Self-Placement in Math Courses at U.S. Community Colleges: Contributing Factors and Impacts on Student Success

Self-placement in math is becoming increasingly popular in community colleges in the U.S., where students will decide for themselves whether to enroll in non-credit developmental (or remedial) math courses. To fully understand the factors associated with students’ math enrollment choices and the long-term effects of initial math enrollment choices, we use data from all first-time-in-college students in the Florida College System to conduct a multinomial logistic regression analysis and an inverse-probability regression adjustment analysis. We find that most students chose to directly enroll in college-level math, with significant differences by gender and high school math preparation. First-year math enrollment choices were significantly associated with likelihood of passing college-level math and the number of college credits by the third year.


Introduction
In the United States, community colleges are usually 2year public institutions of postsecondary education, providing broad access to a wide range of educational programs and services.Developmental education (DE) is a widespread intervention intended to strengthen academic skills of incoming college students with weak academic preparation.Among students who began their postsecondary education at community colleges in 2013 to 2014, nearly 60% took one or more remedial courses within 3 years (Chen et al., 2020).Traditionally, students were sorted into different levels of courses largely based on their performance on placement tests.Students who scored below the college-ready cutoff scores on placement tests were assigned into developmental courses before they could enroll in credit-bearing college-level courses.However, less than one half of students assigned to DE completed the entire sequence to which they were referred (Bailey et al., 2010).Evidence also suggests that placement tests have resulted in many mis-assignments where large numbers of students were incorrectly assigned into developmental programs when they likely would have succeeded in college-level courses (Scott-Clayton et al., 2014).
Accordingly, many states have been implementing alternative placement policies.For example, California passed the Assembly Bill 705 (AB 705) in 2017.AB 705 directs all community colleges in California to maximize the number of students completing transfer-level math and English courses within a 1-year timeframe.To achieve this goal, community colleges across the state have implemented reforms such as removing developmental education course offerings, placing students directly in transfer-level courses with additional supports, and relying on multiple measures (e.g., high school GPA) for course placement (Melguizo et al., 2021).In 2013, Florida passed Senate Bill 1720 (SB 1720) that dramatically changed how DE is offered and for whom it is required across the 28 state and community colleges in the Florida College System (FCS).Under SB 1720, students who entered ninth grade in a Florida public high school in 2003/04 or later and earned a standard high school diploma, and active duty service members became exempt from the placement tests and had the option to skip developmental education regardless of their prior academic preparation.Moreover, SB 1720 required all colleges to replace traditional semester-long developmental courses with new instructional strategies, including compressed, co-requisite, modularized, or contextualized course strategies.
The common idea of these reforms is to help accelerate students into college-level coursework by giving them more choices over where to start their academic trajectory.The strategy of self-placement, when students choose their own coursework under the guidance of their counselors, has received increasing attention in recent years among scholars and policymakers aiming to improve community college student outcomes (Kosiewicz & Ngo, 2020).In light of the emergence of self-placement strategies as alternatives to test-based placement, some research has examined the changing enrollment patterns during self-placement and how these enrollment decisions are related to students' future academic success (Kosiewicz & Ngo, 2020;Park et al., 2018).For example, Park and colleagues (2018) found that in the first semester after the implementation of SB 1720 in Florida, only one third of students who would have been assigned into developmental math prior to the reform enrolled in developmental math after the reform, one third enrolled in college-level math (Intermediate Algebra), and one third enrolled in no math course whatsoever.A more recent study from a large urban community college district found that self-placement led to positive outcomes such as the increased likelihood of completing degree requirements in math, but these benefits were mostly for White, Asian, and male students (Kosiewicz & Ngo, 2020).
This study builds on the work by Park et al. (2018) but extends it in two important ways.First, Park et al. examined the math enrollment choice in the first semester.Instead, in this study, we examine first-year (fall and spring) math enrollment patterns in order to better capture students' coursetaking choices as some students decide to delay taking any math course in the first semester.Second, the outcome examined in Park et al. is the passing rates in college-level math courses within the first semester.We extend the previous analysis by looking at the longer-term impacts of initial math enrollment on passing college-level math and credit accumulation up to 3 years after initial college enrollment.
The purpose of this study is to investigate the math enrollment pattern under the self-placement condition, which allows exempt students to choose their own coursework with guidance from an advisor or faculty member.In particular, we focus our attention on the underprepared exempt students who would have been assigned to developmental math courses under traditional test-based placement policy, because they are the group most directly affected by the new policies brought by SB 1720.We first investigate the factors associated with students' enrollment choices, such as gender, race/ ethnicity, and high school math preparation.We then examine the impacts of the initial math enrollment choice on subsequent postsecondary success.More specifically, two research questions guide this study: (1) what are the contributing factors (such as gender, race/ ethnicity, and high school math preparation) associated with underprepared exempt students' math enrollment choice when DE became optional?And (2) how do these initial math enrollment choices affect students' chance of passing college-level math and credit accumulation by the third year of college?We particularly focus on math because for community college students, math is the most common subject in which remediation is needed, and also the subject in which students are least likely to advance successfully to college-level competency (Bahr, 2013;Valentine et al., 2017).
We proceed as follows: first, we review the literature on DE placement policies and the impacts of DE on student outcomes, with a particular focus on Florida's DE reform.We then describe our data, which consists of student-level records from the entire population of firsttime-in-college (FTIC) students at FCS institutions, and analytic sample and approaches.After presenting the findings, we conclude with a discussion of our results and implications for future research and policy.

