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Abstract

States and broad-access colleges are rapidly scaling corequisite coursework—a model where students concurrently enroll in college-level and developmental coursework—in response to dismal completion rates in traditional “developmental” sequences. At community colleges, evidence suggests that corequisite reforms can dramatically improve students’ completion of required college-level courses, but colleges often implement new programing and sequences with limited information. We analyzed administrative data from Texas community colleges implementing a statewide corequisite mandate. Our results illustrate (a) how colleges structured corequisite courses in response to the statewide mandate and (b) how corequisite coursework characteristics predicted student outcomes. Our results suggest that some corequisite coursework elements—including mixed-ability college-level classes, higher credits for the developmental education (dev-ed) corequisite support course, and using the same instructor across both the college-level and dev-ed course—improve students’ probability of passing college-level math, though these course design elements do not appear to predict long-term outcomes like persistence in college.

Keywords

community colleges corequisite coursework correlational analysis descriptive analysis developmental education educational policy higher education postsecondary education regression analyses

Roughly 60% of 2-year-college entrants do not meet college-readiness standards for college math (Bailey et al., 2010). These students are typically required to complete prerequisite developmental education (dev-ed) courses—which do not count toward a degree—before enrolling in introductory college courses. Because students placed into dev-ed are more likely to come from racially minoritized and lower-socioeconomic-status backgrounds, dev-ed, in its current form, appears to exacerbate inequities in academic outcomes (Bailey et al., 2010; Marshall & Leahy, 2020). In response to dismal rates of dev-ed completion and calls for reform, states and college systems are adopting corequisite coursework: a model where students concurrently enroll in college-level and developmental coursework.

The corequisite model enables students to earn college-level credits immediately while providing hands-on support through a paired dev-ed (or “corequisite”) course. Moving students through their dev-ed requirements and gateway math course can improve their momentum toward graduation (Adelman, 2006; Calcagno et al., 2007; Jenkins & Bailey, 2017; Wang et al., 2017). Inspired by promising evidence from early corequisite adopters across the country (e.g., Denley, 2015, 2016; Logue et al., 2016, 2019; Ran & Lin, 2019), there has been a recent flurry of dev-ed policy reform toward corequisite coursework, where 24 states now include corequisite supports as a means to accelerate student access to college-level coursework (Education Commission of the States, 2021). As a result, states and colleges across the country are rapidly replacing the traditional dev-ed sequence with corequisite coursework.

As corequisite reforms proliferate, colleges must determine how to pair courses and which faculty should teach them. Despite evidence that corequisite models improve efficiency for completing introductory, or “gateway,” college-level courses (Logue et al., 2016, 2019; Meiselman & Schudde, 2021; Miller et al., 2021; Ran & Lin, 2019), some faculty and staff resist adopting them (Brower et al., 2017; Daugherty et al., 2018), with adoption lagging considerably in math compared with English (Cuellar Mejia et al., 2020; Morales-Vale, 2019). As personnel work to scale reforms, evidence of best practices can overcome faculty concerns and inform decision-making.

This study can inform corequisite model development by illuminating how corequisite math course features predict student outcomes. We leverage state administrative data to examine how public 2-year colleges in Texas implemented a statewide mandate for corequisite coursework. Our results offer insights into how colleges structure corequisite courses in response to reforms and how corequisite coursework characteristics predict student outcomes.

Literature Review

Many students placed in dev-ed never complete their dev-ed coursework (Bailey et al., 2010; Clotfelter et al., 2015). Long, multicourse dev-ed sequences may impede student progress and cost students time and money (Deil-Amen & Rosenbaum, 2002; Melguizo et al., 2016). Restructuring dev-ed pathways so that students quickly accrue college-level credits could expedite student progress, where corequisites immediately offer students access to college credit. Next, we describe evidence for the impacts of corequisite coursework, followed by an overview of research on corequisire course characteristics.

