (1.799) (1.654) (2.509) (2.590) (0.015)
Placed into PA x URM 0.089 0.137 0.139+ 0.690 3.163 2.354 3.322 1.683 0.117+
(0.040) (0.049) (0.044) (1.497) (1.980) (1.795) (3.890) (4.605) (0.038)
Rsquared 0.041 0.022 0.018 0.010 0.037 0.039 0.040 0.045 0.039
Observations 1672 1672 1672 1672 1672 1672 1672 1672 1672
Placed into EA
0.010 0.032 0.278 0.076 0.001 1.123 0.190 0.049
(0.093) (0.081) (0.249) (0.795) (0.576) (2.122) (1.675) (0.034)
URM
0.086 0.003 0.545 1.701+ 1.515 1.284 0.278 0.021
110
(0.072) (0.035) (0.713) (0.717) (0.816) (2.367) (2.107) (0.045)
Placed into EA x URM
0.174 0.114 0.412 2.494 2.012+ 5.154 3.813 0.136*
(0.146) (0.108) (0.600) (1.377) (0.807) (4.125) (3.115) (0.026)
Rsquared
0.046 0.025 0.010 0.022 0.023 0.028 0.030 0.023
Observations 1745 1745 1745 1745 1745 1745 1745 1745
Placed into IA
0.095 0.036 2.995 0.050 12.872 6.479 0.242
(0.018) (1.708) (3.544) (2.921) (6.671) (6.017) (0.117)
URM
0.033 0.881 0.706 1.291 3.396 0.243 0.126
(0.090) (0.593) (4.063) (4.050) (12.727) (11.430) (0.171)
Placed into IA x URM
0.155* 0.287 0.647 2.244 5.896 0.882 0.126
(0.005) (2.061) (5.956) (5.436) (12.970) (11.565) (0.171)
Rsquared
0.091 0.068 0.046 0.051 0.071 0.077 0.063
Observations 408 408 408 408 408 408 408
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. All estimations include campus and term
fixed effects. Standard errors are in parentheses.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
111
Table 6
Differential Effect of Developmental Math Placement on Math Progression and STEM Participation for STEMOriented Students
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
Ever took
EA
Ever took
IA
Ever took
TLM
Time in
qtrs
before
taking
first
STEM
course
Total
transferabl
e STEM
units
attempted,
3 yrs
Total
transferabl
e STEM
units
completed,
3 yrs
Number of
transferabl
e STEM
units
attempted
Number of
transferabl
e STEM
units
completed
Took at
least 18
transferabl
e STEM
units
Placed into AR 0.012 0.022 0.048 1.446 0.799 0.421 0.434 0.820 0.104
(0.075) (0.063) (0.083) (0.945) (0.484) (0.495) (2.561) (1.742) (0.069)
STEM Orientation 0.050 0.019 0.021 1.193 2.083+ 2.402* 4.153 3.592+ 0.090
(0.063) (0.048) (0.045) (1.067) (0.512) (0.361) (1.554) (1.028) (0.067)
Placed into AR x STEM
Orientation 0.035 0.025 0.040 1.504 3.100+ 3.083+ 4.943+ 3.076 0.133
(0.191) (0.156) (0.165) (2.690) (0.881) (0.845) (1.397) (1.237) (0.145)
Rsquared 0.055 0.053 0.038 0.020 0.028 0.046 0.045 0.045 0.041
Observations 546 546 546 546 546 546 546 546 546
Placed into PA 0.022 0.080 0.084 0.018 0.780+ 0.328 1.645 1.390 0.050
(0.033) (0.077) (0.091) (0.665) (0.228) (0.377) (1.547) (1.033) (0.034)
STEM Orientation 0.110*** 0.176+ 0.233* 0.725 0.116 0.415 2.458 2.554 0.016
(0.003) (0.044) (0.048) (0.786) (0.657) (0.741) (3.055) (2.458) (0.079)
Placed into PA x STEM
Orientation 0.154* 0.228+ 0.256+ 0.247 0.007 1.108 3.034 2.090 0.061
(0.026) (0.070) (0.062) (0.812) (0.256) (0.900) (2.251) (1.898) (0.056)
Rsquared 0.049 0.028 0.022 0.012 0.043 0.045 0.032 0.035 0.031
Observations 1,495 1,495 1,495 1,495 1,495 1,495 1,495 1,495 1,495
Placed into EA
0.152** 0.044* 0.402 0.829 0.926 1.669 2.147 0.066
(0.022) (0.013) (0.486) (0.954) (0.640) (2.599) (1.988) (0.069)
112
STEM Orientation
0.030 0.020 0.981 2.824+ 1.902 5.045 3.591 0.039
(0.025) (0.027) (0.780) (0.975) (0.965) (2.826) (2.232) (0.061)
Placed into EA x STEM
Orientation
0.004 0.031 0.846 2.576 1.627 2.437 1.092 0.033
(0.028) (0.044) (1.270) (1.218) (1.354) (3.970) (3.482) (0.091)
Rsquared
0.043 0.014 0.010 0.031 0.033 0.037 0.042 0.031
Observations 1,617 1,617 1,617 1,617 1,617 1,617 1,617 1,617
Placed into IA
0.187 1.575 0.102 1.437 1.147 1.365 0.050
(0.070) (1.478) (3.208) (3.687) (7.263) (7.456) (0.193)
STEM Orientation
0.118 0.677+ 3.500 3.840 12.747 12.012 0.309
(0.047) (0.087) (1.842) (1.976) (9.572) (8.904) (0.132)
Placed into IA x STEM
Orientation
0.023 2.653 4.672 4.718 14.362 12.442 0.397
(0.134) (1.284) (4.937) (5.985) (13.550) (12.995) (0.305)
Rsquared
0.103 0.081 0.051 0.063 0.092 0.100 0.079
Observations 391 391 391 391 391 391 391
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. All estimations include campus and term
fixed effects. Standard errors are in parentheses.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
113
Table 7
Differential Effect of Developmental Math Placement on Math Progression and STEM Participation for STEMAspiring Students
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
Ever took
EA
Ever took
IA
Ever took
TLM
Time in
qtrs
before
taking
first
STEM
course
Total
transferabl
e STEM
units
attempted,
3 yrs
Total
transferabl
e STEM
units
completed,
3 yrs
Number of
transferabl
e STEM
units
attempted
Number of
transferabl
e STEM
units
completed
Took at
least 18
transferabl
e STEM
units
Placed into AR 0.020 0.084 0.105 0.684 0.631 0.276 0.922 1.216 0.110
(0.044) (0.056) (0.071) (1.093) (0.566) (0.556) (1.610) (1.307) (0.045)
STEM Aspiration 0.042 0.048 0.040 1.072 1.764 1.676 7.739 4.074 0.121
(0.070) (0.070) (0.070) (1.045) (1.062) (1.200) (3.649) (4.246) (0.104)
Placed into AR x STEM
Aspiration 0.253 0.439+ 0.407+ 3.074 0.946 1.115 3.449 1.493 0.048
(0.154) (0.108) (0.101) (1.293) (1.012) (0.644) (2.461) (4.131) (0.072)
Rsquared 0.057 0.058 0.043 0.030 0.076 0.092 0.089 0.079 0.076
Observations 546 546 546 546 546 546 546 546 546
Placed into PA 0.046 0.070 0.059 0.429 0.754 0.694 2.070 1.627 0.054
(0.032) (0.075) (0.087) (0.645) (0.320) (0.253) (1.681) (1.257) (0.034)
STEM Aspiration 0.100 0.294* 0.251* 3.624 3.938* 3.607* 16.304* 12.264+ 0.270+
(0.037) (0.048) (0.042) (1.497) (0.700) (0.399) (3.717) (3.038) (0.072)
Placed into PA x STEM
Aspiration 0.085 0.329** 0.294** 3.538* 1.132 0.119 7.876 5.402 0.095
(0.068) (0.022) (0.012) (0.768) (1.860) (1.738) (2.760) (2.729) (0.194)
Rsquared 0.049 0.030 0.022 0.013 0.081 0.066 0.112 0.106 0.060
Observations 1,495 1,495 1,495 1,495 1,495 1,495 1,495 1,495 1,495
Placed into EA
0.163* 0.068 0.167 1.481 1.517 3.028 2.817 0.074
114
(0.043) (0.041) (0.513) (1.066) (0.693) (2.459) (1.802) (0.049)
STEM Aspiration
0.047+ 0.036 0.695 4.799** 2.770** 9.049+ 6.436+ 0.143
(0.017) (0.081) (1.046) (0.571) (0.335) (3.279) (2.429) (0.071)
Placed into EA x STEM
Aspiration
0.091 0.099 0.785 1.591 0.219 4.736 2.761 0.191
(0.065) (0.139) (1.759) (2.916) (2.504) (5.499) (4.662) (0.088)
Rsquared
0.055 0.025 0.010 0.087 0.074 0.120 0.110 0.084
Observations 1,617 1,617 1,617 1,617 1,617 1,617 1,617 1,617
Placed into IA
0.199* 0.641 2.006 0.966* 7.539+ 4.587 0.208+
(0.004) (0.265) (0.783) (0.019) (0.807) (0.942) (0.032)
STEM Aspiration
0.043 1.597 10.815+ 8.029 22.670 16.823 0.191
(0.014) (0.388) (1.701) (2.863) (4.166) (8.510) (0.061)
Placed into IA x STEM Aspiration
0.143 2.916 0.229 0.928 3.314 1.175 0.265
(0.096) (2.143) (1.283) (2.933) (1.462) (0.958) (0.239)
Rsquared
0.127 0.064 0.141 0.116 0.204 0.180 0.142
Observations 391 391 391 391 391 391 391
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. All estimations include campus and term
fixed effects. Standard errors are in parentheses.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
115
Table 8
Effect of Developmental Math Placement on Math Progression and STEM Participation Among Enrollees
AR/PA PA/EA EA/IA IA/TLM
Bandwidth +/ 0.86 Bandwidth +/ 0.65 Bandwidth +/ 0.67 Bandwidth +/ 0.61
Dependent Variable
LLR with
FE SE N
LLR with
FE SE N
LLR
with FE SE N
LLR
with FE SE N
Math Progression
Ever took EA 0.022 (0.050) 546 0.059 (0.025) 1495
Ever took IA 0.012 (0.065) 546 0.027 (0.071) 1495 0.154* (0.035) 1617
Ever took TLM 0.039 (0.083) 546 0.021 (0.083) 1495 0.058+ (0.019) 1617 0.180+ (0.017) 391
ShortTerm STEM
Participation
Time in qtrs before taking first
STEM course 1.136 (0.943) 546 0.038 (0.536) 1495 0.026 (0.401) 1617 0.120 (0.550) 391
Total transferable STEM
credits attempted, 3 yrs 0.448 (0.394) 546 0.864** (0.074) 1495 2.011+ (0.757) 1617 2.528+ (0.242) 391
Total transferable STEM
credits completed, 3 yrs 0.030 (0.893) 313 0.631* (0.093) 1014 2.457* (0.463) 1151 0.627 (1.005) 327
LongTerm STEM
Participation
Total transferable STEM
credits attempted 1.212 (2.003) 546 1.022 (1.189) 1495 3.079 (1.342) 1617 9.392+ (0.775) 391
Total transferable STEM
credits completed 2.140 (1.440) 372 0.657 (0.727) 1182 3.954* (0.685) 1339 4.054+ (0.426) 368
Took at least 18 transferable
STEM credits 0.115 (0.048) 546 0.040 (0.015) 1495 0.060 (0.036) 1617 0.175* (0.008) 391
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. The RD coefficient estimates a local linear
regression with campus and term fixed effects. The coefficient estimates the likelihood of observing a significant treatment effect on outcomes around the
specified bandwidth. Outcomes observed up to 2016 for 20052008 entering cohorts. Students who took the math assessment but did not enroll in community
colleges were dropped. Additionally, we drop students who did not attempt a transferable STEM course when estimating the completion outcome. All
estimations include campus and term fixed effects. Standard errors are in parentheses.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
116
Figures
Figure 1
Math Enrollment Rates by Math Placement
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math.
This figure displays the fraction of those enrolled in a math course that is one level above if placed directly in that
course relative to placing one level below among those who enrolled in college.
117
Figure 2
Discontinuity in the Density of the Running Variables across Four Placement Cutoffs
AR/PA PA/EA
EA/IA IA/TLM
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math.
118
Figure 3
Fraction of Students Enrolled in College after Math Assessment
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math.
119
Figure 4
Discontinuity at the Intermediate Algebra/Transferlevel Math Cutoff on Math Progression and
STEM Participation
Note. TLM=transferlevel math.