Assessment and Placement in College Mathematics
Community colleges have traditionally utilized placement tests such as ACCUPLACER and COMPASS to assign students to developmental or college-level coursework.Some states do not use these commercially available instruments and have their own tests, such as the Postsecondary Education Readiness Test (PERT) in Florida.Although it is efficient and cost effective to use tests to help make developmental education assignments, research suggests that these tests often have low predictive validity and result in frequent placement errors (Scott-Clayton et al., 2014).
To address the limitations of test-based placement polices, some states and institutions have started to use multiple measures to determine students' initial course placements.Advocates of this approach believe that incorporating multiple measures such as high school coursework, GPA, test scores, motivation, and selfefficacy into placement decisions can improve placement accuracy, which is supported by some empirical evidence (Ngo et al., 2018;Scott-Clayton et al., 2014).High school grades, often measured by overall GPA, are usually a stronger predictor of postsecondary success than standardized tests, although grading standards vary by school (Atkinson & Geiser, 2009;Brookhart et al., 2016).While integrating multiple factors (such as high school GPA) holds promise for improving placement accuracy, there are concerns about the logistical challenges and administrative burdens associated with the multiple measures policies.A recent study from Florida found that adjusting existing cutoffs on the PERT might lead to greater placement accuracy than using new metrics (Leeds & Mokher, 2020).
Self-placement strategies represent another type of reform in placement polices in addition to the multiple measures approach.Self-placement strategies allow students to choose, sometimes with consultation from faculty or an academic advisor, to take a developmental or entry-level college course that aligns most closely with their scholastic backgrounds and academic and career goals (Kosiewicz & Ngo, 2020).From a selfdetermination perspective, ''students tend to learn better and are more creative when intrinsically motivated, particularly on tasks requiring conceptual understanding'' (Niemiec & Ryan, 2009, p. 136).By letting students determine their course levels, self-placement policies seek to improve student success over test-placement strategies by better fulfilling the self-determination needs of students and allowing them to select the appropriate starting point for their college coursework instead of needing to go through several gatekeeping courses, such as DE courses, prior to enrolling in college-level coursework.
There is some evidence supporting the above proposition.Utilizing a ''natural experiment'' in which a community college accidently gave students a choice to opt into or out of developmental math, Kosiewicz and Ngo (2020) observed some improvement in student outcomes such as the probability of meeting the degree requirements in math compared to students at institutions where traditional test-placement policies were used.A qualitative study on student experiences amid the implementation of SB 1720 in Florida found that most exempt students tend to appreciate the autonomy over course enrollment decisions (Brower et al., 2020).However, some exempt students who opted out of DE ended up struggling academically in college-level coursework.These students received negative feedbacks from staff about their academic abilities that decreased their feelings of competence (Brower et al., 2020).
Additionally, some research has explored the equity implications of self-placement policies.When given the opportunity to self-place into the math sequence, predominantly White, Asian, and male students were most likely to benefit from this opportunity.It was likely because females and racial minority students were more likely to underestimate their abilities and opt into developmental math courses (Kosiewicz & Ngo, 2020).There is a growing concern about the underrepresentation of women and racial minorities in STEM fields (Kricorian et al., 2020).It is thus important to examine whether students' enrollment choices into math courses vary by gender and race/ethnicity under self-placement policies.One limitation of the study by Kosiewicz and Ngo (2020) is that the treatment group only included a small sample of students in one college and the analytic sample excluded students who took no math due to data unavailability, thus limiting the generalizability of the findings.This study will further explore the extent to which there may be gender and racial differences in math enrollment choices under a statewide reform allowing for selfplacement.