Background on Corequisites

Descriptive findings from Tennessee, the first state to mandate corequisite reforms, suggest that corequisite models improve completion rates of gateway college math (Denley, 2015, 2016). To date, one experimental study (Logue et al., 2016, 2019) and two quasiexperimental studies (Meiselman & Schudde, 2021; Ran & Lin, 2019) illustrate positive short-term outcomes of corequisite math coursework, and one experimental study and one quasiexperimental study illustrate positive short-term outcomes of corequisite English coursework (Cho et al., 2012; Miller et al., 2021). In a randomized controlled trial at City University of New York (CUNY), students were placed in either prerequisite algebra—the traditional dev-ed math course (the control group)—or a college-level statistics course with a developmental support course (the treatment group) (Logue et al., 2016). Those in the corequisite statistics coursework were more likely to pass college-level math and, 3 years later, had completed more math courses, finished required coursework more quickly, and graduated at higher rates than those in prerequisite algebra. Studies in Tennessee and Texas found similar short-term positive impacts on passing college-level math, though they showed no increase in degree attainment after 3 years (Meiselman & Schudde, 2021; Ran & Lin, 2019).

Combined, the evidence of these three studies in different contexts supports the notion that corequisite math is more effective than prerequisite dev-ed math at increasing gateway math completion. At the same time, colleges implementing corequisites face logistical and financial concerns and need information about how to structure corequisites for student success.

The Role of Varied Course Designs

In response to policies aimed at increasing corequisite coursework, many institutions are scrambling to pair college-level math courses with corequisite developmental supports. Corequisite models can include several different structural components: Colleges must determine the timing of the corequisite support course, how to assign faculty to teach paired courses, instructional modality, whether to include college-ready students in the college-level course, and which math pathways (e.g., algebra, statistics) to prioritize.

Timing of developmental support

Many corequisite advocates envision that colleges will provide “just-in-time” support for the college-level course, with dev-ed course material concurrently supplementing college-level material; however, this is not always the case (Daugherty et al., 2018). Some corequisite courses are organized sequentially: The dev-ed component is taken first—serving as an embedded prerequisite—and the college-level, second within the same term (Daugherty et al., 2018; Meiselman & Schudde, 2021). Currently, little evidence exists about how timing the corequisite support course predicts student outcomes. Meiselman and Schudde (2021) offered preliminary evidence that students in “embedded prerequisites” were slightly more likely to pass college-level math and persist in college than “true corequisite” students, but their identification strategy did not fully account for selection into the embedded prerequisite model.

Instructor structure and characteristics

Another structural component concerns whether the college-level course and dev-ed support course are taught by the same instructor. If two instructors teach the courses, they must collaborate and communicate to maintain similar pacing and align content. The extent of the alignment between the two courses can improve the student experience; using the same instructor may facilitate alignment (Daugherty et al., 2021).

Non-tenure-track (NTT) faculty have traditionally taught the bulk of developmental coursework (Datray et al., 2014; Grubb & Cox, 2005), but corequisite reforms may shift some of that responsibility to tenure-track (TT) faculty. Faculty with different contractual forms often face different responsibilities and levels of job security (Conley et al., 2002; Ran & Xu, 2018). In a public 2-year-college system with no TT faculty, Ran and Xu (2018) found that students in introductory courses with short-term NTT instructors (i.e., NTT faculty with temporary adjunct contracts), compared with long-term NTT instructors (those with longer-term contracts), experienced higher grades but lower probabilities of taking and passing additional courses in the sequence. Research suggests that contextual and institutional factors related to part-time employment rather than instructor characteristics (e.g., race/ethnicity, gender, and highest degree earned) explain the association between NTT faculty status and student outcomes (Ran & Sanders, 2020).

Instruction modality and type

Research suggests that taking an introductory college-level math course online, as opposed to face-to-face, is associated with a 10-percentage-point decrease in the probability of passing it and a 15-percentage-point increase in the probability of course withdrawal (Xu & Jaggars, 2011). Taking developmental courses online is also negatively associated with student outcomes, including enrolling in and passing subsequent gateway courses (Jaggars & Xu, 2010), although research on hybrid developmental courses offers more optimistic findings. Research from Kentucky suggests that public-2-year-college students in a hybrid developmental math course—a mix of in-person and online sessions—were more likely to persist to the following semester than were those in a face-to-face class (Davidson & Petrosko, 2015). Identifying the effects of instructional modality is challenging because students select course modality aligned with their preferences, where students with the greatest external obligations (working for pay, caring for dependents) are more likely to select online options (Dutton et al., 2002).