120
Appendix
Table A.1
Differential Effect of Developmental Math Placement on Math Progression and STEM Participation for Female Student Enrollees
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
Ever took
EA
Ever took
IA
Ever took
TLM
Time in
qtrs
before
taking
first
STEM
course
Total
transferable
STEM
units
attempted,
3 yrs
Total
transferable
STEM
units
completed,
3 yrs
Number of
transferable
STEM
units
attempted
Number of
transferable
STEM
units
completed
Took at
least 18
transferable
STEM
units
Placed into AR 0.051 0.099** 0.116* 1.280 0.697 1.125 1.234 3.487 0.049
(0.018) (0.006) (0.021) (0.482) (0.381) (0.560) (1.641) (1.797) (0.072)
Female 0.039 0.078 0.080 0.263 0.741 0.403 0.278 1.040 0.067
(0.098) (0.064) (0.064) (0.513) (0.922) (0.319) (5.202) (3.964) (0.156)
Placed into AR x Female 0.145 0.181 0.165 0.048 0.696 2.349+ 0.078 3.165 0.141
(0.153) (0.130) (0.134) (1.609) (0.367) (0.728) (3.660) (3.317) (0.114)
Rsquared 0.049 0.049 0.035 0.025 0.017 0.062 0.034 0.060 0.039
Observations 546 546 546 546 546 313 546 372 546
Placed into PA 0.108 0.007 0.005 0.015 0.878 1.669 5.709* 5.052** 0.130
(0.040) (0.089) (0.102) (1.119) (0.771) (0.832) (1.030) (0.269) (0.065)
Female 0.044 0.006 0.006 0.758 1.411 2.165 8.063* 6.374* 0.209**
(0.019) (0.019) (0.026) (1.027) (0.627) (0.844) (1.602) (1.470) (0.017)
Placed into PA x Female 0.097 0.067 0.053 0.071 3.279 4.069+ 12.820** 10.556** 0.320+
(0.049) (0.085) (0.070) (1.146) (1.148) (1.069) (0.443) (1.045) (0.107)
Rsquared 0.053 0.026 0.020 0.011 0.035 0.042 0.037 0.036 0.036
Observations 1,495 1,495 1,495 1,495 1,495 1,014 1,495 1,182 1,495
121
Placed into EA 0.138* 0.001 0.214 0.936 2.226+ 1.220 4.403+ 0.028
(0.039) (0.022) (0.636) (1.311) (0.803) (2.845) (1.763) (0.083)
Female
0.002 0.035 1.207** 1.642 0.021 2.214 1.107 0.110
(0.039) (0.026) (0.138) (1.493) (1.592) (3.592) (3.243) (0.112)
Placed into EA x Female
0.029 0.116+ 0.409 2.089 0.370 3.554 1.087 0.174
(0.099) (0.047) (0.868) (0.977) (0.627) (2.854) (2.841) (0.108)
Rsquared
0.043 0.015 0.012 0.022 0.034 0.026 0.033 0.023
Observations 1,617 1,617 1,617 1,617 1,151 1,617 1,339 1,617
Placed into IA
0.148* 0.327 3.368 2.546 14.369 5.122 0.284
(0.008) (1.589) (3.764) (5.157) (6.353) (5.698) (0.101)
Female
0.004 0.843 0.180 2.150 2.236 0.601 0.098
(0.025) (0.624) (5.110) (6.086) (15.002) (13.907) (0.223)
Placed into IA x Female
0.055 0.889 1.504 3.452 8.536 1.608 0.184
(0.012) (1.660) (6.147) (7.944) (12.440) (9.808) (0.162)
Rsquared
0.093 0.076 0.051 0.058 0.085 0.080 0.075
Observations 391 391 391 327 391 368 391
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. Students who took the math assessment but
did not enroll in community colleges were dropped. Additionally, we drop students who did not attempt a transferable STEM course when estimating the
completion outcome. All estimations include campus and term fixed effects. Standard errors are in parentheses.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
122
Table A2
Differential Effect of Developmental Math Placement on Math Progression and STEM Participation for URM Student Enrollees
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
Ever took
EA
Ever took
IA
Ever took
TLM
Time in
qtrs
before
taking
first
STEM
course
Total
transferable
STEM
units
attempted,
3 yrs
Total
transferable
STEM
units
completed,
3 yrs
Number of
transferable
STEM
units
attempted
Number of
transferable
STEM
units
completed
Took at
least 18
transferable
STEM
units
Placed into AR 0.327** 0.261+ 0.287+ 0.845* 0.582 1.154* 3.489 5.321* 0.366*
(0.013) (0.080) (0.077) (0.149) (0.985) (0.138) (3.094) (1.060) (0.041)
URM 0.295* 0.192 0.204 1.302 1.532 2.694 4.907 6.084 0.257+
(0.067) (0.067) (0.075) (0.464) (2.023) (1.997) (4.012) (3.420) (0.070)
Placed into AR x URM 0.396** 0.279 0.279 0.250 0.037 1.225 2.672 3.481 0.286*
(0.014) (0.127) (0.142) (1.263) (1.108) (1.008) (2.464) (1.582) (0.033)
Rsquared 0.055 0.050 0.036 0.025 0.029 0.050 0.042 0.053 0.044
Observations 546 546 546 546 546 313 546 372 546
Placed into PA 0.113 0.077 0.087 0.708 1.859 1.299 1.472 0.135 0.059+
(0.080) (0.137) (0.141) (1.818) (1.676) (1.464) (3.202) (3.025) (0.014)
URM 0.032 0.010 0.028 1.179 2.589 2.404 7.116* 5.572** 0.204**
(0.036) (0.037) (0.042) (1.751) (1.703) (1.246) (1.558) (0.503) (0.013)
Placed into PA x URM 0.063 0.122 0.126 0.867 3.201 2.325 3.101 1.163 0.119+
(0.091) (0.085) (0.069) (1.532) (1.966) (1.635) (2.772) (3.147) (0.029)
Rsquared 0.043 0.018 0.014 0.010 0.038 0.047 0.040 0.042 0.040
Observations 1,495 1,495 1,495 1,495 1,495 1,014 1,495 1,182 1,495
Placed into EA
0.047 0.001 0.143 0.197 1.074 0.504 0.847 0.039
(0.079) (0.080) (0.212) (1.031) (1.145) (2.296) (2.121) (0.041)
123
URM
0.056 0.037+ 0.753 1.543 1.670 0.666 0.900 0.009
(0.052) (0.015) (0.907) (0.968) (1.364) (2.642) (2.636) (0.053)
Placed into EA x URM
0.139 0.079 0.227 2.338 1.763 4.692 4.131 0.130*
(0.128) (0.101) (0.811) (1.470) (1.132) (4.416) (3.481) (0.035)
Rsquared
0.044 0.019 0.011 0.023 0.034 0.031 0.035 0.026
Observations 1,617 1,617 1,617 1,617 1,151 1,617 1,339 1,617
Placed into IA
0.148* 0.327 3.368 2.546 14.369 5.122 0.284
(0.008) (1.589) (3.764) (5.157) (6.353) (5.698) (0.101)
URM
0.004 0.843 0.180 2.150 2.236 0.601 0.098
(0.025) (0.624) (5.110) (6.086) (15.002) (13.907) (0.223)
Placed into IA x URM
0.055 0.889 1.504 3.452 8.536 1.608 0.184
(0.012) (1.660) (6.147) (7.944) (12.440) (9.808) (0.162)
Rsquared
0.093 0.076 0.051 0.058 0.085 0.080 0.075
Observations 391 391 391 327 391 368 391
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. Students who took the math assessment but
did not enroll in community colleges were dropped. Additionally, we drop students who did not attempt a transferable STEM course when estimating the
completion outcome. All estimations include campus and term fixed effects. Standard error in parentheses.
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
124
Table A.3
Robustness of Main RD Estimates across Minimum and Maximum Bandwidth
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
Bandwidth
Ever
took EA
Ever took
IA
Ever took
TLM
Time in
qtrs
before
taking
first
STEM
course
Total
transferable
STEM
units
attempted,
3 yrs
Total
transferable
STEM
units
completed,
3 yrs
Number of
transferable
STEM
units
attempted
Number of
transferable
STEM
units
completed
Took at
least 18
transferable
STEM
units
AR/PA +/ 0.67 0.046 0.005 0.028 0.957 0.555 0.087 2.405 2.073 0.138*
(0.043) (0.031) (0.054) (0.829) (1.255) (1.140) (1.560) (0.890) (0.029)
450 450 450 450 450 450 450 450 450
AR/PA +/ 1.1 0.036 0.030 0.008 0.870 0.512+ 0.422 0.082 0.041 0.048
(0.017) (0.017) (0.034) (0.586) (0.133) (0.176) (1.148) (0.883) (0.034)
808 808 808 808 808 808 808 808 808
PA/EA +/ 0.56 0.043 0.024 0.022 0.267 0.670+ 0.467 0.277 0.421 0.028
(0.037) (0.079) (0.088) (0.542) (0.198) (0.239) (1.206) (0.801) (0.018)
1414 1414 1414 1414 1414 1414 1414 1414 1414
PA/EA +/ 0.75 0.040 0.036 0.032 0.001 0.795* 0.629* 1.016 0.767 0.042
(0.022) (0.060) (0.066) (0.319) (0.115) (0.099) (1.095) (0.858) (0.017)
1898 1898 1898 1898 1898 1898 1898 1898 1898
EA/IA +/ 0.49
0.152* 0.061 0.311 1.331 1.168+ 2.629 2.529 0.048
(0.037) (0.042) (0.529) (0.893) (0.479) (2.085) (1.400) (0.052)
1268 1268 1268 1268 1268 1268 1268 1268
EA/IA +/ 0.84
0.113 0.022 0.490 1.712+ 1.506* 2.657 2.506+ 0.058
(0.048) (0.029) (0.253) (0.589) (0.360) (1.152) (0.910) (0.030)
2195 2195 2195 2195 2195 2195 2195 2195
IA/TLM +/ 0.47
0.220* 0.277* 2.985 1.244 8.827* 5.005* 0.164
(0.005) (0.010) (0.856) (0.780) (0.351) (0.114) (0.029)
125
336 336 336 336 336 336 336
IA/TLM +/ 0.76
0.188** 0.153 2.488 1.568 9.487 6.297 0.182*
(0.000) (0.646) (0.534) (0.861) (1.774) (1.607) (0.006)
487 487 487 487 487 487 487
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. The coefficient estimates the likelihood of
observing a significant treatment effect around a range of bandwidth using the algorithm recommended by Calonico, Cattaneo, and Titiunik (2014).
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
126
Table A.4
Robustness of STEMAspiring Interaction Estimates across Minimum and Maximum Bandwidth for those around the AR/PA and
PA/EA Cutoffs
Note. AR=arithmetic; PA=prealgebra; EA=elementary algebra. The coefficient estimates the likelihood of observing a significant treatment effect around a
range of bandwidth using the algorithm recommended by Calonico, Cattaneo, and Titiunik (2014).
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Bandwidth
Ever took
EA
Ever took
IA
Ever took
TLM
Time in qtrs
before
taking first
STEM
course
Total
transferable
STEM units
attempted, 3
yrs
Total
transferable
STEM units
completed, 3
yrs
Number of
transferable
STEM units
attempted
Number of
transferable
STEM units
completed
Took at least
18
transferable
STEM units
AR/PA +/ 0.67 Placed into AR 0.064 0.141 0.173 0.529 0.185 0.039 2.661 2.448 0.184
(0.095) (0.109) (0.134) (1.368) (0.992) (0.725) (2.506) (2.164) (0.072)
STEM Aspiration 0.007 0.072 0.071 0.675 1.650 1.676 7.740 4.348 0.107
(0.088) (0.064) (0.077) (0.497) (2.026) (2.196) (4.516) (5.571) (0.169)
Placed into AR x STEM Aspiration 0.233 0.434 0.417 2.605 1.153 2.032 5.995 3.892 0.033
(0.235) (0.223) (0.232) (1.745) (0.691) (1.752) (5.251) (6.833) (0.206)
379 379 379 379 379 379 379 379 379
AR/PA +/ 1.1 Placed into AR 0.037 0.067 0.092 0.494 0.354 0.430 0.553 0.480 0.070
(0.031) (0.040) (0.058) (0.851) (0.396) (0.326) (1.093) (1.049) (0.041)
STEM Aspiration 0.035 0.080 0.070 0.862 2.162+ 2.062+ 7.653 4.477 0.120
(0.079) (0.067) (0.064) (0.447) (0.658) (0.480) (3.351) (3.867) (0.139)
Placed into AR x STEM Aspiration 0.176 0.382+ 0.385+ 2.611 0.270 0.850 1.885 0.407 0.009
(0.133) (0.110) (0.116) (1.082) (2.568) (0.453) (2.694) (3.817) (0.109)
680 680 680 680 680 680 680 680 680
PA/EA +/ 0.56 Placed into PA 0.071 0.043 0.042 0.203 0.389 0.393 1.196 1.175 0.045
(0.029) (0.076) (0.088) (0.691) (0.286) (0.221) (1.705) (1.228) (0.039)
STEM Aspiration 0.097+ 0.308* 0.269* 3.682 3.753* 3.749* 18.005+ 14.467+ 0.290*
(0.032) (0.065) (0.049) (1.651) (0.848) (0.498) (5.053) (4.268) (0.064)
Placed into PA x STEM Aspiration 0.029 0.309* 0.303* 4.822 1.908 0.326 9.181 7.207 0.143
(0.070) (0.048) (0.055) (1.707) (2.448) (2.408) (4.632) (3.480) (0.205)
1,263 1,263 1,263 1,263 1,263 1,263 1,263 1,263 1,263
PA/EA +/ 0.75 Placed into PA 0.066 0.045 0.040 0.330 0.773 0.742+ 1.799 1.406 0.048
(0.028) (0.066) (0.075) (0.394) (0.303) (0.245) (1.422) (1.122) (0.029)
STEM Aspiration 0.023 0.187 0.164 2.595 3.985* 3.430* 15.424+ 11.709+ 0.241*
(0.090) (0.124) (0.119) (1.639) (0.523) (0.632) (4.591) (3.591) (0.047)
Placed into PA x STEM Aspiration 0.016 0.154 0.143 2.964 0.750 0.408 5.006 4.279 0.007
(0.137) (0.073) (0.077) (1.318) (2.104) (1.692) (2.922) (2.698) (0.140)
1,697 1,697 1,697 1,697 1,697 1,697 1,697 1,697 1,697
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
127
Table A.5
Robustness of STEMAspiring Interaction Estimates across Minimum and Maximum Bandwidth for those around the EA/IA and
IA/TLM Cutoffs
Note. EA=elementary algebra; IA=intermediate algebra; TLM=transferlevel math. The coefficient estimates the likelihood of observing a significant treatment
effect around a range of bandwidth using the algorithm recommended by Calonico, Cattaneo, and Titiunik (2014).
p < 0.10 +, p < 0.05 *, p < 0.01 **, p < 0.001 ***
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Bandwidth
Ever took
EA
Ever took
IA
Ever took
TLM
Time in qtrs
before
taking first
STEM
course
Total
transferable
STEM units
attempted, 3
yrs
Total
transferable
STEM units
completed, 3
yrs
Number of
transferable
STEM units
attempted
Number of
transferable
STEM units
completed
Took at least
18
transferable
STEM units
EA/IA +/ 0.49 Placed into EA 0.155* 0.056 0.521 0.889 1.089 2.564 2.560 0.061
(0.038) (0.056) (0.774) (1.188) (0.724) (2.987) (2.181) (0.063)
STEM Aspiration 0.050 0.052 0.782 3.903** 1.988* 9.344 6.086 0.123
(0.039) (0.077) (1.468) (0.531) (0.601) (4.667) (3.669) (0.064)
Placed into EA x STEM Aspiration 0.043 0.031 1.294 1.421 0.241 5.549 3.903 0.200
(0.052) (0.140) (2.931) (2.407) (2.099) (6.694) (5.837) (0.140)
379 379 379 379 379 379 379 379
EA/IA +/ 0.84 Placed into EA 0.147+ 0.052 0.288 1.494 1.497+ 3.107 2.677 0.077
(0.052) (0.044) (0.494) (0.762) (0.633) (2.143) (1.779) (0.048)
STEM Aspiration 0.056* 0.036 0.788 5.247** 3.464** 11.526+ 8.889+ 0.214
(0.014) (0.086) (0.669) (0.673) (0.506) (3.666) (3.271) (0.092)
Placed into EA x STEM Aspiration 0.101 0.118 1.027 1.873 0.550 2.922 0.875 0.114
(0.064) (0.126) (1.962) (3.438) (2.979) (6.328) (5.756) (0.132)
680 680 680 680 680 680 680 680
IA/TLM +/ 0.47 Placed into IA 0.216 0.778 1.955 0.586 5.358 2.861 0.173*
(0.041) (0.618) (1.372) (0.717) (2.054) (1.935) (0.012)
STEM Aspiration 0.020 2.511+ 11.599* 8.907 25.362 18.808 0.303+
(0.042) (0.240) (0.250) (2.043) (5.567) (11.306) (0.046)
Placed into IA x STEM Aspiration 0.149 4.695 0.859 0.079 7.341* 3.310 0.190
(0.175) (1.574) (1.738) (3.497) (0.253) (0.631) (0.203)
1,263 1,263 1,263 1,263 1,263 1,263 1,263
IA/TLM +/ 0.76 Placed into IA 0.206** 0.182 2.727+ 1.850 8.907+ 6.018+ 0.249
(0.002) (0.643) (0.230) (0.509) (0.784) (0.644) (0.043)
STEM Aspiration 0.042 0.617 9.085 6.562 20.333 14.793 0.134
(0.011) (0.207) (2.417) (3.326) (4.492) (8.106) (0.074)
Placed into IA x STEM Aspiration 0.214 0.592 3.644* 3.302 1.819 2.469 0.432
(0.094) (0.985) (0.215) (1.134) (2.422) (2.960) (0.252)
1,697 1,697 1,697 1,697 1,697 1,697 1,697
Math Progression ShortTerm STEM Participation LongTerm STEM Participation
128
Figure A.1
Measures of Math Progression and STEM Participation around the Arithmetic/PreAlgebra Cut
off with Local Linear Regression Fit on Each Side
Note .Bandwidth +/ 0.86
129
Figure A.2
Measures of Math Progression and STEM Participation around the PreAlgebra/Elementary
Algebra Cutoff with Local Linear Regression Fit on Each Side
Note. Bandwidth +/ 0.65
130
Figure A.3
Measures of Math Progression and STEM Participation around the Elementary
Algebra/Intermediate Algebra Cutoff with Local Linear Regression Fit on Each Side
Note. Bandwidth +/0.66
131
Essay III. Comparative Advantage in STEM and the STEM Gender Gap in Community
College
Abstract
While the STEM gender gap at universities has received more attention in the literature,
fewer studies examined the STEM gender gap at community colleges. Addressing this gap, I first
estimate the magnitude of the STEM gender gap at community colleges, disaggregating by Life
Science (LS) and Physical Science/Engineering (PS/E) and by initial placement into
developmental education. Then, I investigate a potential mechanism driving this gap called
comparative advantage. Comparative advantage is the notion that students pursue future study
based on early feedback of their relative strength in certain subjects. Results indicate no evidence
of a STEM gender gap among academically prepared PS/E students. However, there exists a
persistent STEM gender gap among PS/E students who placed into low levels of developmental
education. Moreover, comparative advantage in STEM exacerbated this gap as men outpaced
women in completing transferable science courses. This study discusses potential explanations
and concludes with policy implications.