Impact of DE on College Success
There is some evidence suggesting a potential negative effect of taking developmental courses on college success.A meta-analysis of studies on the impacts of assignment to DE showed that relative to their peers who were on the margin of college readiness but who were placed into college-level courses, students scoring just below collegeready who were assigned to developmental courses earned fewer college credits within 3 years, and were about 1.5 percentage points less likely to complete a degree (Valentine et al., 2017).However, these results may not be generalizable to students with lower levels of academic ability.Boatman and Long (2018) presented evidence on the potential benefits of developmental courses for students with lower levels of academic preparation, emphasizing developmental education as an intervention that might differ in its impact according to student needs.
Moreover, many students never enrolled in the developmental courses they were assigned (or the subsequent corresponding college-level course), resulting in an overall negative effect of assignment into DE (Bailey, et al., 2010;Chen, 2016).Understanding the impact of assignment into DE is important from a policy perspective because states or institutions can change placement policies to manipulate the assignment.However, it is also important to know the impact of enrolling in a developmental course.If developmental education does not help students even if they took all the courses they were assigned, giving more students the option to skip DE or a complete removal of DE might be reasonable.However, if the problem is attributed to large number of students not enrolling in DE, institutions should put more effort into ensuring students take the courses they need.In this study, we investigate the impact of enrolling in DE by looking at whether exempt students who score below college-ready and opt into both developmental and college-level math courses perform better compared to similar students who directly enroll in a college-level math course.
In addition, assignment into DE may send a message to students about their lack of college readiness, and as a result, students assigned to DE may be less likely to enroll (Scott-Clayton & Rodriguez, 2015).Whether the stigma effects exist or not is an empirical question that merits more research, it is safe to say that the stigma effects, if any, would be minimal for exempt students who voluntarily opt into DE after the implementation of SB 1720.The difference in stigma is due to exempt students having the opportunity to be self-placed (rather than test-placed) into different levels of courses that they believe would align closest with their backgrounds and goals.By examining the short-and long-term outcomes of exempt students who voluntarily enrolled in developmental courses, this study offers insights on the impacts of taking developmental education that is taught through new instruction strategies under SB 1720 without worrying about the stigma effects.