The dev-ed support course can be structured in several ways. It can be course based—structured primarily as a lecture in a traditional course format—or non–course based, where the supports are offered outside of traditional classroom instruction (Daugherty et al., 2018). A non-course-based dev-ed section has the potential to align content with student needs; for example, it can include sections offered at a tutoring center with modularized computer-adaptive instruction or with an instructor who supports students with various levels of needs at their own pace. To date, no studies have explored the roles instructional modality or type play in student outcomes within a corequisite model.

Class composition and size

In structuring corequisite coursework, practitioners must decide whether to include both college-ready and dev-ed students in the college-level course. The mixed-ability model has some support in K–12 math settings, where research indicates that students with lower prior achievement benefit the most from collaborating with peers on math problems (Boaler, 2008; Fuchs et al., 1997, 2001). Some evidence suggests that similar peer effects occur in college science, technology, engineering, and mathematics (STEM) classrooms, although the only work in this area examines students at an elite university (Ost, 2010). In the only study (to our knowledge) on peer effects on course outcomes at community colleges, Liu and Xu (2021) found that the percentage of dual-enrollment students (those taking college coursework for credit during high school) enrolled in a community college course was negatively correlated with academic performance among non-dual-enrollment students (Liu & Xu, 2021). Parallels may exist with mixed-ability classrooms, in which students who need developmental support take college-level math with college-ready peers, but because those students are also college students, their presence may not evoke the same response. Mixed-ability classes may also increase teacher expectations for students with the lowest prior achievement, as teachers tend to teach to the middle-range ability group when confronted with varied student ability (Tomlinson, 2014).

Class size is also linked with student outcomes, where K–12 research suggests that smaller classes improve students’ academic performance, perhaps through shifts in teachers’ instructional strategies or increased social and academic engagement compared with larger classes (Finn et al., 2003). Class size has not been focal in higher education research, though some studies in university settings link larger class sizes to fewer interactions with faculty and peers and lower grades (Beattie & Thiele, 2016; Johnson, 2010; Kokkelenberg et al., 2008).

Math pathways

Dev-ed reforms have often coincided with math pathways reforms, which reconsider the status quo algebra-for-all approach to college math requirements. Under math pathways, students can select quantitative reasoning (QR), statistics, or algebra depending on their desired major (Bryk & Treisman, 2010). Math-pathways reforms focus on changing both the content and instruction of math in college, offering options for math content and shifting instructional approaches for how they learn it (Zachry Rutschow et al., 2019). In a randomized controlled trial in Texas, Zachry Rutschow and colleagues (2019) illustrated that the Dana Center Math Pathways model, which accelerated dev-ed course sequences and reformed math curricula across three math pathways, positively impacted college-level math course completion and number of math credits earned.

Research on the link between math pathway—which type of math course students take—and student outcomes is limited. Extant experimental research on corequisite math in the CUNY system (Logue et al., 2016, 2019) targeted students whose majors did not require algebra. The experiment identified stronger effects of corequisite statistics coursework on several long-term academic outcomes, including transfer and degree attainment, compared with studies focused on corequisites in contexts with a mix of math pathways or primarily algebra (Meiselman & Schudde, 2021; Ran & Lin, 2019); it is difficult to know whether the differences in findings result from math pathways or different study contexts. Ran and Lin (2019) found that there were differential effects of corequisite math coursework across math pathways, where the positive effects of corequisite math coursework on completing college-level math were largely driven by students taking non-algebra college math rather than college algebra.

Although interest in corequisite models has increased, little research has explored the efficacy of different approaches and how students in corequisite coursework respond to corequisite course structures and characteristics. College personnel implementing corequisite reforms need this information to build efficient, effective math pipelines for students.

Research Questions

To help meet the pressing need for information about the link between corequisite coursework characteristics and student outcomes, we address the following research questions:

As colleges worked to implement a statewide corequisite mandate, how did they structure corequisite math coursework, including timing of course pairings, instructional modalities, math pathway offerings, and instructor assignments?

How do corequisite course structures and characteristics predict student outcomes?