132
Recent studies indicate that women surpass men in degree attainment, but there remains a
persistent gender gap in the attainment of STEM degrees (i.e., “STEM gender gap”) (Chen &
Soldner, 2013; Ceci & Williams, 2011; National Science Board, 2015; National Science
Foundation, 2017). Concerns over the STEM gender gap have inspired scholarship on ways to
reduce this gap notably at fouryear institutions. Scholars have examined factors like access to
high school STEM courses (Darolia et al., 2018), success in high school STEM coursework
(Card & Payne, 2017), ability beliefs and prosocial values (Shi, 2018), and perceived gender bias
associated with certain STEM majors (Ganley et al., 2017), mostly at fouryear institutions.
However, fewer scholars have examined the STEM gender gap at community colleges.
Community colleges – as open access institutions serving many underrepresented
students – are poised to play an important role in reducing the STEM gender gap (Dowd,
Malcom, & Bensimon, 2009; MalcomPiqueux et al., 2012). Yet, nationwide statistics indicate
that the STEM gender gap is also evident at community colleges, particularly in Physical
Science/Engineering (PS/E) (Leslie, Cimpian, Meyer, & Freeland, 2015; Ost, 2010; Riegle
Crumb King, Grodsky, & Muller, 2012; Shi, 2018). For example, in 2014, only 18% of all
Associate’s degrees awarded in PS/E were awarded to women whereas 82% of all Associate’s
degrees awarded in PS/E were awarded to men (National Center for Education Statistics, 2017).
1
While these trends indicate a gender gap in PS/E attainment at community colleges, little is
known regarding the factors contributing to this gap.
To unpack why there exists a STEM gender gap in community college, I first estimate the
magnitude of the STEM gender gap, disaggregating by LS and PS/E and by initial math and
English placement levels. It is important to distinguish students’ initial math and English
placement levels because students who place into low levels of developmental education do not
133
have the same kinds of access to transferlevel (i.e., collegelevel) math, and subsequently upper
level STEM courses, as students who place directly in transferlevel math. In ensuing analyses, I
investigate a mechanism potentially driving the STEM gender gap called comparative advantage.
Comparative advantage is the notion that students pursue future study based on early feedback of
their relative strength in STEM courses compared to nonSTEM courses (Card & Payne, 2017;
Stoet & Geary, 2018). For example, if women received higher grades in STEM courses relative
to nonSTEM courses, her comparative advantage is in STEM.
Comparative advantage is a relevant concept to investigate in studies of the STEM
gender gap because students make future educational decisions based on their performance in
different subjects (Kugler, Tinsley, Ukhaneva, 2017; Sabot & WakemanLynn, 1991). Previous
studies that measured comparative advantage constructed this measure using high school records
(Card & Payne, 2017; RiegleCrumb et al., 2012; Stoet & Geary, 2018). Here, comparative
advantage is determined by examining students’ coursetaking records and grades during their
first year of community college. First year of community college is particularly relevant because
attrition from STEM pathways occurs most during the initial postsecondary years (Chen &
Soldner, 2013). Therefore, I investigate whether comparative advantage is a driving mechanism
behind the STEM gender gap in community college.
This study can be summarized by three research questions:
1. Is there a STEM gender gap by LS and PS/E subfields and by initial level of academic
preparation in community college?
2. Does comparative advantage in STEM during the first year of community college predict
persistence in STEM?
134
3. Does the STEM gender gap in LS and PS/E narrow as students demonstrate comparative
advantage in STEM during their first year of community college?
I use unique, linked studentlevel data of graduates from a large, urban school district in
California and who also attended a community college in the same metropolitan area. To ensure
that I compare men and women with similar demographic characteristics, academic preparation,
and intentions, I use propensityscore matching in which I find an observationally equivalent
male student for each female student.
2
I use PSM for three reasons. First, the data include a rich
set of demographic and high school coursetaking variables, rendering PSM a possible analytical
approach. Second, the linked data only include a subpopulation of high school graduates who
attended community colleges. Therefore, I use a more rigorous and transparent analytical design
to properly eliminate baseline differences. Third, if men and women are significantly different
across the distribution of baseline covariates, covariate adjustments (e.g., linear regression) will
lead to extrapolation and bias. By not assuming a particular functional form, I minimize the need
to extrapolate to cases that deviate far from the average.
This study contributes to the literature in several ways. First, previous studies examined
academic preparation as a contributor of the STEM gender gap, but these studies did not
explicitly examine whether a gap still exists if men and women enter college with
observationally equivalent academic backgrounds and with similar aspirations. Therefore, this
study provides new evidence on whether a STEM gender gap still exists among men and women
with similar academic preparation. Second, underrepresented minorities enroll in community
college at a high rate; thus, this study has implications for increasing the representation of
women of color in STEM fields. Third, this study investigates a mechanism that may help
explain the existence of a STEM gender gap – students’ comparative advantage in STEM. This
135
study, therefore, elucidates both the existence as well as a rationale, thereby providing evidence
based implications for policy and practice.
The paper is organized as follows. First, I introduce the conceptual framework and prior
literature on the STEM gender gap. Then, I provide an overview of the study context and data.
Next, I detail propensity score matching as the empirical strategy. Finally, I present results and
conclude with policy implications.
Conceptual Framework
Academic preparation undoubtedly plays a large role in ushering more students into
STEM fields. Prior achievement and experiences in high school influence students’ college
experiences and subsequent connection to their chosen degree (Crisp, Nora, Taggart, 2009).
Also, adequate academic preparation prior to college is often touted as a requirement to
successfully pursue and complete a degree in STEM (Goodman, 2017; Regional Educational Lab
Southwest, 2017; Rodriguez, 2017; Stinebricker & Stinebricker, 2014). Therefore, students
become interested in STEM fields through various academic experiences in high school (Wang,
2013).
In this study, the STEM pathway refers to cultivating an interest in STEM and sustaining
momentum from high school to community college (Wang, 2015, 2017). Research shows that
students’ early credit load and enrollment patterns in community college predict persistence and
degree attainment in STEM fields (Wang, 2015). Therefore, students who attempt and complete
considerable early STEM coursework display behavioral patterns conducive to persisting and
succeeding in the STEM pathway.
Figure 1 is a diagram of the conceptual framework that links high school math and
science preparation, persistence in the STEM pathway, and eventual STEM attainment in
136
community college. Figure 1 shows that the process of selecting a college major is influenced by
exposure to and achievement in high school math and science courses (Xie & Shauman, 2003;
Wang, 2013). In other words, prior experiences in high school are acknowledged as important
drivers of STEM aspirations. Once students decide to enroll in community college, students
submit their college application in which they mark their intended major. The students who
indicate in their college application that they would like to pursue LS or PS/E are considered
“LSaspiring” or “PS/Easpiring” students. This figure includes shortterm outcomes like the
number of quarters before passing the first STEM course and longterm outcomes like the
number of transferable STEM units completed overall.
The outcomes listed in Figure 1 are measures of steady progress through the STEM
pathway and do not imply that students pursue their STEM interest in a linear, rigid series of
stages. Particularly in the community college setting, attaining an Associate’s degree or
transferring is not the only measure of progress. Several studies document gains in the labor
market from taking just a few courses (Bahr, 2014; Dadger & Trimble, 2015; Hodara & Xu
2016). Moreover, many individuals who work in STEM fields do not possess a STEM degree,
suggesting that students benefit from a STEMfocused education regardless of a formal degree
(NSB, 2015). By examining markers that indicate steady progress in the STEM pathway like
accumulating transferable STEM units, this study underscores that pursuing a STEMfocused
education—in and of itself—is an important outcome. More specifically, measures of
accumulating STEM units are proxies for learning relevant skills for success in the knowledge
economy and warrant attention even if students do not graduate with a STEM degree.
137
Below is a synthesis of literature on prior academic preparation in math and science, the
community college placement process, and students’ comparative advantage in STEM during the
first year.
Empirical Literature
Prior Preparation in Math and Science
According to Figure 1, students develop aspirations to pursue STEM fields based on early
exposure to and achievement in math and science courses. Indeed, research shows that
expectations formed during formative years have a significant effect on the likelihood of
attaining a Bachelor’s degree in STEM (Tai, Liu, Maltese, & Fan, 2006; Morgan et al., 2013).
Specifically, of students who graduated with baccalaureate degrees, those who expected as
eighth graders to have a sciencerelated career at age 30 were 1.9 times more likely to earn a LS
baccalaureate degree than those who did not expect a sciencerelated career. Students with
expectations for a sciencerelated career were 3.4 times more likely to earn PS/E degrees than
students without similar expectations (Tai et al., 2006).
Examining the factors that influence STEM entry, Wang (2013) concluded that early
exposure to high school math and science courses played an important role in determining who
enters STEM fields in college. Also, Gottfried and Bozick (2016) found that taking math and
science courses in high school led to higher odds of majoring in STEM at both two and four
year colleges. Importantly, advanced coursetaking in physics and calculus were correlated with
pursuing and persisting as STEM majors (Card & Payne, 2017; Crisp et al., 2009; Morgan et al.,
2013; RiegleCrumb et al., 2012; Sadler & Tai, 2001). Moreover, scholars found that high school
GPA also predicted the likelihood of pursuing and completing a STEM degree (Espinosa, 2011;
Maltese & Tai, 2011; RiegleCrumb et al., 2012). Therefore, greater exposure to and success in
138
high school math and science courses are associated with increased STEM aspirations,
underscoring the importance of high school academic preparation in developing students’ STEM
interest.
Next, once students decide to enroll in community college, they must take the math or the
English placement test.
3
The results from the placement test determine students’ initial math and
English course level. As of 2016, all California community colleges used some form of
placement test to assess students’ initial math and English levels, though the specific
matriculation policy varied by campus (Rodriguez, Mejia, & Johnson, 2016).
4
The conceptual
framework explicitly includes both students’ math and English placement levels because initial
course placement tends to determine access to advanced coursework (Bailey, Jeong, & Cho,
2010; Valentine, Konstantopoulos, & GoldrickRab, 2017). Furthermore, evidence suggests that
students’ math placement is associated with STEM persistence in community colleges (Park,
Ngo, & Melguizo, 2018). Specifically, studies conclude that students who place in lowerlevel
math were more likely to exit STEM pathways (Bahr et al., 2017) and attempt fewer transferable
STEM courses (Park et al., 2018; Park & Ngo, 2019) than those who begin one level above.
Taken together, initial placement in math and English affects students’ access to upperlevel
STEM courses that are required for degree attainment and/or transfer.
Comparative Advantage in STEM
Recently, scholars have introduced the notion of comparative advantage in studies of the
STEM gender gap (Card & Payne, 2017; RiegleCrumb et al., 2012; Stoet & Geary, 2018).
Essentially, comparative advantage is the idea that students recognize their relative areas of
strength based on their performance in various courses and that they are more likely to pursue
future study in areas in which they are relatively strong. If early experiences and preparation in
139
math and/or science courses are influential in building momentum towards STEM persistence
(Wang, 2015), then students’ comparative advantage in STEM may signal their “fit” in STEM
fields. Course grades serve as an important signal of one’s comparative advantage in a subject. If
a student receives A’s on her math or science courses while receiving B’s on her English
language arts or history courses, the high marks in math or science courses serve as a feedback
mechanism on her relative strength in STEM subjects (Sabot & WakemanLynn, 1991).
There are at least two reasons to hypothesize this pattern. First, grades are impressionable
to students and influence students’ decisions to switch majors (Kugler, Tinsley, Ukhaneva,
2017). Specifically, those with lower STEM grades switched majors more often than those with
equal or higher STEM grades (Chen & Soldner, 2013). Also, there is some evidence that female
students are more responsive to math and science grades than male students (Kugler et al., 2017;
Nix, PerezFelkner, & Thomas, 2015; Ost, 2010). Specifically, Kugler et al. (2017) found that
women in maledominated STEM majors were more likely to switch majors than men due to low
grades in STEM courses. Therefore, female students who exhibit a comparative advantage in
STEM during early college years may be more inclined to persist in the STEM pathway, and this
pattern may be more consequential for women than men.
Second, studies show that students make future educational decisions based on their own
relative performance (Eccles, 1994, 2009; Stoet & Geary, 2018; Wang, Eccles & Kenny, 2013).
It is likely that students who receive higher grades in reading relative to math would gain more
confidence in reading compared to math. Wang, Eccles, & Kenny (2013) found that female
students with high math and moderate verbal ability chose to pursue STEM fields in college at a
higher rate than women who excelled in both math and verbal equally. Their explanation of this
pattern was that female students who performed well in all subjects had more college majors
140
open to them. In contrast, female students who excelled more in math than verbal internalized a
signal that their verbal ability is not as strong as their math ability and chose a college major
corresponding to their perceived strengths.