Florida's context
SB 1720 is a comprehensive developmental reform among all 28 Florida College System (FCS) institutions (the former community colleges) that includes three primary components.First, students who started ninth grade at a Florida public high school in 2003 to 2004 or later and graduated with a standard high school diploma, and students who were active-duty military personnel, became exempt from developmental education and could opt to enroll directly to college-level coursework.Second, the legislation required all FCS institutions to adopt new instructional strategies in DE, such as compressed, corequisite, modularized, and modularized courses.Third, institutions were asked to provide enhanced advising and student support services.
Prior research has documented significant positive effects of SB 1720 on student outcomes.For example, following the reform, intermediate algebra and gateway math courses enrollment rates increased by 8.19 and 4.89 percentage points, respectively; cohort-based passing rates increased by 3.48 and 2.94 percentage points in intermediate algebra and gateway math courses (Park-Gaghan et al., 2020).Moreover, students have accumulated an additional 0.3 college credits by the third year after the reform (Mokher et al., 2020).Moreover, studies indicated that Black and Hispanic students tend to experience even greater gains from the reform than White students, reducing existing achievement gaps (Mokher et al., 2020;Park-Gaghan et al., 2020).While existing studies have examined the overall effects of SB 1720 by comparing student outcomes before and after the reform, this study pays special attention to the new self-placement strategy introduced by SB 1720 and examines student enrollment choices in math under this new placement policy.As institutions and states across the country are experimenting with new assessment and placement polices, results from this study based on Florida's experiences can contribute to informing decision making and policy.By looking at the impact of initial enrollment choices, this study will also help students make more informed decisions about which courses to select in an era of increased choice.

Data
We used data from Florida's K-20 Education Data Warehouse (EDW), which tracked all Florida public school students remaining in-state from kindergarten to postsecondary education.For the purposes of this study, we limited our sample to first-time-in-college (FTIC) students who began their studies in the fall semesters of 2014 and 2015 at one of the 28 colleges in the FCS, which consisted of two cohorts who were enrolled after the developmental education reform (N = 135,547).We then narrowed our sample to the exempt students who had the option to bypass developmental math courses under SB 1720 (69%; N = 93,599).Because we were particularly interested in the math enrollment choices of students who would have been placed into DE math under the old placement policies, we excluded students who scored higher than the college-ready cut-off score (113 or above) (N = 20,151) and students who had no PERT math scores (N = 28,008).PERT was not required for exempt students but some students were advised to take it upon college enrollment to help with placement decisions.Many high school graduates in our data had also taken the PERT while they were still enrolled in high school as part of the Florida College and Career Readiness Initiative in high schools (Mokher et al., 2018).Our final analytic sample included 45,440 students, with each cohort having about 22,000 students.In this article, we referred the students in our sample as ''underprepared exempt students.''