Policy Contexts

Half of all first-time college students at Texas public 2-year institutions do not meet college-readiness standards in math—a score of 350 on the math Texas Success Initiative (TSI) assessment, a placement test taken at college entrance (Texas Higher Education Coordinating Board [THECB], 2016). Seeking stronger student outcomes, some colleges implemented corequisite coursework as early as 2014 but enrolled only a small fraction of students in corequisite math offerings (Meiselman & Schudde, 2021). In 2017, Texas’s 85th Texas Legislature passed House Bill 2223 (HB2223), a mandate for colleges to scale corequisites for students who do not meet college-readiness standards. HB2223 required colleges to enroll at least 25% of all developmental students in each subject (i.e., math and English) in corequisite coursework by fall 2018, 50% by fall 2019, and 75% by fall 2020 (THECB, 2018). Using rulemaking authority, the THECB recently amended the policy to require that colleges move to 100% corequisites by fall 2021 (THECB, 2020).

HB2223 allowed colleges to determine how to structure corequisite math coursework. The recently enacted policy allows for sequential corequisite models as long as the dev-ed and college-level courses are offered within the same term. State policy requires that faculty with appropriate credentials teach the college-level component; this standard may shape colleges’ decisions to assign the same instructor across paired courses, because dev-ed instructors may lack the credential needed to teach college-level courses.

Method

To answer our research questions, we used statewide administrative data provided through a restricted-use agreement with the Texas Education Research Center (ERC), a research center and data clearinghouse at the University of Texas at Austin. We defined corequisite math coursework as enrolling in dev-ed and introductory college-level math courses in the same semester. Our analytic sample includes community college students who enrolled in corequisite math in a fall or spring term between fall 2018 and spring 2020. We relied on descriptive statistics to capture the structure and characteristics of corequisite math coursework. We used regression to explore the relationship between course characteristics and student outcomes, such as course passing, persistence in college, and vertical transfer.

Data

The ERC data includes student-level data for the entire population of secondary and postsecondary students in Texas. We used student-level data collected by the THECB, including files capturing student demographics, college enrollment, course enrollment and grades, placement test scores, and financial aid information, along with demographic and occupational information on course instructors.

To create the analytic sample, we first identified community college students who enrolled in dev-ed and college-level math within the same semester in the period after HB2223 was enacted (fall 2018 to spring 2020) (N = 103,260). We restricted the analytic sample to students who had placement test scores (N = 69,301), so that we could include the TSI score as a proxy for math ability.¹ In the final analytic sample, 1% of students took module-based dev-ed math or multiple corequisite math courses in the same term, which resulted in two or more dev-ed math attempts in the same semester as the college-level course. Thus, the final analytic sample captured 70,026 corequisite dev-ed course enrollments among 69,301 students between fall 2018 and spring 2020.

Variables

Our main independent variables of interest capture corequisite math course structures and characteristics. For the college-level math course, we included class size, instructional modality, an indicator of mixed-ability composition (mix of developmental and college-ready students), and math pathway: college algebra, math for business, quantitative reasoning, and statistics. For the developmental-level math course, we used measures of class size, semester credit hours, instructional modality, whether the course was lecture based (as opposed to a lab or independent study), and whether the college-level course was taught by the same instructor as the developmental course.² We also captured four categories of dev-ed support courses based on the timing and duration of support: full-term concurrent, compressed concurrent, embedded prerequisite, and “boot camp” prerequisite (where the boot camp prerequisite is shorter than the embedded prerequisite, but both occur before the college-level course).

We also capture characteristics of developmental math course instructors, including gender, race/ethnicity, age, faculty type (NTT vs. TT) and employment intensity, educational attainment, and 9-month salary.³ Our regression models include student characteristics and academic and financial background information as statistical controls. For example, we used math placement scores as a proxy for student ability. Because some students had non-TSI placement scores, we calculated each student’s z-score on the placement test taken. Appendix A includes definitions and descriptive statistics for variables used in our main and supplemental analytic models.

We focus on five separate outcome measures that capture student performance in the college-level course and subsequent college outcomes. We created measures for passing the college-level math course (as opposed to either failing or withdrawing) and withdrawing from it (as opposed to persisting to the end of the course). To measure academic progress, we captured whether students persisted into the subsequent semester and into the subsequent year and whether they transferred to a 4-year institution within 1 year. We ran analyses for several additional outcomes, including dev-ed math course outcomes, subsequent math course enrollment, and major switching, which we present in Appendix B.