To date, only a handful of scholars examined students’ comparative advantage in studies
of the STEM gender gap. Card and Payne (2017) and RiegleCrumb et al. (2012) found that
students who earned better grades in high school math or science courses than in English courses
were more likely to declare a STEM major. Extending the relevance of the comparative
advantage measure across different contexts, Stoet and Geary (2018) measured students’
comparative advantage using the Programme for International Student Assessment survey, the
world’s largest educational survey administered to high school students. Stoet and Geary (2018)
found that in all countries, girls’ relative strength in reading was greater than that of boys while
boys’ relative strength in math was greater than that of girls. While these studies are instructive,
there is more to understand about comparative advantage in studies of the STEM gender gap.
Specifically, this paper contributes to the comparative advantage literature by examining this
concept during the first year of community college.
First Year of Community College
This paper examines comparative advantage during the first year of community college
given that the first year is a critical time in students’ college trajectory (Johnson et al., 2007;
NSF, 2017). Students report feeling uncertain and even lost during the first year in college
(Hurtado et al., 2007). Unsurprisingly, STEM attrition occurs more during the first year relative
to later years (Chen & Soldner, 2013). For these reasons, several interventions aimed at
increasing college retention target early college years (e.g., Angrist, Autor, Hudson, & Pallais,
2014; Melguizo, Martorell, Chi, Park, & Kezar, 2018).
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Studies suggest that students who develop momentum in a particular subject during the
early stages of college are more likely to embark on and persist in the STEM pathway (Wang,
2015, 2017). Specifically, Wang (2013) found that underrepresented students who displayed
early math achievement were more likely to have higher math selfefficacy and subsequently
more likely to declare STEM as their major than White and Asian students who showed similar
achievement. In a different study, Wang (2015) examined students’ number of STEM credits
completed and the grades received in those courses during the first year of college. She found
that students who developed sufficient early STEM momentum had a higher likelihood of
attaining a Bachelor’s degree. Studies, therefore, suggest that the first year is a critical time point
for college students.
In summary, grades received in nonSTEM relative to STEM courses indicate students’
comparative advantage and may contribute to the STEM gender gap (RiegleCrumb et al., 2012).
Many studies demonstrated women’s advantage in reading relative to math (e.g., Card & Payne,
2017; Guiso, Monte, Sapienza, & Zingales, 2008; Reardon, Kalogrides, Fahle, Podolsky, &
Zarate, 2018; Stoet & Geary, 2018), but fewer studies examined whether comparative advantage
in a subject like reading can be a reason behind the STEM gender gap. Furthermore, among the
few studies that examined comparative advantage as an explanation, those studies
operationalized comparative advantage in the high school setting. Therefore, the present study
extends previous studies’ examination of comparative advantage in STEM by exploring this idea
in the community college setting.
Hypothesis
I begin with the assumption that female students should be just as likely to embark on and
persist in the STEM pathway as male students given equivalent high school academic
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preparation. Then, I examine whether female students divert from the pathway more than their
male peers. I make the following hypotheses:
1. LS and PS/E aspiring female students are as likely to persist in STEM as male students
given similar academic preparation.
2. Comparative advantage in STEM will predict persistence in STEM.
3. Female students’ comparative advantage in STEM during their first year of college will help
reduce or reverse any gender gap.
Data and Sample
The data used in this study are linked longitudinal transcript data obtained through
partnerships with a large, urban school district (LUSD) and a large, urban community college
district (LUCCD) in the same metropolitan area. This rich longitudinal data include students’
complete high school and community college transcript data, demographic information, and
placement test score information and outcomes. The sample comprises of students who entered
community colleges from 20052014 with outcomes observable through 2016. Appendix A.1
details how the STEM specific dataset was constructed.
I start with 68,491 LUSD students who enrolled in LUCCD between 20052012 and who
are not concurrent high school students (i.e., not dualenrolled). Out of the 68,491students, 3,771
(6%) are PS/Easpiring students, and 7,071 (10%) are LSaspiring students. Among the 3,771
PS/Easpiring students, only 19% (n=727) are women whereas among the 7,071 LSaspiring
students, 76% (n=5,392) are women.
To determine whether students are PS/Easpiring or LSaspiring, I create measures that
categorize students’ intended major as LS or PS/E. The transcript data include the name of the
major as well as the corresponding Taxonomy of Program (TOP) code. The TOP code represents
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numerical codes used at the state level to align local programs into similar program categories. In
contrast, the U.S. Department of Education classifies different majors and programs using the
Classification of Instructional Programs (CIP) codes. I use a crosswalk of TOP codes and CIP
codes published by the California Community College Chancellor’s Office and Wang’s (2016)
study on community college STEM pathway to classify different majors into LS or PS/E.
Appendix Table A.2 presents the crosswalk of the name of the program at the college, the TOP
codes, and the 2digit CIP codes implemented in this study.
As mentioned previously, students’ access to transferlevel courses are determined by
initial placement in math and English (Bailey, Jeong, & Cho, 2010; Fong, Melguizo, & Prather,
2015). Therefore, all analyses are conducted separately by initial placement levels. Again, initial
math placement is a strong predictor of how far students advance in their STEM education (Park
et al., 2018) and English placement is also predictive of students’ access to upperlevel
English/writingbased courses.
Therefore, I conduct separate analyses by LSaspiring and PS/Easpiring students and by
initial level of placement. Specifically, I conduct separate analyses on four samples: (1) 883
academically prepared PS/Easpiring students who placed in transferlevel or one level below
transferlevel in both math and English, (2) 2,938 academically underprepared PS/Easpiring
students who placed in two or more levels below transfer into developmental math and English,
(3) 1,094 academically prepared LSaspiring students who placed in transferlevel or one level
below transferlevel in both math and English, and (4) 5,977 academically underprepared LS
aspiring students who placed in two or more levels below transfer into developmental math and
English. In short, this study, by design, do not compare students who placed in transferlevel or
144
one level below transfer in math and English with students who placed in low levels of
developmental math and English.
Empirical Strategy
In this linked LUSDLUCCD dataset, I do not observe LUSD students if they dropped
out, took gap years, or entered a fouryear institution; I only observe LUSD graduates who
enrolled in one of the community colleges in LUCCD. Based on a report obtained from the
school district, about 4045% of LUSD graduates enroll in community colleges each year.
5
Therefore, the analytical method employed is propensity score matching (PSM) (Guo &
Fraser, 2010; Rosenbaum & Rubin, 1983, 1985). I use PSM to match women with
observationally similar men at the start of college. If all of the highly motivated, collegebound
female students attended fouryear institutions whereas highly motivated collegebound male
students decided to attend community colleges, I may artificially observe a larger STEM gender
gap. However, if two students are observationally equivalent at the start of college, I can be more
confident in attributing any divergence in the STEM pathway to factors occurring at college as
opposed to selfselection (Ganley et al., 2018). Given the availability of a rich set of pre
community college variables like measures of high school coursetaking and demographic
indicators, PSM is the method of choice.
Importantly, I do not use PSM to draw causal inference “but rather as a technique to
identify individuals in different groups—here, men and women—who share common individual
level precollege characteristics, thereby making the comparisons more transparent and less
reliant on statistical adjustment” (Ganley et al., 2018, pg.16). One way to account for self
selection is to assume a particular functional form and hold constant a rich set of covariates to
adjust for confounders that may bias differences in potential outcomes.
145
The benefit to using a propensity score !(#) rather than conditioning on covariate # is
that the researcher is freed from assuming a specific functional form (Ho, Imai, King & Stuart,
2007). Therefore, I use PSM as a nonparametric statistical adjustment technique that relies on
one less modeling assumption. I first match PS/Easpiring female students with observationally
similar PS/Easpiring male students and LSaspiring female students with observationally similar
LSaspiring male students using the MatchIt package in R (Ho, Imai, King, & Stuart, 2007,
2011). Using this preprocessed balanced dataset, I estimate a parametric model to estimate the
outcome equation (Green & Stuart, 2014). This method possesses the desirable “doublyrobust”
property. That is, if either the outcome regression or the propensity score model is correctly
specified, the estimation is consistent (Bang & Robins, 2005).
Rosenbaum and Rubin (1983) proved that if the potential outcomes are independent of
the treatment % conditional on p set of covariates, then conditioning on the propensity score
results in the same condition (i.e., #='(
)
,…(
,

.
012 34 (5
6
,5
)
)⊥%# then (5
6
,5
)
)⊥
%!(#)) . Because conditioning on a large number of covariates results in the problem of
dimensionality, the propensity score estimation conditions on the probability or the propensity of
treatment instead (Dehejia & Wahba, 2002; Guo & Fraser, 2010; Imbens & Rubin, 2015;
Rosenbaum & Rubin, 1983, 1985). I estimate the propensity score !(#) using a logistic
regression, specified in equation (1).
9:;3<[!(>?@A4BC09B)
D
] =F
6
+#H+I+J+K+L
D
(1)
Essentially, I match students using the following covariates informed by the conceptual
framework:
• High school math and science preparation indicators. Early exposure and achievement in
math and science courses were determined to be critical in both developing students’
146
aspirations in STEM fields and establishing the academic foundation necessary to
successfully pursue STEM in college. Therefore, # represents the following high school
academic preparation indicators such as: taking at least three years of UC/CSU approved
math courses and two years of UC/CSU approved science courses; the number of AP math
and science courses as well as the number of AP English and humanities courses; whether
students took physics or calculus in high school (irrespective of grade); and high school
GPA.
• Demographic variables. Also included in # are demographic indicators. Specifically, I
include a measure of whether students were in an AP or an Honors track. Moreover, students
who are designated into special education programs or have limited English proficiency are
often placed in low ability track and have limited opportunities to take advanced courses
(Klopfensten, 2004). Therefore, I hold constant limited English proficiency and special
education status. Also, I include measures of race.
• Transfer Intent. Students’ transfer intent is an important correlate to actual transfer (Cohen,
1994). Therefore, I adjust for students’ goals for attending community college (e.g., to obtain
a vocational certificate, complete an Associate’s degree, transfer, etc).
• Fixed effects. Finally, I include high school fixed effects (M), college fixed effects (N), and
year fixed effects (O) . In other words, I hold constant groupspecific, time invariant effects of
attending a specific LUCCD college, graduating from a specific LUSD high school and
enrolling during a particular year. Any unobserved, timeinvariant omitted variables at the
high school, college, or year level are accounted for in this model.
To estimate the outcome equation, I estimate equations (2) and (3) using Stata 15.
5
DP
= H
6
+H
)
!(>?@A4BC09B
Q
)
DP
+#H+J+K+L
DP
(2)
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5
DP
= H
6
+H
)
!'>?@A4BC09B
Q

DP
+H
R
S:C!T2U>?@A
DP
+
H
V
[S:C!T2U>?@A∗!'>?@A4BC09B
Q

DP
]+#H+J+K+L
DP
(3)
5
DP
represents the following outcomes: time to first transferable STEM course (in
quarters), the number of transferable math (science) units attempted and completed in three
years, the overall number of transferable math/science units attempted and completed, and the
number of STEM courses completed out of all STEM courses attempted.
S:C!T2U>?@A refers to whether students have a higher, lower, or equal STEM GPA
relative to nonSTEM GPA during the first year of community college. Students’ first year
STEM GPA is the weighted average of grades and course units in health/biology, chemistry,
math, statistics, engineering, physics, and/or physical science during the first year. Students’ first
year nonSTEM GPA is the weighted average of grades and course units in English/reading,
foreign language, speech, social science, and humanities. I subtract each students’ nonSTEM
GPA from students’ STEM GPA to create the comparative advantage indicator. Students with a
comparative advantage in STEM have a positive value, students with equal comparative
advantage have a value of “0” and students with a comparative advantage in nonSTEM have a
negative value. H
V
represents the interaction of gender and the measure of comparative
advantage. # includes the same variables as mentioned previously. Finally, the model also
includes college fixed effects (N) and year fixed effects (O).
Once I estimate the propensity score, I visually inspect whether there is sufficient
common support between the groups. First, I observe the densities of the propensity score to
examine the region of common support across the two groups. This check ensures that there is
sufficient overlap between treatment and control groups (Murnane & Willett, 2011). Appendix
A.3 shows the densities of the propensities across the four treatment and control groups. These
figures display that there is sufficient overlap between the treated and control units.
148
Nearest Neighbor Matching without Replacement
Next, I use nearest neighbor matching with a prespecified caliper and without
replacement. This nearest neighbor matching algorithm is a distancebased algorithm that
minimizes the distance function of the control unit and therefore finds the closest control unit to
match with the treatment unit (Guo & Fraser, 2010). In nearest neighbor matching with
replacement, the treated units are matched upon searching the entire set of control units and
control units can match with more than one treatment units. In contrast, matching without
replacement does not allow control units to serve as controls for multiple treatment observations.
The drawback to matching with replacement is the increase in variance whereas the benefit is the
potential reduction in bias of the matching estimator. The increase in variance is due to the
repeated use of a handful of “very good” control units to match with the treatment unit unlike in
the matching algorithm without replacement. I define a caliper such that caliper Y ≤ 0.25^,
where ^ represents the propensity score estimation’s standard deviation (see e.g., Rosenbaum &
Rubin, 1985). By specifying a caliper, the algorithm selects the first treated participant i and
finds j as a match for i participant if the absolute difference of propensity scores between i and j
falls into a predetermined caliper c (Guo & Fraser, 2010).
Finally, I check the groups’ balance across the matched covariates. A commonly used
measure of whether the “treatment” and “control” groups are balanced across the distribution of
covariates is the standardized mean difference (SMD) (Austin, 2009).
6
This measure examines
the mean difference in, for example, the percentage of students who took Honors or AP courses
in high school within each group divided by the pooled standard deviation. The SMD assesses
how different the two groups are after matching based on the estimated propensity score.
149
In all analyses, I estimate the average treatment effect on the treated (ATET). The ATET
is the conditional expectations of the potential outcomes among those who received the
treatment.
7
The ATET is the estimate of interest as opposed to the average treatment effect
because the estimation results are most relevant to PS/E or LSaspiring students as opposed to
all community college students.
Results
Comparison with LUSD Graduates and California High School Graduates
To get a sense of how community college enrollees compare to all LUSD graduates and
all California high school graduates, I reference publicly available data from the California
Department of Education to produce Table 1. Table 1 indicates that, relative to all high schools
in California, LUSD is a diverse school district where a larger proportion of students are
categorized as socioeconomically disadvantaged, students of color, and English Learners. In
addition, fewer LUSD students scored “proficient” or “advanced” in state standardized tests
relative to school districts in the state; therefore, students from LUSD performed below the state
average on several academic indicators.
The community college bound students in this study (i.e., “LUSDLUCCD students”) are
more disadvantaged and performed below average on academic measures relative to both LUSD
and California high school graduates. The race and gender breakdown of the LUSDLUCCD
sample and the LUSD graduates are similar with over 80% of students identified as Black or
Hispanic students. However, a higher proportion of LUSDLUCCD students are eligible for free
or reducedpriced lunch than all LUSD graduates. This suggests that LUSD graduates who
attended LUCCD have lower income levels, on average, compared to all LUSD graduates. In
150
terms of academic preparation, fewer LUSDLUCCD students scored proficient or advanced in
the math and science state standardized test.