Variables
The first outcome of interest for this study is students' enrollment choice in math courses within the first year.It is a categorical variable including three values: (1) took no math; (2) opted into DE math; and (3) only took college-level math.There are two subgroups among students who opted into DE math: (2a) students who only enrolled in DE math and (2b) students who enrolled in both DE and college-level math.The key difference between these two subgroups is whether or not passing the DE math in the first semester.Students who failed in DE math in the first semester were not able to progress into a college-level math whereas students who passed DE math in the fall semester could enroll in a collegelevel math in the spring semester.Only around 20% of the students who enrolled in both DE and college-level math courses enrolled them within the same semester, and the majority of the students first enrolled in DE math in the fall semester and then in college-level math in the spring semester.In addressing our second research question concerning the relationship between initial math enrollment and 3-year outcomes, we first compare the overall students who opted into DE with students who either took no math or only took college-level math, and then disaggregate the results into the two subgroups.
The first college-level math course offered in many FCS institutions is Intermediate Algebra (MAT 1033), which counts for elective credit only, and covers topics such as linear equation, introduction to function, and quadratic equations.Next in the math sequence are four courses that can fulfill the associate's degree requirements in math: College Algebra (MAC1105); Liberal Arts Math 1 (MGF1106); Liberal Arts Math 2 (MGF1107); and Introductory Statistics (STA2023).In addition, certain students may take more advanced math courses.We capture all of these when creating indicators for enrollment in college-level math.
Our second set of outcome measures were intended to reflect students' academic outcomes by the end of third year in college.First, we created a binary indicator for passing college-level math by the end of third year.Second, we used a continuous indicator for the number of college-level credits (in any subject) earned 3 years following the initial enrollment.Developmental education courses did not count toward the number of college-level credits.If a student did not enroll in any courses in any of the subsequent semesters after initial entry, they were still included in the sample with zero credit earned during the semester(s) of non-enrollment.
Our control variables included student background characteristics for race/ethnicity (coded as a categorical variable for White, Black, Hispanic students, with all other students [including Asian] classified in a fourth, ''Others'' category), sex, free and reduced-price lunch status during high school, and age (aged below 25 as reference).There was no missing data for any of these variables in the analytic sample.
Based on students' high school transcript records for math courses and related literature on high school academic preparation, we constructed a categorical variable for high school academic preparation.Students were classified as on an ''at-risk'' track if they never enrolled in Algebra II and failed one or more high school course, a ''basic'' track if they never enrolled in Algebra II but passed all high school math courses, a ''standard'' track if they completed Algebra II but no advanced math courses beyond that, and an ''advanced'' track if they completed Algebra II plus at least one more advanced course.We consider whether students have passed Algebra II because it has been identified in the literature as an important gatekeeper course for success in early college outcomes (Gaertner et al., 2014;Kim et al., 2015).For students who do not have high school transcript records in the administrative data, we used the dummy variable adjustment method where the value the missing control variable was set to a constant value of zero, and an additional dummy variable was added to the model to indicate whether the actual value was missing (Cohen & Cohen, 1983).Finally, we controlled for students' placement test (PERT) math score.
Table 1 presents summary statistics by cohort for the analytic sample.Most underprepared exempt students chose to directly enroll in a college-level math course, and the share of students directly enrolling in collegelevel math increased from 43.49% in 2014 to 53.44% in 2015.On the contrary, the share of underprepared exempt students who opted into DE math decreased from 35.14% in 2014 to 28.11% in 2015.The percentage of underprepared exempt students who did not enroll in any math course remained around 20% across cohorts.In addition, the passing rates for college-level math by the third year increased from 46% in 2014 to 52% in 2015.The number of college-level credits earned by the third year remained around 25.
Student background characteristics were similar across cohorts, with around 55% females, 36% White, 24% Black, 33% Hispanic, 52% eligible for free and reduced price lunch, and 4% aged 25 or above.The distribution into high school math tracks also remained similar across cohorts.Roughly 26% were classified as at-risk, 37% in the basic track, 12% in the standard track, and 18% in the advanced track.In other words, the majority of students in the analytic sample were below a standard track in high school math.

Analytic Approach
To answer our first research question, we ran a multinomial logistic regression predicting students' math enrollment choices within the first year.We estimated the following model for student i at college j: In this specification, b 1 captures the impact of student background characteristics, including race/ethnicity, sex, free and reduced price lunch status, age, and PERT math score.b 2 captures the impact of high school math preparation, and j j is a college fixed effect to account for unobserved heterogeneity across institutions.
Our second research question focused on the longterm effects of initial math enrollment choices.The outcome variable in the first research question-math enrollment choice within the first year-became the independent variable in our second question.A methodological challenge in exploring relationship between students' math enrollment choice and outcomes by the third year lies in the differences in the types of students who made different math enrollment choices.For example, there may be some student characteristics that were associated with both math enrollment choice and 3-year outcomes.We utilized inverse probability-weighted regression adjustment (IPWRA) to address this issue (Wooldridge, 2010).
WRA is a doubly robust approach where in the first stage, we ran a multinomial logistic regression to predicting the probability of different math enrollment choices relative to only enrolling in college-level math (the most common choice in our sample).This is the same regression model as the one we ran for our first research question.From the multinomial regression results, we calculated the predicted probability of selecting into individual math enrollment choice (t) among (T) available choices, and for individual i we defined this predicted probability as P (T i = t).We then defined the weights (W) as the inverse of the of the generalized propensity score using the following equation: The second stage of IPWRA consists of regression adjustment to predict the number of college-level credits earned by the third year and the probability of passing college-level math by the third year.We estimated a linear regression model for the continuous variable (i.e., the number of college-level credits by year 3) and a logistic regression model for the dichotomous indicator (i.e., passing college-level math by year 3) as follows: y i = g 0 + g t + GX , With inverse probability weighs (W iT ) based on P (T i = t).y i are the outcomes of interests.g 0 represents the intercept, g t . is the effect of selecting into choice t, and X is the matrix of covariates representing the same set of student characteristics as the first stage.We assess the covariate balance after weighting by calculating the standardized mean difference for each covariate among students who enrolled in no math relative to students opting into developmental math or enrolling in college-level math.According to the What Works Clearinghouse (2020), differences less than 0.05 standard deviations indicate acceptable covariate balance.There are some large differences in student characteristics by math enrollment choice that exceed the 0.05 standard deviation criteria prior to matching (see Supplemental Appendix Table A).However, after weighting, all of the differences are less than 0.05 standard deviation units.We acknowledge that math enrollment decisions are inherently endogenous and IPWRA cannot completely address the endogeneity issue.Therefore, we are not able to establish a causal relationship between students' initial math enrollment decisions and 3-year outcomes.Nevertheless, our detailed administrative records allow us to account for a large set of covariates that are correlated with enrollment decisions and performance outcomes, such as student characteristics and high school academic preparations.Results from this study can thus provide suggestive evidence of the outcomes of students who make different enrollment decisions.