Analytic Approach

To understand the structure and characteristics of corequisite coursework implemented at Texas community colleges (Research Question 1), we leveraged descriptive statistics. We then used logistic regression, given the dichotomous nature of our dependent variables, to examine which variables predict student outcomes while controlling for student background (Research Question 2).

We used the following model for student i at college j in semester t:

L o g i t (p_{i j t}) = b_{0} + b_{1} X_{1} + b_{2} X_{2} + \dots + b_{n} X_{n} + ξ_{j} + λ_{t}

where p_ijt is the probability of a discrete outcome’s occurring, b₀ is the intercept, X₁ to X_n are the independent variables, b₁ to b_n are the associated regression weights, ξ_j is a college fixed effect, and λ_t is a semester fixed effect. The logit transformation ensures that the predicted probability of the outcome’s occurring lies within the 0-to-1 bound. This approach allows for a more realistic representation of the curvilinear association because of the dichotomous outcome variable, and it tends to linearize the association between the predicted outcome and the set of predictors (Raudenbush & Bryk, 2002). We included college and semester fixed effects to control for other sources of between-college variation and factors changing each semester.

Because we rely on regression, the results do not represent causal relationships. When we use observational data, a regression with rich covariates is our strongest analytic strategy for examining which course features predict student success. We included a variety of control variables capturing student and instructor background; nevertheless, the estimated relationships could still partially be explained by unobserved factors. Several factors we expect to predict course selection and student outcomes, such as student motivation, social networks, and instructional quality, are unobservable in the data. Thus, the results are correlations that partially reflect sorting into specific courses (i.e., some students are more inclined to enter a given math course type than others, and those unobserved characteristics may also predict subsequent academic outcomes). Despite these limitations, the results stand to inform the extant literature on corequisite implementation.

Results

Description of Corequisite Math Coursework

We begin by describing, in Table 1, course and instructor characteristics for the developmental and college-level courses within community colleges’ corequisite offerings since HB2223. The average developmental-support course was larger than the college-level course (by about 1.5 students) and worth fewer credits. Both courses were predominantly lecture based (95% of college-level courses and 77% of dev-ed courses) and taught in person. Over one half of the paired college-level and developmental-support courses were taught by the same instructor. Colleges primarily offered dev-ed math corequisite courses that ran concurrently with the college-level course. Most—88%—of the dev-ed support courses were run as full-term concurrent courses: Students co-enrolled in the support course and college-level math course throughout the semester. The remaining dev-ed support courses were structured as compressed concurrent dev-ed (6% coincided with the college-level course but were shorter in duration) and embedded prerequisites (5% of dev-ed courses preceded the college-level course within the same term). Very few courses (approximately 1%) were set up as boot camp prerequisites, where the developmental course occurred before the college-level course and lasted less than 2 weeks. Nearly one half of the college-level courses were college algebra, with the remainder offered as QR and statistics and, less often, math for business.

Table 1

Descriptive Statistics of Corequisite Math Coursework: Developmental and College-Level Course Characteristics

Variable	Math course level
Variable	Dev-ed (% or M)	College (% or M)
Course N	6,671	7,290
Course characteristics
Class size	15.7	14.2
Number of credits	2.3	3.0
Lecture section	76.65%	94.84%
Instruction modality
Face-to-face	88.01%	84.65%
Online	10.54%	13.47%
Hybrid	1.45%	1.88%
Same instructor for paired courses	55.81%	51.59%
Dev-ed course type
Boot camp prerequisite	1.09%	—
Embedded prerequisite	4.96%	—
Compressed concurrent	6.09%	—
Full-term concurrent	87.86%	—
College-level composition
Mixed ability	—	43.61%
All dev-ed students	—	56.39%
College-level math pathway
Algebra	—	49.97%
Math for business	—	12.04%
Quant reasoning	—	19.22%
Statistics	—	18.77%
Instructor characteristics
Female	57.40%	53.40%
Race
White	60.58%	61.32%
Black	10.03%	8.55%
Hispanic	18.33%	18.74%
Asian	7.99%	8.68%
Other	3.07%	2.72%
Age	50.2	49.9
Faculty type
Tenured	13.58%	14.10%
Tenure-track	3.42%	4.36%
Full-time non-tenure-track	48.34%	52.47%
Part-time non-tenure-track	26.47%	19.56%
Unknown	8.18%	9.51%
Highest education level
Doctoral degree	9.29%	11.21%
Master’s degree	70.47%	83.48%
Bachelor’s degree	17.45%	2.95%
Associate degree or certificate	<1%	<1%
No degree	2.07%	2.13%
Full-time employed	73.36%	80.26%
Calculated 9-month salary	$44,910	$48,770