Further disaggregating the LUSDLUCCD sample by gender, Table 1 shows that female
and male students are similar along various racial and socioeconomic characteristics. Yet, more
male students scored proficient or advanced in math and science state standardized tests
compared to female students.
Pre and PostMatching Balance
Table 2 shows the descriptive statistics of the prematched and postmatched PS/E
students and Table 3 shows the descriptive statistics of the prematched and postmatched LS
aspiring students. Each table shows how the distribution of the covariates differ pre and post
match using the estimated propensity score. There are a few common trends across all four pre
matched student samples. Examining two high school courses correlated with entering STEM
fields – physics and calculus, more men than women took physics in high school whereas the
calculus enrollment pattern is mixed across the four prematched samples. Yet, women, on
average, graduated with higher high school GPA than men across all four prematched samples.
These differences provide additional evidence for the need to statistically adjust for covariate
imbalance between male and female students.
After male and female students are statistically matched to one another, these differences
are no longer apparent. The standardized mean differences fall below one and in most cases are
close to zero, indicating good balance between male and female students across all four matched
samples.
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Is there a STEM gender gap by LS and PS/E subfields and by initial level of academic
preparation in community college?
To answer the first research question, I examine the STEM gender gap among the four
samples. Again, in each student sample, female students are matched to male students based on
prior preparation in math and science, key demographic variables, the high school attended, the
college attended, and the year in which they began college.
Table 4 indicates no evidence of a STEM gender gap among academically prepared
PS/Easpiring students. That is, PS/Easpiring women who placed in upperlevels of math and
English were just as likely to persist in STEM as PS/Easpiring men. In contrast, PS/Easpiring
women who placed in low levels of developmental math and English were less likely to attempt
transferable math and science units by their third year than similar PS/Easpiring men. When
examining the overall attempt and completion of math and science courses, I observe a persistent
STEM gender gap. Specifically, academically underprepared PS/Easpiring female students, on
average, attempted and completed two fewer transferable science and math units than
underprepared PS/Easpiring male students.
Among academically prepared LSaspiring students, women, on average, attempted about
two fewer math units by their third year in college. Moreover, the gender gap in transferable
math attainment persisted in the long run. Although the negative coefficients suggest that there
may also be a gender gap in transferable science attainment, the confidence intervals are too
large to indicate statistical significance. Thus, among academically prepared LSaspiring
students, the gender gap is only evident in math attainment.
Finally, academically underprepared LSaspiring female students were less likely to
accumulate both transferable math and science units than their male counterparts. However, the
152
magnitude of the coefficients is small indicating that underprepared LSaspiring students
generally attempted very few transferable STEM courses.
In summary, I find no evidence of a STEM gender gap among academically prepared
PS/Easpiring students. In contrast, I observe a STEM gender gap among academically
underprepared PS/Easpiring students and prepared and underprepared LS students. Next, I
examine whether comparative advantage is a mechanism behind the STEM gender gap.
Does comparative advantage in STEM during the first year of community college predict
persistence in STEM?
Table 5 indicates that each additional point increase in comparative advantage is
associated with persistence in STEM, but mostly in the shortterm. In general, students’
comparative advantage during their first year was not a strong predictor of STEM persistence in
the longterm. The only exception is when examining underprepared PS/Easpiring students. For
underprepared PS/Easpiring students, comparative advantage in STEM was associated with
increased attempt in transferable science courses both in the short and longterm. Finally, the
magnitude of the coefficients suggests that comparative advantage influenced science attainment
more than math attainment.
Next, I present findings on whether the gender gap narrowed as students demonstrate
comparative advantage in STEM during their first year in community college.
Does the STEM gender gap in LS and PS/E narrow as students demonstrate comparative
advantage in STEM during their first year of community college?
Initially, I hypothesized that comparative advantage in STEM during the first year would
reduce or even reverse the STEM gender gap. In Table 6, Panel A I find some evidence
supporting this hypothesis as academically prepared PS/Easpiring women attempted more math
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courses with indication that their comparative advantage is in STEM. The positive interaction
term suggests that academically prepared PS/Easpiring women with a comparative advantage in
STEM took more transferable math units than academically prepared PS/Easpiring men.
However, comparative advantage did not affect women any more or any less than men long
term. Overall, the table suggests that comparative advantage operates similarly for academically
prepared male and female students.
However, the findings differ among PS/Easpiring students who placed in low levels of
developmental math and English. With each additional point increase in comparative advantage,
academically underprepared PS/Easpiring men attempted and completed more transferable
science units than underprepared PS/Easpiring women. The negative and statistically significant
female coefficient and the interaction terms suggest that comparative advantage in STEM
operated negatively for academically underprepared PS/Easpiring women. Specifically, female
students attempted fewer transferable science units by year three than male students with each
additional point increase in comparative advantage in STEM. This gender gap in the attempt and
completion of transferable science courses remained evident in the longterm.
Table 7 shows the interaction results among observationally equivalent LSaspiring male
and female students who initially placed in upper and lowerlevels of math and English. Among
academically prepared LSaspiring students, comparative advantage in STEM operated similarly
for men and women. Among underprepared LSaspiring students, there is some evidence that
comparative advantage in STEM exacerbated the math attempt rate. However, it is also worth
noting, again, that the magnitude of the coefficients is small when examining underprepared LS
aspiring students.
154
Given the general insignificance of the interaction terms among LSaspiring students, I
only present graphs for PS/Easpiring students and refer to the appendix for interaction graphs of
LSaspiring students. Echoing the results in Table 7, the appendix graphs indicate that LS
aspiring male and female students similarly persisted in STEM irrespective of their comparative
advantage (see Appendix A.4 and A.5).
Graphical Representation of the Findings
Figure 2 displays how the men and women slopes differ depending on the value of
comparative advantage for academically prepared PS/Easpiring students. Corresponding to
Table 6, the math attempt and completion graphs indicate that academically prepared PS/E
aspiring women whose comparative advantage is in STEM attempted more transferable math
units than PS/Easpiring men, evidenced in steeper positive slopes. The remaining graphs
indicate that male and female students similarly persisted in STEM irrespective of their
comparative advantage.
In contrast, Figure 3 shows that underprepared women attempted and completed fewer
transferable science courses than underprepared men despite their comparative advantage in
STEM. Specifically, men with a definite comparative advantage in STEM (i.e., a value of “4”)
attempted twelve transferable science units by the third year of enrollment whereas women with
a definite comparative advantage in STEM attempted eight transferable science units. This gap
translates to four transferable science units or attempting about one fewer transferable science
course by the third year. This gender gap in the attempt of science courses doubles to eight units
in the longterm, equating to women attempting two fewer transferable science courses than
men. Therefore, academically underprepared PS/Easpiring women completed fewer science
155
units than academically underprepared PS/Easpiring men despite their comparative advantage in
STEM.
Sensitivity Analyses
In order to examine whether the main results are robust to different model specifications,
I reestimate my models using two different model specifications: ordinary least squares (OLS)
and inverseprobability weighting (IPW). Each model adjusts for the same covariates in the PSM
specification and uses cluster robust standard errors. As shown in Appendix A.6 through A.9, the
direction, magnitude, and statistical significance are all qualitative similar to the main results and
the story remains the same. In fact, there are more statistically significant relationships using
OLS and IPW models. The PSM results, therefore, can be considered conservative estimates
across model specifications.
Discussion
Ongoing concerns regarding the lack of diversity in STEM fields has generated
substantial scholarship and discussion on ways to usher underrepresented students like women
into STEM fields. While there exists ample scholarship on the STEM gender gap at fouryear
institutions, there exists scant empirical evidence on the STEM gender gap at community
colleges. Therefore, the present study first examined whether a STEM gender gap exists at
community colleges, disaggregated by LS and PS/E. Then, the study explored a mechanism
potentially driving the gap called comparative advantage, a notion that students make future
educational decisions based on grades received in STEM courses compared to nonSTEM
courses. The hypothesis was that women with a comparative advantage in STEM would be just
as if not more likely to persist in STEM relative to men.
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First, I found a STEM gender gap in math attainment among academically prepared LS
aspiring students. One explanation driving this finding may be that LSaspiring women have less
incentives to take multiple transferable math courses. In this community college district, while
upperlevel PS/E courses have math prerequisites, upperlevel LS courses often do not have math
prerequisites. As such, women may have opted out of math courses above and beyond what is
required for their major. Another explanation may be that more women switched to applied LS
majors that typically demand fewer math courses than men. Supporting this idea, Bahr et al.
(2017) noted that women diverted from their prescribed math curriculum to statisticsbased
pathways at higher rates than men at community colleges. This study pointed to the existence of
a gender gap in math attainment among academically prepared LSaspiring students. Future
research should first investigate whether women are switching to applied LS majors at higher
rates than men and then confirm that LSaspiring women are completing the math requirements
for their major similarly as LSaspiring men.
Among academically underprepared LSaspiring students, women were less likely to
accumulate not only transferable math units but also transferable science units. However, the
magnitude of the STEM gender gap was small as few academically underprepared LSaspiring
students attempted and completed transferable math and science courses.
Before unpacking results pertaining to academically underprepared PS/Easpiring
students, it is worth emphasizing that PS/Easpiring women persisted in STEM at similar rates as
men if they initially placed in upperlevels of math and English. In fact, there was suggestive
evidence that academically prepared PSEaspiring women outpaced men if their comparative
advantage was in STEM. Still, women who aspired to major in PS/E comprised of only 19% of
the PS/Easpiring sample, suggesting a gender gap in initial aspiration. Previous studies found
157
that academically prepared women were less likely to major in STEM than academically
prepared men (Wang, Eccles, & Kenny, 2013). A discussion on raising academically prepared
women’s STEM aspirations is beyond the scope of this paper, but this study underscores that low
initial interest in PS/E among women deserves ongoing scrutiny.
Unlike academically prepared women in PS/E, academically underprepared women in
PS/E were more likely to attrit from the STEM pathway than academically underprepared men at
community colleges. Moreover, comparative advantage in STEM—rather than reducing the gap
—widened it. That is, underprepared PS/Easpiring women attempted fewer transferable science
courses relative to underprepared PS/Easpiring men, indicating that women undercapitalized on
their comparative advantage in STEM.
In practical terms, underprepared PS/Easpiring women attempted one to two fewer
transferable science courses than underprepared men despite their comparative advantage in
STEM. This is a significant deterrent for PS/Easpiring students if they hope to eventually
transfer to a fouryear institution. To be considered for transfer at one of the California State
Universities with a major in Computer Science, for example, PS/Easpiring students must
complete at least 60 semester units, of which 18 must be transferable STEM units.
8
And, 18
transferable STEM units equate to about four to five STEM courses. Therefore, attempting
approximately two fewer transferable science courses out of four or five STEM courses required
for transfer is a considerable setback especially for PS/Easpiring women aiming to transfer to a
university.
Here, I offer possible explanations behind the widening gender gap in science attainment
among underprepared PS/Easpiring female students with a comparative advantage in STEM.
For one, women who placed in low levels of developmental math and English, on average, may
158
have started college with more uncertainty about their abilities or potential for success in STEM
fields than men. Empirical research supports the notion that women have disproportionately
lower STEM selfefficacy than men (Eccles, 1994; Nix et al., 2015; Shi, 2018; Stoet & Geary,
2018). Therefore, performing relatively well during the first year may not have negated women's
initial low confidence in their STEM abilities. Another reason may be due to women’s
perception of men’s performance and fit in STEM fields. Science is largely regarded as a
masculine field (Blickenstaff, 2005; Kim, Sinatra, & Seyranian, 2018) and women may be more
susceptible to feeling marginalized and excluded in science classrooms by the sheer lack of
women representation (see e.g., Carrell, Page, & West, 2010; Li & Koedel, 2017; Solanki & Xu,
2018). Furthermore, studies suggest that women in PS/E majors are more influenced by the
performance of their peers than men in PS/E majors (Ost, 2010). Rather than comparing their
performance in nonSTEM courses relative to STEM courses (internal comparison), perhaps
women were comparing their performance relative to their male counterparts (external
comparison).
Policy implication
The findings of this study imply that community colleges should consider providing
customized support to aspiring women scientists and engineers who are identified as
academically underprepared at the start of college. Given that this study found no evidence of a
STEM gender gap among men and women in PS/E who were identified as academically
prepared, colleges can marshal their resources towards supporting academically underprepared
women in PS/E.
If the STEM gender gap is indeed due to external comparisons in which women are
comparing one’s performance to men rather than to one’s relative performance in various
159
subjects, colleges may want to consider ways to buffer against negative social comparisons. At
Sacramento City College in California, for example, faculty are spearheading a program where
women interested in Computer Information Sciences are cohorted as a way to provide
community and support from start to graduation. Cohorting is a model used to group students so
that they go through a common educational experience. As empirical research suggests that
effective cohorting of students helps its members feel a greater sense of belonging (Barnett,
Basom, Yerkes, & Norris, 2000), cohorting may be a helpful strategy to increase women’s sense
of belonging in STEM fields.
Another viable approach may be to expand programs like Mathematics, Engineering, and
Science Achievement (MESA). This program supports lowincome STEMaspiring students who
placed in elementary algebra or below (i.e., two or more levels below transferlevel math) in
community college. MESA provides a suite of complementary support system including career
advising, connections with industry professionals, and workshops. However, the program does
not provide customized support and advice for PS/Easpiring women. Colleges that are
implementing this program may, therefore, want to place special attention towards
underprepared women in PS/E.
Similar to expanding programs like MESA, colleges may want to experiment with
interventions like STEM learning communities (Carrino & Gerace, 2016). A learning community
enhances the social component of learning by complementing courses with peer academic
mentoring, rich cocurricular activities, and in some cases, common housing. Not only would
interactions with STEM professionals, faculty, and/or advisors help females in PS/E majors gain
the necessary information to persist in STEM, it may further help students develop their STEM
identity (Carrino & Gerace, 2016). Studies on various learning community programs found that
160
participating in learning communities can boost sense of mattering and help marginalized
students develop an academic identity (Kitchen, Hypolite, & Kezar, 2018; Melguizo, Martorell,
Chi, Park, & Kezar, 2018). In addition, preliminary evidence note that STEMfocused learning
communities can help women develop a STEM identity within a structured and supportive
environment (Carrino & Gerace, 2016). While this approach merits further examination, there is
some empirical evidence supporting its efficacy.
Finally, these strategies can be structured to complement existing efforts like the guided
pathways reform (Bailey, Jaggars, & Jenkins, 2015), a measure to provide a more structured
educational experience for community college students. Students are provided with course
sequence and guided support so they can successfully attain their college goals. As part of the
guided pathways effort, colleges can specifically monitor the progress of different cohorts of
underprepared PS/Easpiring women. In particular, colleges should monitor whether PS/E
aspiring women disproportionately take fewer science courses than men during the first few
years of college and encourage them to persist in science. Taken together, the findings of this
study highlight the need to help underprepared PS/Easpiring women feel more like they belong
in STEM fields.