Factors Associated with Math Enrollment Choice
We begin with the results from our multinomial logistic regression model, which helps us understand factors associated with the math enrollment choices made by underprepared exempt students.Here we particularly focus on the probability of opting into DE math relative to directly enroll in college-level math.We report these results in Table 2.We then disaggregate the students enrolling in DE math into two subgroups: (1) those who only enrolled in DE; and (2) those who enrolled in both DE math and college-level math.We also compare these two subgroups against the only college-level group and the results are reported in Table B in the Supplemental Appendix.
As shown in Table 2, compared to males, females were less likely to directly enroll in college-level math versus opting into developmental math (relative risk ratio [rrr] = 0.95, p \ .001).This is largely because females were more likely than males to enroll in both collegelevel and DE courses relative to only enroll in either college-level or DE courses (see Table B).In addition, females were less likely to enroll in ''no math'' than were males relative to enrollment in either DE or college-level courses.
There is no significant difference between White students and students of color in the probability of directly enrolling in college-level math versus opting into DE math.However, high school math preparation was significantly associated with students' enrollment choice in math courses.Students at the at-risk and basic tracks were less likely than students at the standard track to directly enroll in college-level math relative to enrolling in developmental math (rrr = 0.65 for at-risk and 0.79 for basic, p \ .001).Students at the advanced track were more likely than students at the standard track to enroll in college-level math relative to opting into developmental math (rrr = 1.64, p \ .001).

First-year Math Enrollment Choice and 3-year Outcome
We now turn to focus on the relationship between students' math enrollment choices in the first year and their outcomes by the end of the third year.We begin with the descriptive portraits showing the probability of passing college-level math and the number of credits earned by the end of year 3.As shown in Figure 1, there was a clear divergent trend in the cumulative probability of passing college-level math depending on whether students enrolled in a college-level math course in the first year.For those who enrolled in a college-level math, the probability of passing college-level math by the third year was greater than 65%, compared to around 42% for those who opted into developmental math and about 20% for those who enrolled in no math within the first year.It is worth noting that although students who enrolled in college-level math plus DE math fell behind their peers who directly enrolled in college-level math in the first year, they caught up and outperformed by the end of the second fall semester.By the end of year 3, the probability of passing college-level math for students who enrolled in college-level math plus DE math was 68%, compared to 65% for students who directly enrolled in college-level math.
The results for the outcome of number of college-level credits completed were very similar.As shown in Figure 2, students who enrolled in a college-level math within the first year accumulated more credits by year 3 than those who opted into developmental math.Again, students who enrolled in both college-level math and DE math performed better than those who only enrolled in college-level math, although they may have lagged behind in the first year.By the end of third year, students who enrolled in college-level math plus DE math accumulated 31.77credits, compared to 30.54 credits earned by students who only enrolled in college-level math.
The IPWRA results, presented in Table 3, confirmed the patterns we found in the descriptive analyses.In both outcomes, students who directly enrolled in college-level math performed better than students who opted into developmental math or those who took no math within the first year.However, a subgroup of students who opted into developmental math-students who enrolled in both developmental and college-level math in the first yearperformed better than those who only enrolled in collegelevel math.The predicted probability of passing collegelevel math by the end of the third year for students who enrolled in college-level math plus DE math was 66%, compared to 62% for students who only enrolled in college-level math (p \ .05;see Panel A of Table 3).The predicted number of college credits earned by students who enrolled in both college-level math and DE math was 31.20 by the end of the third year, compared to 28.96 for students who only enrolled in college-level math within the first year (p \ .05;see Panel B of Table 3).