Note. The table describes characteristics of corequisite math courses and instructors (reported at the course level, where columns 1 and 2 show results for the dev-ed support course and college-level course, respectively). We provide means for continuous variables and percentages for categorical measures. The measures of college-level course instructor characteristics are not included in the regression models because the majority of corequisites were taught by same instructor. Dev-ed = developmental education.

In addition to corequisite course structures and characteristics, Table 1 describes instructor characteristics. Over one half of all courses were taught by female instructors, and the racial-ethnic representations looked fairly similar across both course types, with White faculty teaching approximately 61% of courses. The age of instructors was also similar, with an average age of 50. Only 17% to 18% of instructors were TT or tenured in either course type. The majority of instructors for both courses were NTT, where the bulk of instructors were full-time NTT (48.3% for dev-ed and 52.5% for college level). A larger portion of dev-ed instructors than of college-level instructors were part-time NTT (27% and 20%, respectively). The educational backgrounds of instructors differed across college-level and dev-ed courses. A smaller portion of dev-ed instructors held a graduate degree (about 80%) compared with college-level instructors (about 95%). On average, college-level instructors earned more, by about $4,000, than dev-ed instructors per academic year.

Regression Results: Course and College Outcomes

Table 2 presents the results for a series of logistic regression models predicting college-level course outcomes and subsequent college outcomes. For ease of interpretation, we present results using average marginal effects (AMEs) rather than log-odds or odd ratios; AMEs can be interpreted as the change in predicted probability for a one-unit change in the independent variable (holding other independent variables at their mean). The first and second columns present results from regressions on passing or withdrawing from the college-level math course, and the final three columns present results for persistence into next semester, persistence into the next year, and transferring to a university within 1 year.