Conclusion
As the share of jobs that require STEM skills continue to grow, community colleges play
a key role in diversifying the talent pool in STEM fields. These institutions provide access to
gateway courses and have low tuition rates making them appealing to underserved students. The
findings of this study inform ways to increase representation of women – especially women of
color – in PS/E fields who are initially identified as academically underprepared. Future studies
should probe the various factors that lead to students’ internalization of their comparative
161
advantage in STEM. For instance, students’ first year STEM GPA in college is only one of many
different types of feedback students receive regarding their fit in STEM fields from preK to
college. Future studies should examine how, where, and from whom students receive these types
of feedback and their subsequent impact on STEM persistence.
162
Endnote
1
Author’s calculation using publicly available data from the National Science Foundation. Retrieved from:
https://www.nsf.gov/statistics/2017/nsf17310/static/data/tab41.pdf. Available upon request. I include health and
engineering technologies as part of Life Science fields.
2
I use male/men and female/women interchangeably. In cases where I make male/female distinctions, it is to
emphasize that they are male and female students.
3
Students are also referred to take the English as a Second Language (ESL) test if English is not their dominant
language. Less than 2% of the students in this study were referred to take the ESL test.
4
Recently in 2017, the state passed Assembly Bill (AB) 705 which requires California community colleges to
incorporate high school academic indicators when placing students (Burks, 2016). Specifically, colleges are required
to move away from placement tests and use either high school GPA, prior coursework, and/or other relevant
transcript information to place students into courses.
5
This information is obtained from the National Student Clearinghouse summary report.
6
For continuous covariates, the formula to calculate the SMD is:
2 =
_
`abc`
−_
Pef`aeg
hi
`abc`
R
+i
Pef`aeg
R
/2
For dichotomous variables, the formula to calculate the SMD is:
2 =
!
`abc`
−!
Pef`aeg
h!
`abc`
(1−!
`abc`
)+!
Pef`aeg
(1−!
Pef`aeg
)/2
7
This equation shows that the ATET is the average difference those in the treated and control groups for those who
receive/are impacted by the treatment (% =1). T?@? =@
,(l)
[@(5!(_),% =1)−@(5!(_),% =0)% =1]
8
This information was obtained through the assist.org website. The specific criteria vary depending on the major.
For example, to transfer with a Biology major, students need 40 majorspecific units and in Biochemistry students
need 44 majorspecific units.
163
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Tables
Table 1
Comparison of California Graduates, LUSD Graduates and the LUSDLUCCD Sample, 201213
Note. LUSD = Large, Urban School District; LUCCD = Large, Urban Community College District. The data under
LUSD column comes from publicly available from the California Department of Education for the 201213 school
year. The data under LUSDLUCCD column comes from the school districts. The LUSDLUCCD column limits the
sample to LUCCD entering cohort of 2013 and 2014 and who are not concurrent high school students. Because the
linked data include students who enrolled within three years of their graduation, the 2013 and 2014 cohort include
high school graduates between 20112014. 24% of the observations for the FRPL indicator is missing; therefore,
this number may not be an accurate representation. CST refers to the California standardized test. Until 2013,
California's Standardized Testing and Reporting (STAR) program measured the achievement of California content
standards for grades two through eleven. STAR results include Englishlanguage arts and mathematics in grades 2
11 and science in grades 5 and 811. Therefore, math and science CST scores are a reflection of the courses in which
the student is enrolled. This table refers to 10th and 11th grade math and science CST results. There are five
benchmarks that indicate a student's proficiency on the CST. "Proficient" or "Advanced" indicates that a student is
meeting or exceeding state standards, which is the desired achievement goal for all students.
CA LUSD Female Male Total
Female 51% 52%   50%
Asian 14% 8% 5% 7% 6%
Black 6% 9% 10% 10% 10%
Hispanic 47% 72% 74% 71% 72%
Other 3% 2% 5% 5% 5%
White 30% 9% 6% 7% 6%
Free and reducedprice lunch 60% 75% 92% 91% 92%
Limited English Proficient categorization 21% 27% 13% 15% 14%
Honors or AP Enrollee N/A N/A 9% 10% 10%
AP Exam Takers 15% 7% N/A  N/A
AP Exam Takers with Score of 3 + 17% 12% N/A  N/A
Scoring at Proficient or Advanced in Math CST 50% 45% 7% 10% 9%
Scoring at Proficient or Advanced in Science CST 59% 52% 17% 24% 21%
N 422177 37234 6487 6581 13068
LUSDLUCCD
174
Table 2
Pre and PostMatching Balance of PS/EAspiring Students
Note. SMD = standardized mean difference. Sample limited to those who took at least one STEM course during their first year. Concurrent high school students
are not included.
Variables Male Female SMD Male Female SMD Male Female SMD Male Female SMD
Mean or % Mean or % Mean or % Mean or % Mean or % Mean or % Mean or % Mean or %
Asian (%) 0.13 0.16 0.09 0.16 0.17 0.04 0.09 0.12 0.07 0.12 0.12 0.01
Black (%) 0.04 0.04 0.00 0.04 0.03 0.04 0.08 0.11 0.10 0.09 0.10 0.04
Hispanic (%) 0.60 0.51 0.19 0.49 0.49 0.01 0.67 0.61 0.13 0.59 0.61 0.04
White (%) 0.17 0.20 0.08 0.21 0.21 0.00 0.09 0.10 0.05 0.11 0.10 0.04
Other (%) 0.06 0.08 0.11 0.10 0.10 0.00 0.07 0.07 0.00 0.08 0.07 0.06
Took Honors/AP Courses in High School (%) 0.30 0.28 0.04 0.26 0.30 0.09 0.08 0.08 0.01 0.06 0.08 0.07
Special Education (%) 0.02 0.01 0.09 0.01 0.01 0.07 0.12 0.06 0.22 0.06 0.06 0.01
Limited English Proficiency (%) 0.01 0.05 0.23 0.01 0.03 0.16 0.18 0.18 0.00 0.18 0.18 0.01
Took Calculus in High School (%) 0.13 0.14 0.05 0.14 0.15 0.02 0.04 0.04 0.03 0.04 0.04 0.01
Took Physics in High School (%) 0.45 0.39 0.13 0.44 0.41 0.06 0.22 0.21 0.02 0.22 0.21 0.03
% UC/CSU Eligible 0.67 0.72 0.09 0.79 0.74 0.13 0.34 0.39 0.10 0.40 0.39 0.01
# of AP Math/Sci Taken 1.21 1.25 0.02 1.06 1.32 0.14 0.36 0.38 0.02 0.37 0.39 0.01
# of AP English/Humanities Taken 1.95 2.49 0.19 2.52 2.54 0.01 0.67 0.98 0.17 0.95 1.00 0.03
HS GPA 2.72 3.11 0.68 3.09 3.09 0.01 2.32 2.55 0.36 2.55 2.55 0.00
N 667 166 146 146 2377 561 546 546
PostMatch
PS/EAspiring Students Placed in Upper Levels PS/EAspiring Students Placed in Lower Levels
PreMatch PreMatch PostMatch
175
Table 3
Pre and PostMatching Balance of LSAspiring Students
Note. SMD = standardized mean difference. Sample limited to those who took at least one STEM course during their first year. Concurrent high school students
are not included.
Variables Male Female SMD Male Female SMD Male Female SMD Male Female SMD
Mean or % Mean or % Mean or % Mean or % Mean or % Mean or % Mean or % Mean or %
Asian (%) 0.40 0.26 0.30 0.37 0.34 0.07 0.27 0.11 0.43 0.26 0.20 0.14
Black (%) 0.02 0.03 0.06 0.02 0.02 0.02 0.06 0.12 0.19 0.06 0.11 0.15
Hispanic (%) 0.38 0.51 0.26 0.40 0.44 0.07 0.54 0.66 0.26 0.54 0.57 0.06
White (%) 0.15 0.14 0.02 0.15 0.16 0.02 0.07 0.05 0.05 0.07 0.06 0.01
Other (%) 0.05 0.05 0.02 0.05 0.05 0.03 0.06 0.06 0.02 0.06 0.05 0.04
Took Honors/AP Courses in High School (%) 0.27 0.18 0.20 0.24 0.23 0.01 0.06 0.03 0.15 0.06 0.06 0.01
Special Education (%) 0.02 0.01 0.09 0.01 0.01 0.03 0.08 0.06 0.05 0.08 0.08 0.01
Limited English Proficiency (%) 0.01 0.01 0.03 0.01 0.01 0.06 0.16 0.15 0.03 0.17 0.17 0.00
Took Calculus in High School (%) 0.09 0.07 0.06 0.08 0.08 0.02 0.02 0.01 0.11 0.02 0.02 0.01
Took Physics in High School (%) 0.36 0.32 0.09 0.35 0.34 0.02 0.19 0.15 0.11 0.19 0.18 0.03
% UC/CSU Eligible 0.71 0.70 0.03 0.71 0.71 0.01 0.35 0.34 0.01 0.35 0.35 0.00
# of AP English/Humanities Taken 1.08 0.91 0.10 1.02 1.10 0.04 0.28 0.19 0.10 0.27 0.26 0.01
# of AP Math/Sci Taken 2.15 2.39 0.09 2.22 2.37 0.06 0.72 0.77 0.03 0.72 0.79 0.04
HS GPA 2.86 3.02 0.31 2.91 2.93 0.04 2.35 2.44 0.14 2.36 2.39 0.05
N 392 702 325 325 1287 4690 1264 1264
PreMatch PostMatch
LSAspiring Students Placed in Upper Levels LSAspiring Students Placed in Lower Levels
PreMatch PostMatch
176
Table 4
Gender Gap in STEM Persistence, Four Matched Samples
Note. Each panel and column combination represent different regression results. STEMaspiring male and female students were matched based on the following
covariates: took honors/AP courses in high school, special education status, limited English proficiency status, took calculus in high school, took physics in high
school, UC/CSU eligible, # of AP math/sci taken, # of AP English/humanities taken, total # of AG math and science courses, HS GPA, high school fixed
effects, year fixed effects, and college fixed effects.. Panels A and C include STEMaspiring students who placed into transfer level (collegelevel) or one level
below transfer level in math and English. Panels B and D include STEMaspiring students who placed into lower levels of developmental math and English.
Cluster robust standard errors at the college level are in parentheses. This doublyrobust estimation unlinks the outcome regression from the propensity score
estimation and requires that only one of the two estimations are correct for the results to be consistent.
+ p<0.10, * p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Quarters Until
First
Transferable
Math/Sci Since
Math
Assessment
Transferable
Math Units
Attempted by
Year Three
Transferable
Math Units
Completed by
Year Three
Transferable
Science Units
Attempted by
Year Three
Transferable
Science Units
Completed by
Year Three
Total
Transferable
Math Units
Attempted
Total
Transferable
Math Units
Completed
Total
Transferable
Science Units
Attempted
Total
Transferable
Science Units
Completed
A. PS/EAspiring Students Placed in Transfer or One LBT in Math & English
PS/E Female 0.36 0.68 0.58 0.73 0.23 0.39 0.08 0.06 0.68
(0.23) (0.89) (0.76) (1.37) (1.27) (0.65) (0.38) (2.42) (2.22)
N 292 292 292 292 292 292 292 292 292
B. PS/EAspiring Students Placed in Two+ LBT in Math & English
PS/E Female 0.54 0.49 0.25 1.88** 1.58*** 1.54* 0.74 2.28** 2.04***
(0.38) (0.27) (0.21) (0.38) (0.27) (0.64) (0.46) (0.50) (0.36)
N 1092 1092 1092 1092 1092 1092 1092 1092 1092
C. LSAspiring Students Placed in Transfer or One LBT in Math & English
LS Female 0.96+ 1.72*** 1.33*** 1.35 1.16 2.31*** 1.83*** 0.89 1.34
(0.50) (0.14) (0.10) (0.99) (0.95) (0.39) (0.31) (1.96) (1.67)
N 650 650 650 650 650 650 650 650 650
D. LSAspiring Students Placed in Two+ LBT in Math & English
LS Female 0.14 0.23*** 0.15** 0.61* 0.43* 0.87** 0.48*** 0.67 0.66+
(0.16) (0.02) (0.04) (0.20) (0.13) (0.20) (0.07) (0.46) (0.32)
N 2528 2528 2528 2528 2528 2528 2528 2528 2528
177
Table 5
Relationship between Comparative Advantage and STEM Persistence, Four Matched Samples
Note. Each panel and column combination represent different regression results. STEMaspiring male and female students were matched based on the following
covariates: took honors/AP courses in high school, special education status, limited English proficiency status, took calculus in high school, took physics in high
school, UC/CSU eligible, # of AP math/sci taken, # of AP English/humanities taken, total # of AG math and science courses, HS GPA, high school fixed
effects, year fixed effects, and college fixed effects.. Panels A and C include STEMaspiring students who placed into transfer level (collegelevel) or one level
below transfer level in math and English. Panels B and D include STEMaspiring students who placed into lower levels of developmental math and English.
Cluster robust standard errors at the college level are in parentheses. This doublyrobust estimation unlinks the outcome regression from the propensity score
estimation and requires that only one of the two estimations are correct for the results to be consistent.
+ p<0.10, * p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Quarters Until
First
Transferable
Math/Sci Since
Math
Assessment
Transferable
Math Units
Attempted by
Year Three
Transferable
Math Units
Completed by
Year Three
Transferable
Science Units
Attempted by
Year Three
Transferable
Science Units
Completed by
Year Three
Total
Transferable
Math Units
Attempted
Total
Transferable
Math Units
Completed
Total
Transferable
Science Units
Attempted
Total
Transferable
Science Units
Completed
A. PS/EAspiring Students Placed in Transfer or One LBT in Math & English
Comparative Advantage 0.23** 0.83** 0.71* 1.09** 1.06*** 0.43 0.07 0.93 0.89+
(0.05) (0.24) (0.22) (0.24) (0.17) (0.52) (0.29) (0.52) (0.47)
N 292 292 292 292 292 292 292 292 292
B. PS/EAspiring Students Placed in Two+ LBT in Math & English
Comparative Advantage 0.10 0.32** 0.24*** 0.75*** 0.71*** 0.59+ 0.41+ 0.91** 0.77**
(0.10) (0.07) (0.03) (0.10) (0.08) (0.28) (0.19) (0.26) (0.17)
N 1092 1092 1092 1092 1092 1092 1092 1092 1092
C. LSAspiring Students Placed in Transfer or One LBT in Math & English
Comparative Advantage 0.36*** 0.19* 0.16* 1.20** 1.16** 0.09 0.01 0.44 0.75
(0.04) (0.06) (0.06) (0.26) (0.24) (0.13) (0.09) (0.40) (0.46)
N 650 650 650 650 650 650 650 650 650
D. LSAspiring Students Placed in Two+ LBT in Math & English
Comparative Advantage 0.11+ 0.11** 0.08** 0.42** 0.37** 0.15* 0.11+ 0.46+ 0.40
(0.05) (0.03) (0.02) (0.10) (0.10) (0.07) (0.06) (0.25) (0.22)
N 2528 2528 2528 2528 2528 2528 2528 2528 2528
178
Table 6
Differential Effect of Comparative Advantage and Gender on STEM Persistence, Matched PS/E Sample
Note. Each panel and column combination represent different regression results. Panel A include PS/Easpiring students who placed in transfer level or one level
below transfer level in math and English. Panel B includes PS/Easpiring students who placed in two or more levels below transfer level in math and English.