Discussion and Conclusion
A growing number of states and colleges have begun to adopt new placement strategies to improve the accuracy of initial course placement over the past decade, such as incorporating multiple measures to assess students' college readiness instead of solely relying on placement tests (Rutschow et al., 2019).Florida launched a more drastic reform in developmental education through SB 1720 that gave the majority of incoming students at FCS institutions the opportunity to opt out of DE regardless of their prior academic preparation.Against this context, this study investigated first-year math enrollment choices of underprepared exempt students who would have been placed into DE math, as well as the impacts of these choices on the probability of passing college-level math and credit accumulation by the third year.
Our results indicate that most of the underprepared exempt students took the opportunity offered by SB 1720 to skip DE into which they would have been placed prior to the reform.According to a survey of students at two FCS institutions in Fall 2014, career goals, time to degree, cost of DE, and high school grades were the top four factors shaping their math enrollment decisions (Park et al., 2016).It is thus understandable that most underprepared exempt students chose to bypass DE courses as taking those courses could increase the costs to students and prolong the time to degree.However, some students still took developmental math even though it was optional.About 28% and 35% of underprepared exempt students chose to take developmental math within the first year in 2014 and 2015, respectively.Some of them were convinced by advisors or college personnel to enroll in DE and others believed it was appropriate based on their level of academic preparation (Brower et al., 2020).
We did not find significant racial differences in math enrollment patterns under the self-placement strategy.Prior to the reform, Black and Hispanic students were less likely than White students to enroll in college-level math within the first year (Park-Gaghan et al., 2020).Yet this study shows that after the reform, students had a similar likelihood of enrolling in college-level math regardless of race/ethnicity.This is consistent with prior research from both Florida and California suggesting that Black and Hispanic students experienced greater increases in enrollment in college-level math than White students when shifting from a test-placement to a selfplacement policy (Melguizo et al., 2021;Park-Gaghan et al., 2020).Self-placement policies thus hold promise to reduce or even eliminate the existing racial gaps in access to college-level math likely by dismantling placement policies that have historically been inequitable.
Our results are different from the study by Kosiewicz and Ngo (2020) in which they found ''female students and students of color were more likely to choose lower courses under a self-placement regime relative to test placement'' (p.1382).As the authors acknowledged, their study focused on a small sample of students in one college (i.e., the treatment group), thus limiting the generalizability of their results.Also, their analytic sample did not include students who did not take any math, which may lead to biased estimates.Moreover, in their study, the opt out policy was an ''accident'' and it seems like the most advantaged students with greatest access to social and cultural capital may be more likely to know about the option to opt out and take advantage of it.In Florida, however, SB 1720 required colleges to develop plans for enhanced advising and support services, which probably increased the likelihood that all students would know that they could opt out.Students with higher levels of high school preparation in math are more likely to directly enroll in college-level math within the first year of college enrollment.This result is consistent with prior research indicating that high school course-taking can predict passing rates for college-level coursework and college success more broadly (Long et al., 2012;Park-Gaghan et al., 2021;Woods et al., 2018).Our results also suggest that high school coursework is an important factor students and advisors should consider to inform course-taking decisions.Thus, high schools should make greater efforts to improve students' academic preparation.For example, the Tennessee Seamless Alignment and Integrated Learning Support (SAILS) program moves developmental math courses from college to high school in order to save students time and money in college.There is evidence documenting the positive effects of this program on improving the enrollment rates in college-level math and credit accumulation (Boatman & Bennett, 2021), although a more recent study suggests that co-requisite remediation may be more effective than high school remediation at supporting college math completion (Kane et al., 2021).