Table 2

Regression Model Predicting Student Outcomes

Variable	College-level math course		Persistence and transfer
	Passedthe course	Withdrewfrom the course	Persistence into the subsequent semester	Persistence into the subsequent year	Transfer to a 4-year institution within 1 year
	AME(SE)	AME(SE)	AME(SE)	AME(SE)	AME(SE)
Passed the college-level math course^a			0.298*** (0.006)	0.342*** (0.007)	0.038 *** (0.003)
College-level course characteristics
Class size	0.002** (0.001)	−0.002*** (0.001)	0.000(0.000)	0.000(0.001)	0.000(0.000)
Mixed ability	0.029* (0.013)	−0.012(0.007)	0.006(0.009)	0.014(0.014)	−0.002(0.005)
Instruction modality (ref. face-to-face)
Online	−0.080** (0.029)	0.014(0.014)	−0.011(0.012)	−0.014(0.017)	0.009(0.007)
Hybrid	0.070(0.043)	−0.085** (0.021)	0.019(0.024)	0.017(0.030)	0.001(0.017)
Math pathway (ref. algebra)
Math for business	−0.003(0.016)	0.004(0.017)	0.014* (0.006)	0.005(0.008)	0.007(0.005)
Quantitative reasoning	0.107*** (0.013)	−0.080*** (0.006)	−0.048*** (0.008)	−0.066*** (0.011)	−0.014*** (0.004)
Statistics	0.005(0.015)	−0.016* (0.008)	−0.012(0.007)	−0.028*** (0.008)	−0.001(0.004)
Dev-ed support course characteristics
Class size	0.000(0.000)	0.000(0.000)	0.000(0.000)	0.000(0.000)	0.000(0.000)
Number of credits	0.016* (0.008)	−0.011** (0.004)	−0.013(0.008)	−0.014(0.008)	0.000(0.003)
Lecture section	0.017(0.024)	−0.037* (0.018)	−0.002(0.012)	−0.015(0.014)	0.002(0.006)
Instruction modality (ref. face-to-face)
Online	−0.054* (0.026)	0.028* (0.014)	0.014(0.012)	0.009(0.017)	0.006(0.007)
Hybrid	−0.127*** (0.032)	0.112*** (0.034)	−0.012(0.019)	0.040(0.027)	0.019(0.019)
Same instructor	0.037* (0.015)	−0.019* (0.009)	−0.010(0.012)	−0.008(0.014)	−0.001(0.003)
Dev-ed course type (ref. full-term concurrent)
Boot camp prerequisite	0.039(0.041)	−0.064* (0.026)	0.028(0.026)	−0.012(0.042)	−0.033* (0.009)
Embedded prerequisite	−0.007(0.050)	−0.032(0.031)	0.085* (0.033)	0.003(0.024)	−0.015(0.006)
Compressed concurrent	0.013(0.022)	−0.014(0.016)	0.129** (0.032)	−0.036* (0.015)	−0.008(0.005)
Dev-ed support course instructor characteristics
Female	0.015(0.011)	-0.006(0.007)	0.006(0.004)	0.009(0.005)	0.001(0.002)
Race (ref. White)
Black	−0.003(0.017)	0.000(0.012)	0.000(0.007)	0.004(0.008)	0.000(0.005)
Hispanic	0.024(0.017)	−0.016(0.011)	−0.009(0.006)	−0.008(0.009)	−0.007(0.004)
Asian	−0.017(0.016)	0.005(0.007)	0.002(0.007)	0.010(0.009)	−0.008(0.007)
Other	−0.064*** (0.018)	0.031* (0.015)	−0.016(0.011)	0.001(0.010)	−0.016(0.012)
Age	0.000(0.000)	0.000(0.000)	0.000(0.000)	0.000(0.000)	0.000* (0.000)
Faculty type (ref. tenured)
Tenure-track	0.041(0.036)	−0.035(0.022)	−0.009(0.011)	0.011(0.014)	−0.011(0.007)
Full-time non-tenure-track	0.047** (0.018)	−0.037** (0.012)	−0.005(0.008)	−0.011(0.011)	0.009(0.006)
Part-time non-tenure-track	0.048(0.026)	−0.025(0.017)	−0.021(0.014)	−0.015(0.016)	−0.007(0.011)
Unknown	0.058* (0.027)	−0.049** (0.017)	−0.005(0.010)	0.006(0.013)	0.003(0.006)
Highest education level (ref. no degree)
Doctoral degree	0.004(0.029)	0.005(0.023)	0.005(0.024)	−0.019(0.028)	−0.002(0.008)
Master’s degree	0.002(0.023)	−0.001(0.022)	0.004(0.023)	−0.012(0.023)	0.002(0.006)
Bachelor’s degree	0.002(0.026)	0.002(0.023)	0.010(0.023)	0.000(0.025)	0.000(0.007)
Associate degree	0.014(0.035)	0.005(0.054)	−0.050(0.042)	−0.015(0.035)	−0.013(0.016)
Calculated 9-month salary	0.000(0.000)	0.000(0.000)	0.000(0.000)	0.000(0.000)	0.000(0.000)
Sample size	70,026	70,019	70,026	52,307	52,029

Note. Table presents full logistic regression results, where each column represents a separate logistic regression model. All models included the following student characteristics: gender, race/ethnicity, age, major, financial aid application, Pell grant recipient, enrollment intensity, first time in college, and a z-score for their math placement test score. All models also included semester and college fixed effects and used robust standard errors clustered by semester and college. We present average marginal effects (AME) and standard errors (SE) for each covariate included in the binary logistic regression models. For statistical significance tests, we rely on raw p values in the table. To adjust for multiple comparisons across regression models, we also estimated Benjamini et al.’s (2006) sharpened q values, following guidance from Anderson (2008), and present the results in Appendix D. The first three analyses included the entire sample, and the subsequent analyses excluded students in spring 2020 from the analytic sample because the follow-up data have not yet been released to capture outcomes after 1 year. The sample size across outcomes varies slightly because of the inclusion of both semester and college fixed effects, where some colleges with no variation in a given outcome (e.g., course withdrawal and transfer) during a given term were dropped from those analyses. For ease of interpretation, the sample means for the outcomes of interest in each of the five regressions are passed college math: 0.613; withdrew from college math: 0.171; persistence next semester: 0.741; persistence next year: 0.558; transfer: 0.047. Ref. = reference.