Comparative advantage is the difference between students’ nonSTEM GPA and STEM GPA. PS/Easpiring male and female students were matched based on
the following covariates: took honors/AP courses in high school, special education status, limited English proficiency status, took calculus in high school, took
physics in high school, UC/CSU eligible, # of AP math/sci taken, # of AP English/humanities taken, total # of AG math and science courses, HS GPA, high
school fixed effects, year fixed effects, and college fixed effects. Cluster robust standard errors at the college level are in parentheses. This doublyrobust
estimation unlinks the outcome regression from the propensity score estimation and requires that only one of the two estimations are correct for the results to be
consistent.
+ p<0.10, * p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Quarters Until
First
Transferable
Math/Sci Since
Math
Assessment
Transferable
Math Units
Attempted by
Year Three
Transferable
Math Units
Completed by
Year Three
Transferable
Science Units
Attempted by
Year Three
Transferable
Science Units
Completed by
Year Three
Total
Transferable
Math Units
Attempted
Total
Transferable
Math Units
Completed
Total
Transferable
Science Units
Attempted
Total
Transferable
Science Units
Completed
A. PS/EAspiring Students Placed in Transfer or One LBT in Math & English
Comparative Advantage 0.21* 0.52 0.33 1.20** 1.03** 0.23 0.39 0.80 0.42
(0.07) (0.31) (0.32) (0.30) (0.21) (0.89) (0.53) (0.68) (0.69)
Female 0.63* 0.42 0.62 0.01 0.71 0.05 0.70 1.22 2.36
(0.24) (1.11) (0.93) (1.27) (1.27) (1.37) (0.66) (2.82) (2.58)
Comparative Advantage X Female 0.11 0.65+ 0.86* 0.12 0.18 0.25 0.93 0.52 1.22
(0.23) (0.28) (0.31) (0.37) (0.26) (1.17) (0.80) (0.77) (0.68)
N 292 292 292 292 292 292 292 292 292
B. PS/EAspiring Students Placed in Two+ LBT in Math & English
Comparative Advantage 0.22+ 0.19 0.14+ 0.97*** 0.89*** 0.32 0.22 1.53** 1.17**
(0.10) (0.10) (0.07) (0.15) (0.13) (0.54) (0.33) (0.42) (0.33)
Female 0.64 0.28 0.09 1.96*** 1.60*** 1.16 0.46 2.74** 2.29***
(0.40) (0.28) (0.23) (0.29) (0.18) (0.70) (0.47) (0.57) (0.39)
Comparative Advantage X Female 0.24 0.20* 0.16 0.52* 0.41* 0.38 0.29 1.28* 0.85+
(0.14) (0.08) (0.09) (0.18) (0.18) (0.49) (0.25) (0.39) (0.38)
N 1092 1092 1092 1092 1092 1092 1092 1092 1092
179
Table 7
Differential Effect of Comparative Advantage and Gender on STEM Persistence, Matched LS Sample
Note. Each panel and column combination represent different regression results. Panel A include LSaspiring students who placed in transfer level or one level
below transfer level in math and English. Panel B includes LSaspiring students who placed in two or more levels below transfer level in math and English.
Comparative advantage is the difference between students’ nonSTEM GPA and STEM GPA. PS/Easpiring male and female students were matched based on
the following covariates: took honors/AP courses in high school, special education status, limited English proficiency status, took calculus in high school, took
physics in high school, UC/CSU eligible, # of AP math/sci taken, # of AP English/humanities taken, total # of AG math and science courses, HS GPA, high
school fixed effects, year fixed effects, and college fixed effects. Cluster robust standard errors at the college level are in parentheses. This doublyrobust
estimation unlinks the outcome regression from the propensity score estimation and requires that only one of the two estimations are correct for the results to be
consistent.
+ p<0.10, * p<0.05, ** p<0.01, *** p<0.001
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Quarters Until
First
Transferable
Math/Sci Since
Math
Assessment
Transferable
Math Units
Attempted by
Year Three
Transferable
Math Units
Completed by
Year Three
Transferable
Science Units
Attempted by
Year Three
Transferable
Science Units
Completed by
Year Three
Total
Transferable
Math Units
Attempted
Total
Transferable
Math Units
Completed
Total
Transferable
Science Units
Attempted
Total
Transferable
Science Units
Completed
A. LSAspiring Students Placed in Transfer or One LBT in Math & English
Comparative Advantage 0.23+ 0.23+ 0.20 1.35** 1.30** 0.34* 0.14 0.07 0.33
(0.11) (0.12) (0.15) (0.35) (0.30) (0.13) (0.11) (0.42) (0.44)
Female 0.67 1.82*** 1.41** 1.73 1.50 1.72* 1.46* 0.29 0.39
(0.57) (0.23) (0.35) (1.29) (1.15) (0.53) (0.45) (1.97) (1.67)
Comparative Advantage X Female 0.28 0.08 0.06 0.25 0.21 0.51 0.33 1.07+ 0.89
(0.21) (0.20) (0.24) (0.43) (0.36) (0.28) (0.25) (0.53) (0.54)
N 650 650 650 650 650 650 650 650 650
B. LSAspiring Students Placed in Two+ LBT in Math & English
Comparative Advantage 0.08 0.13* 0.09* 0.33* 0.30+ 0.23** 0.16* 0.63* 0.59+
(0.08) (0.04) (0.03) (0.11) (0.14) (0.06) (0.06) (0.28) (0.28)
Female 0.22 0.27*** 0.16+ 0.39 0.25 1.03** 0.58*** 0.95 1.00*
(0.19) (0.05) (0.07) (0.26) (0.18) (0.26) (0.11) (0.60) (0.35)
Comparative Advantage X Female 0.08 0.05 0.03 0.19 0.16 0.18 0.11* 0.35 0.40
(0.13) (0.04) (0.04) (0.14) (0.14) (0.10) (0.04) (0.30) (0.25)
N 2528 2528 2528 2528 2528 2528 2528 2528 2528
180
Figures
Figure 1
The High School to Community College STEM Pathway
181
Figure 2
Adjusted Marginal Means for Academically Prepared PS/EAspiring Men and Women
Note. Sci = science. Comp = completed. These graphs are a direct result from the estimations
182
Figure 3
Adjusted Marginal Means for Academically Underprepared PS/EAspiring Men and Women
Note. Sci = science. Comp = completed. These graphs are a direct result from the estimations shown in Table 6.
183
Appendix
Appendix A.1
Construction of the STEM Dataset
1. High School Transcript Data
The dataset we received from the public school district and the community college school
district included a unique student identifier that was used to match students across districts. The
LUSDLUCCD unique identifier included 104,906 students who graduated from LUSD and
enrolled in one of the LUCCD colleges in 20052014. I first matched in the LUSDLUCCD
identifier with the LUSD transcript file for a data file with 5,407,513 studentcourse
observations. Using this data file, I created STEM variables like: taking a math course in 912
th
grade; passing the math course with a D, B, B or A, or A. Using the high school transcript data, I
created an indicator that flagged all high school STEM course if they were offered in these
departments: Science, Health Careers, Engineering, or Computer Science. Finally, I collapsed
each record down to one observation per student. The collapsed high school transcript file
resulted in 97,678 students from 211 different high schools. I merged this file in with the student
demographics file.
2. Community College Transcript Data
The community college student enrollment data include 3,298,277 studentcourse
observations. Using this data file, I created community college STEM coursetaking variables
like: the total math units completed (remedial or not), the total transferable math units attempted
and completed, and the total transferable science units attempted and completed. Creating these
variables required multiple steps. First, I exported out all possible course names listed in the
enrollment records into a separate dataset that resulted in 248 unique course names. Then, I
looked at the community college district website to identify each course. Each college had
184
different definitions of what counted as transferable. For example some of the upperlevel
Nursing course at college X would be considered vocational but at college N, that same course
would count as a transferable science course. Upon devising a complete set of rules for all nine
campuses within this district, I executed the rules in Stata 15. Then, I merged in the assessment
records in with the enrollment records. Finally, I collapsed each record down to one observation
per student. The collapsed high school to community college transcript file results in 118,649
student observations.
3. Merging the Data & Sample
Using the community college transcript data file, I merged in the high school transcript
data by using the unique student identifier. The final merged data includes 118,649 students who
enrolled in LUCCD. However, there are 20,971 students (118,64997,678) for whom I do not
observe their high school coursetaking information.
185
Table A.1
Crosswalk of major name, Classification of Instructional Program (CIP) code, and the Taxonomy of Program (TOP) code by Life
Science and Physical Science/Engineering
Life Science Physical Science/Engineering
Major 2digit CIP Code 3 or 4digit TOP
Code
Major 2digit CIP Code 3 or 4digit TOP
Code
Agricultural Sciences 01 101, 102 Computer and
Information Sciences
11 116, 119, 614, In
between 701799
Natural Sciences and
Conservation
03 114, 115, 301, 302, 399 Engineering 14 901, 934
Biological and
Biomedical Sciences
26 401, 402, 403, 407, 410 *Engineering
Technologies,
Technicians
15 924, 934, 935, 943,
946, 953, 956, 957,
961, 999
Medical Assistant+ 51 120, 121, 122, 123,
124, 125, 126, 129,
136, 1201, 1251, 1260,
1261
Mathematics and
Statistics
27 1701, 1799
Physical Science 40 1901, 1919, 1930, 1999
*Science Technologies,
Technicians
41 1920
*Mechanic, Repair
Technologies,
Technicians
47 943, 953, 947, 948,
949, 950, 962,
Biological and Physical
Science and
Mathematics+
30 4902, 990
Note. Aligning with Wang’s 2016 study, the * indicates majors flagged as “likely terminal” meaning these are not majors in which students will pursue if they
transfer to a University. Medical assistant is flagged with a “+” symbol. This is to note that the major was not included in Wang’s study but is included in this
study as medical assistants take a significant number of STEM courses. The medical assistant major is also flagged as likely terminal. Furthermore, Biological
and Physical Science and Mathematics is included in this study but was also not included in Wang’s 2016 study.
186
Table A.2
Robustness of the STEM Gender Gap across Different Estimation Procedures
Note. PSM = propensity score matching. IPW = inverse probability weighting. OLS = ordinary least squares. All three estimates hold constant the same
covariates.
PSM IPW OLS PSM IPW OLS PSM IPW OLS PSM IPW OLS
Quarters Until First Transferable Math/Sci Since
Math Assessment 0.36 0.26 0.48 0.54 0.58* 0.52 0.96+ 0.80** 0.80* 0.14 0.29 0.25*
Transferable Math Units Attempted by Year 3 0.68 1.10 0.92 0.49 0.49* 0.55* 1.72*** 1.45** 1.55*** 0.23*** 0.25** 0.25***
Transferable Math Units Completed by Year 3 0.58 0.65 0.52 0.25 0.28 0.29* 1.33*** 1.19** 1.23*** 0.15** 0.15* 0.16**
Transferable Science Units Attempted by Year 3 0.73 1.16 1.16 1.88** 2.15*** 1.98*** 1.35 1.03 1.21 0.61* 0.44+ 0.55**
Transferable Science Units Completed by Year 3 0.23 0.90 0.85 1.58*** 1.74*** 1.60*** 1.16 0.94 1.10 0.43* 0.32+ 0.45**
Total Transferable Math Units Attempted 0.39 1.21 0.59 1.54* 1.49** 1.51* 2.31*** 2.31*** 2.55*** 0.87** 0.91*** 0.80**
Total Transferable Math Units Completed 0.08 0.37 0.26 0.74 0.71+ 0.72+ 1.83*** 1.86*** 2.07*** 0.48*** 0.50*** 0.45***
Total Transferable Science Units Attempted 0.06 0.54 0.10 2.28** 2.69** 2.61** 0.89 1.06 1.67 0.67 0.64 0.56
Total Transferable Science Units Completed 0.68 0.23 0.31 2.04*** 2.40*** 2.31*** 1.34 1.49 2.16 0.66+ 0.73 0.63+
PS/E Major in Upper Levels PS/E Major in Lower Levels LS Major in Upper Levels LS Major in Lower Levels
187
Table A.3
Robustness of the Relationship between Comparative Advantage and STEM Persistence across Different Estimation Procedures
Note. PSM = propensity score matching. IPW = inverse probability weighting. OLS = ordinary least squares. All three estimates hold constant the same
covariates.