While prior research has largely focused on the impact of assignment into developmental courses, this study investigates the outcomes of students opting into developmental courses compared to students who made opted out.Our results indicate that the overall opting into developmental math is associated with worse outcomes by the third year.Compared to students who directly enrolled in college-level math in the first year, students who opted into developmental math had a significantly lower chance of passing college-level math and accumulated fewer college credits by the end of the third year.This may be related to the reality that the co-requisite format is not common in Florida and most students opting into developmental math take the course in the first semester through either the compressed or the modularized format.More than half of the students opting into developmental math failed to progress into college-level math.Thus, the worse performance outcomes of students opting into developmental math are largely driven by students who opted in but did not complete it.
However, we do find that if students can successfully progressed into college-level courses as soon as they completed the developmental math course, they would achieve better outcomes by the third year than students who only enrolled in college-level math, though these differences are modest in magnitude (with an increase of four percentage points in the probability of passing college-level math, and an addition of three credits by the third year).We acknowledge that it is difficult to rigorously establish the causal effect of completing the developmental math due to selection bias and we call for more future studies that adopt an experimental research design.In addition, due to data limitation, we only examined the probability of passing college-level math courses and the number of credits in the study.Future research can explore more outcome variables such as degree completion.But as shown in Table B, students at lower high-school-math ranks were more likely to enroll in both DE and college-level math versus directly enrolling in college-level math, suggesting that they achieved better outcomes with weaker high school preparations (when comparing students who directly enroll in collegelevel math).This may provide some evidence that what students have learnt in developmental math courses contribute to their success.These results imply that at least some underprepared exempt students can benefit from the developmental math course, particularly for those who plan to take a college-level math immediately after the completion of the developmental course.Institutions may consider to offer paired courses that allow for seamless transition from developmental to college-level math.
Our findings suggest that underprepared exempt students and advisors should be cautious about opting into developmental courses as these courses seem to be barriers in most cases.Nevertheless, both Florida and California that underwent developmental education reforms that allow more students to enroll in collegelevel courses regardless of their prior academic preparation have witnessed decreases in course-based passing rates for college-level math after the reforms (Melguizo et al., 2021;Park-Gaghan et al., 2020).These results call for more comprehensive math education reforms to enable more students to take and pass college-level math.For example, although exempt students were given the option to skip developmental math, many of them still need to take Intermediate Algebra, the pre-requisite math course in Florida, before they can enroll in gateway math courses.A recent study from Texas shows that creating alternatives to college algebra (such as statistical and quantitative reasoning) can contribute to increases in college math enrollment and completion (Schudde & Keisler, 2019).Another promising practice is the corequisite model that allows students to complete developmental education alongside college coursework (Logue et al., 2016;Kane et al., 2021).Institutional leaders at FCS colleges should consider how to offer more corequisite classes and encourage students who really need remediation to enroll in these classes given the current small enrollments in co-requisite courses.

Figure 1 .
Figure 1.Cumulative percentage of students passing collegelevel math in each semester by the end of year 3.

Figure 2 .
Figure2.Cumulative college-level credits earned in each semester by the end of year 3.

Table 1 .
Descriptive Statistics for Students in the Analytic Sample, by Cohort.
Note.Standard deviations in the parentheses.

Table 2 .
Multinomial Logistic Regression Estimates of Math Enrollment Choice in the First Year.

Table 3 .
Predicted Probabilties of Passing College-Level Math and Number of College Credits by the Third Year.