PSM IPW OLS PSM IPW OLS PSM IPW OLS PSM IPW OLS
Quarters Until First Transferable Math/Sci Since
Math Assessment 0.23** 0.26*** 0.29** 0.10 0.14* 0.21** 0.36*** 0.39*** 0.44*** 0.11+ 0.17** 0.25***
Transferable Math Units Attempted by Year 3 0.83** 0.75*** 0.49* 0.32** 0.33*** 0.19** 0.19* 0.28** 0.28*** 0.11** 0.12*** 0.09***
Transferable Math Units Completed by Year 3 0.71* 0.57*** 0.34* 0.24*** 0.25*** 0.12** 0.16* 0.25** 0.23*** 0.08** 0.08*** 0.07**
Transferable Science Units Attempted by Year 3 1.09** 0.75** 0.70** 0.75*** 0.85*** 0.88*** 1.20** 1.13*** 1.13*** 0.42** 0.40*** 0.45***
Transferable Science Units Completed by Year 3 1.06*** 0.72** 0.64** 0.71*** 0.80*** 0.80*** 1.16** 1.10*** 1.10*** 0.37** 0.36*** 0.38***
Total Transferable Math Units Attempted 0.43 0.01 0.24 0.59+ 0.55*** 0.24 0.09 0.12 0.12 0.15* 0.16* 0.09*
Total Transferable Math Units Completed 0.07 0.20 0.03 0.41+ 0.41*** 0.17 0.01 0.00 0.11 0.11+ 0.10* 0.05+
Total Transferable Science Units Attempted 0.93 0.16 0.40 0.91** 0.75*** 0.83*** 0.44 0.01 0.38 0.46+ 0.43* 0.33
Total Transferable Science Units Completed 0.89+ 0.22 0.30 0.77** 0.71*** 0.73*** 0.75 0.30 0.58+ 0.40 0.45** 0.32
PS/E Major in Upper Levels PS/E Major in Lower Levels LS Major in Upper Levels LS Major in Lower Levels
188
Table A.4
Robustness of the Differential Effect of Comparative Advantage and Gender across Different Estimation Procedures in the PS/E
Aspiring Sample
Note. PSM = propensity score matching. IPW = inverse probability weighting. OLS = ordinary least squares. All three estimates hold constant the same
covariates.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Quarters
Until First
Transferable
Math/Sci
Since Math
Assessment
Transferable
Math Units
Attempted
by Year
Three
Transferable
Math Units
Completed
by Year
Three
Transferable
Science
Units
Attempted
by Year
Three
Transferable
Science
Units
Completed
by Year
Three
Total
Transferable
Math Units
Attempted
Total
Transferable
Math Units
Completed
Total
Transferable
Science
Units
Attempted
Total
Transferable
Science
Units
Completed
A. PS/EAspiring Students Placed in Transfer or One LBT in Math & English
Comparative Advantage 0.21* 0.52 0.33 1.20** 1.03** 0.23 0.39 0.80 0.42
Female 0.63* 0.42 0.62 0.01 0.71 0.05 0.70 1.22 2.36
Comparative Advantage X Female 0.11 0.65+ 0.86* 0.12 0.18 0.25 0.93 0.52 1.22
Comparative Advantage 0.36*** 0.39 0.13 0.81** 0.66** 0.23 0.55 0.18 0.00
Female 0.34 0.15 0.39 0.71 0.16 1.35 0.16 0.45 0.53
Comparative Advantage X Female 0.15 0.65+ 0.88* 0.07 0.21 0.22 0.63 0.05 0.63
Comparative Advantage 0.31** 0.40+ 0.23 0.67* 0.59** 0.27 0.04 0.40 0.24
Female 0.69* 0.06 0.34 0.59 0.16 0.75 0.36 0.44 1.05
Comparative Advantage X Female 0.01 0.49 0.59* 0.10 0.23 0.30 0.10 0.05 0.49
B. PS/EAspiring Students Placed in Two+ LBT in Math & English
Comparative Advantage 0.22+ 0.19 0.14+ 0.97*** 0.89*** 0.32 0.22 1.53** 1.17**
Female 0.64 0.28 0.09 1.96*** 1.60*** 1.16 0.46 2.74** 2.29***
Comparative Advantage X Female 0.24 0.20* 0.16 0.52* 0.41* 0.38 0.29 1.28* 0.85+
Comparative Advantage 0.21*** 0.23*** 0.17** 1.13*** 1.01*** 0.26 0.24+ 1.21*** 1.01***
Female 0.65* 0.30 0.13 2.35*** 1.87*** 1.08+ 0.43 3.16*** 2.69***
Comparative Advantage X Female 0.16 0.20+ 0.14 0.63*** 0.49** 0.50+ 0.30 1.02* 0.72*
Comparative Advantage 0.25** 0.13** 0.08* 0.96*** 0.85*** 0.11 0.08 0.93*** 0.80***
Female 0.64 0.33 0.12 2.09*** 1.64*** 1.04+ 0.38 2.84*** 2.44***
Comparative Advantage X Female 0.23 0.24*** 0.20*** 0.48* 0.35* 0.59** 0.41* 0.61** 0.43*
OLS
PSM
IPW
OLS
PSM
IPW
189
Table A.5
Robustness of the Differential Effect of Comparative Advantage and Gender across Different Estimation Procedures in the LS
Aspiring Sample
Note. PSM = propensity score matching. IPW = inverse probability weighting. OLS = ordinary least squares. All three estimates hold constant the same
covariates.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Quarters
Until First
Transferable
Math/Sci
Since Math
Assessment
Transferable
Math Units
Attempted
by Year
Three
Transferable
Math Units
Completed
by Year
Three
Transferable
Science
Units
Attempted
by Year
Three
Transferable
Science
Units
Completed
by Year
Three
Total
Transferable
Math Units
Attempted
Total
Transferable
Math Units
Completed
Total
Transferable
Science
Units
Attempted
Total
Transferable
Science
Units
Completed
A. LSAspiring Students Placed in Transfer or One LBT in Math & English
Comparative Advantage 0.23+ 0.23+ 0.20 1.35** 1.30** 0.34* 0.14 0.07 0.33
Female 0.67 1.82*** 1.41** 1.73 1.50 1.72* 1.46* 0.29 0.39
Comparative Advantage X Female 0.28 0.08 0.06 0.25 0.21 0.51 0.33 1.07+ 0.89
Comparative Advantage 0.25* 0.29 0.30* 1.23*** 1.21*** 0.48 0.17 0.76 0.31
Female 0.52+ 1.49** 1.34** 1.37 1.31 1.43+ 1.46* 0.71 0.10
Comparative Advantage X Female 0.27* 0.01 0.09 0.17 0.19 0.72+ 0.33 1.49+ 1.20+
Comparative Advantage 0.28** 0.29* 0.26+ 1.36** 1.34** 0.18 0.07 0.03 0.33
Female 0.54 1.57*** 1.29** 1.71 1.63 2.00** 1.74*** 0.95 1.73
Comparative Advantage X Female 0.25** 0.00 0.03 0.33 0.35 0.47* 0.28 0.63 0.41
B. LSAspiring Students Placed in Two+ LBT in Math & English
Comparative Advantage 0.08 0.13* 0.09* 0.33* 0.30+ 0.23** 0.16* 0.63* 0.59+
Female 0.22 0.27*** 0.16+ 0.39 0.25 1.03** 0.58*** 0.95 1.00*
Comparative Advantage X Female 0.08 0.05 0.03 0.19 0.16 0.18 0.11* 0.35 0.40
Comparative Advantage 0.06 0.15** 0.11* 0.32** 0.32* 0.25** 0.18* 0.72 0.72
Female 0.52* 0.29* 0.19* 0.27 0.23 1.06** 0.64*** 1.11* 1.18*
Comparative Advantage X Female 0.25* 0.06 0.05 0.15+ 0.07 0.20* 0.16* 0.61* 0.58+
Comparative Advantage 0.08 0.12* 0.09* 0.30* 0.27+ 0.21** 0.15* 0.57+ 0.53+
Female 0.46** 0.27** 0.19** 0.35* 0.30* 0.93** 0.56*** 0.81+ 0.85*
Comparative Advantage X Female 0.23* 0.04 0.03 0.19* 0.14 0.16* 0.13+ 0.32 0.28
OLS
PSM
IPW
OLS
PSM
IPW
190
Figure A.1
Common Support of Four Samples Pre and PostMatching
191
Figure A.2
Adjusted Marginal Means for Academically Prepared LSAspiring Males and Females
Note. Sci = science. Comp = completed. These graphs are a direct result from the estimations shown in Table 7.
192
Figure A.3
Adjusted Marginal Means for Academically Underprepared LSAspiring Males and Females
Note. Sci = science. Comp = completed. These graphs are a direct result from the estimations shown in Table 7.
193
Conclusion
Taken together, this dissertation examined potential barriers and explanations behind
differential STEM participation in community college. The barriers that were examined include
math remediation and misaligned math expectations. In addition, this dissertation explored why
fewer female students persisted in STEM compared to their male counterparts despite similar
aspirations. Each study placed special focus on STEMaspiring students, or students who
indicated interest in STEM fields in their college application. All three essays provided policy
recommendations to better support STEMaspiring students in community college, many of
whom are from historically marginalized backgrounds.
To summarize, in the first paper, my coauthors and I found that a substantial number of
students placed in developmental math despite taking advanced math courses in high school
(e.g., precalculus). We termed this experience math misalignment. Students who were not
misaligned by placing directly in transferlevel math attempted more transferable STEM courses
compared to students who repeated the math level that they completed in high school. In
particular, math misalignment hindered those with a clear interest in STEM.
Extending the research findings of the first study, my coauthor and I examined the causal
effect of developmental math placement on early math progression and STEM participation
using a regression discontinuity (RD) design. We found clear negative effects from
developmental math placement among students who were at the cusp of transferlevel math
(intermediate algebra versus transferlevel math). Importantly, STEMaspiring and STEM
oriented students were negatively affected by lower placement relative to their peers, suggesting
that lower math placement hindered those most poised to enter STEM fields.
194
Then, the third study focused on the STEM gender gap among men and women who
indicated interest in STEM and disaggregated the findings by initial math and English placement
and by STEM subfields. This study found that the STEM gender gap was most prominent
among Physical Science/Engineering (PS/E)aspiring students who placed in low levels of
developmental math and English. Additionally, while many argue that students make educational
decisions based on their comparative advantage, this study found that comparative advantage
exacerbated the STEM gender gap among these students who were initially identified as
academically underprepared.
Common Themes
Based on the two essays that examined math remediation as a structural barrier, a
common theme that emerged is that placing in developmental math hindered students from
attempting upperlevel math and persisting in STEM relative to students who placed directly in
transferlevel math. This finding aligns with prior evidence that students who placed in
developmental education were less likely to pass collegelevel courses, earn college credits, and
attain a degree (Valentine, Konstantopoulos, & GoldrickRab, 2017). Both essays argued for
removing structural barriers like math misalignment and math remediation particularly for
students who displayed considerable STEM selfefficacy and momentum.
The third paper added nuance to the discussion by examining the STEM gender gap
within different levels of initial math and English placement. Both the second and the third study
underscored the problematic nature of placing into elementary algebra or below. The second
study showed that female students at the lower end of the developmental math sequence were
diverted from the STEM pathway and the third study showed that the STEM gender gap was
pronounced among PS/Easpiring women who placed in low levels of developmental education.
195
Notably, all studies examined the outcomes of STEMaspiring students. In two out of the
three essays, STEMaspiring students took more transferable STEM courses and attempted more
upperlevel math courses relative to nonSTEMaspiring students. In addition, PS/Easpiring
women who initially placed in upperlevels of math and English were just as likely if not more
likely to persist in STEM as PS/Easpiring men who placed in upperlevels of math and English.
Finally, two of the three studies specifically disaggregated the findings by race and/or
gender. The second essay examined the effect of placing into developmental math on STEM
participation and estimated whether this effect varied by race and gender. The third essay
examined the gender gap in STEM persistence. In addition, while the first essay did not
explicitly examine differences by race, over 75% of the student sample were URMs, suggesting
implications for supporting URMs in STEM.
Implications for Policy and Practice
This dissertation provides several recommendations for policy and practice. First, given
that many students experience math misalignment as they transition from high school to
community college, it is important to align academic readiness standards between sectors. While
in the past, community colleges used an offtheshelf placement test to place students, colleges
are now using high school records to determine students’ initial math and English levels (Scott
Clayton, 2018). The findings from this dissertation research suggest that using students’ high
school achievement measures will provide more STEMaspiring students with access to upper
level math and science courses.
Second, the findings of this dissertation show that STEMaspiring students tend to take
more transferable STEM courses in community college, underscoring their motivation and
interest in STEM fields. However, math remediation and misalignment were identified as
196
potential pitfalls for STEMaspiring students in community college. Therefore, colleges should
examine existing practices and remove any undue barriers so that these students can successfully
persist and attain their STEMrelated goals.
Many of the community colleges in this district are implementing innovative programs
to support STEMaspiring students. Some of these efforts include structured mentorship
opportunities, partnership with the local feeder high schools and the local California State
Universities, and STEM summer camps. As part of this effort, colleges in this district may want
to identify STEMaspiring students and monitor their early progress through the math sequence.
These students have indicated STEM as their intended major and thus are identifiable based on
their college application. In addition to increasing the overall number of students interested in
STEM fields, colleges should ensure that those who displayed a clear interest to major in STEM
at the start of college successfully achieve their STEMrelated goals.
Finally, community colleges may want to pay special attention to female scientists and
engineers, especially if they are initially identified as academically underprepared based on their
math and English placement. Some ideas to support these students include a cohort model or
customizing existing STEM support programs to directly assist aspiring female scientists and
engineers. Thus, colleges should explore ways to incorporate a customized support system for
underrepresented minorities and female students aspiring to pursue STEM.
Future Research
This dissertation suggests several directions for future research. The math misalignment
study examined students who took advanced math courses (i.e., algebra 2 or higher) as opposed
to all students. However, a considerable number of STEMaspiring students in this district 
197
precisely 23% of all community college bound STEMaspiring students took geometry as their
highest high school math. Therefore, future studies should examine math misalignment and
STEM trajectory of students who do not take advanced math in high school. In addition, the RD
study generalized to students around the placement cutoff as opposed to all students at each math
level. By design, we were unable to make inferences to the average student at each math level.
Still, the RD study examined all five math levels and provided a nuanced view of students’
developmental math experiences. Also, the STEM gender gap study is generalizable to
community college bound graduates from one large urban school district in California. Future
research should examine the college trajectory of all students who graduated from this district.
Next, future study should examine the causal impact of using multiple measures (i.e.,
high school coursetaking information and GPA) to place students. In tandem with this
placement reform, many community colleges in states like California and Texas are shifting
towards corequisite models (Mangan, 2019). Corequisite models allow students, who under the
old placement regime may have placed in developmental education, to directly place in transfer
level courses with additional support. Much more empirical evidence is needed to assess the
effect of this paradigm shift.
Specific to California, the language of the new assessment and placement policy,
Assembly Bill 705, states that nonSTEMaspiring students who meet the high school math
criteria will place directly into transferlevel Statistics and Liberal Arts math while STEM
aspiring students will directly place into transferlevel Business and STEM math. Future studies
should examine the math and STEM progress of students who place into either type of transfer
level math courses. In particular, future studies should explore how early sorting of students into
198
transferlevel algebrabased versus statisticsbased math courses affect those who decide to
switch into STEM fields at a later point in time.
Finally, the STEM gender gap study was motivated by the hypothesis that aspiring
female scientists and engineers with a comparative advantage in STEM will similarly persist in
STEM as male scientists and engineers. However, that study found that women took fewer
science courses than men despite their comparative advantage in STEM if these students initially
placed in low levels of developmental education. To better explain this finding, a qualitative or
mixed methods study is needed to unpack the decisionmaking processes of aspiring women
scientists and engineers in community college. Specifically, a qualitative or mixed methods study
can inform where, how, and from whom students receive feedback on their comparative
advantage in STEM.
199
References
Mangan, K. (2019, February). The end of remedial courses. The Chronicle of Higher Education.
Retrieved from: https://www.chronicle.com/interactives/Trend19RemediationMain
ScottClayton, J. (2018, March). Evidencebased reforms in college remediation are gaining
steam  and so far living up to the hype. The Brookings Institution: Evidence Speaks.
Retrieved from: https://www.brookings.edu/research/evidencebasedreformsincollege
remediationaregainingsteamandsofarlivinguptothehype/#footnote11
Valentine, J. C., Konstantopoulos, S., & GoldrickRab, S. (2017). What happens to students
placed in developmental education? A metaanalysis of regression discontinuity studies.
Review of Educational Research, 87(4), 806833.
Abstract (if available)
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Asset Metadata
Creator
Park, So Yun Elizabeth
(author)
Core Title
Three essays on the high school to community college STEM pathway
School
Rossier School of Education
Degree
Doctor of Philosophy
Degree Program
Urban Education Policy
Publication Date
07/11/2019
Defense Date
04/22/2019
Publisher
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Community Colleges,economics of education,gender gap,Higher education,math remediation,OAIPMH Harvest,STEM education
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Tags
economics of education
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