“Passed the college-level math course” is included as an independent variable only in regressions on persistence and transfer outcomes.

p < .05. **p < .01. ***p < .001.

Predictors of college-level math course passing and withdrawal

Looking at predictors of college-level course outcomes, we note several patterns. The class size of the college-level course appeared to have a small positive association with passing and negative association with withdrawal—the larger the class size, the more likely students were to pass and less likely they were to withdraw. Taking a mixed-ability college-level math section was associated with a 3-percentage-point increase in the probability of passing compared with taking a section where all students did not meet college-readiness standards. In terms of instructional modality, students in an online college-level course were 8 percentage points less likely to pass the course than students in a face-to-face course. Students in hybrid courses, however, appeared less likely to withdraw than those in face-to-face courses. Finally, the math pathway of the college-level course was associated with both passing and withdrawal. Compared with the students taking college algebra, taking QR was associated with a 10.7-percentage-point increase in the probability of passing the course. Taking either QR or statistics, as opposed to algebra, negatively predicted course withdrawal.

Several developmental course characteristics also predicted college-level course outcomes. Increased credit hours of the dev-ed section positively predicted passing the college-level math course (and negatively predicted withdrawal), possibly indicating that students benefit from more time-intensive developmental support courses. Enrolling in a lecture-based dev-ed course, as opposed to a lab or independent study, predicted a decrease in withdrawal from the college-level course. Instructional modality of developmental courses also predicted college math course outcomes, where taking online or hybrid developmental courses, compared with face-to-face courses, was associated with a decreased probability of passing college-level math and an increased probability of course withdrawal. Taking corequisite coursework where the same instructor taught the college-level math and the dev-ed math support courses was associated with a 3.7-percentage-point increase in the probability of passing college-level math and 1.9-percentage-point decrease in the probability of withdrawing, compared with a corequisite model in which the paired courses were taught by different instructors. Finally, the timing and duration of the developmental support course (dev-ed math course type) did not appear to predict passing college-level math, but enrolling in a boot camp–style prerequisite dev-ed course was associated with a somewhat lower probability of withdrawing from the college-level course than was enrolling in a full-term concurrent dev-ed support course.

Regarding developmental instructors’ characteristics, we found that those taking the dev-ed support course with a full-time NTT instructor experienced a 4.7-percentage-point boost in the probability of passing college math compared with those taking the course with a tenured professor. (We similarly see a decrease in their probability of withdrawal.) The “unknown” faculty category was also associated with improved passing and decreased course withdrawals. Although we cannot avow that all the faculty in that category are full-time NTT instructors, we suspect that they are—that group largely comprises faculty at a handful of colleges that do not classify faculty and have no tenure (although we can see that most “unknown” instructors work full-time).

Predictors of persistence and transfer

As we turn to longer-term outcomes, a prominent predictor of student success was whether the student had passed their college-level math course. Passing the college-level math course was associated with a 30- and 34-percentage-point increase in the probability of persisting into the subsequent semester and the following year, respectively, and with a 3.8-percentage-point increase in the probability of transferring to a university within a year.

Although several college-level math and developmental course characteristics that predicted short-term success in college-level math did not predict persistence and transfer, the math pathway of the college-level course and the timing of the dev-ed course appeared consequential for those outcomes. Taking QR or statistics, compared with algebra, negatively predicted persistence and vertical transfer, though the observed pattern for statistics was significant only for persistence into the next year. Students in math for business were more likely to persist into the subsequent year than algebra students, but the relationship was no longer significant a year out. The timing of the developmental support course appeared to predict persistence in college, where the embedded prerequisite and compressed concurrent models positively predicted persistence into the next term, compared with a full-term concurrent dev-ed course structure. The relationships are no longer significant (and, for compressed concurrent, actually reverse direction) for the outcome capturing persistence into the next year. Boot camp–style prerequisites appeared more negatively related to transferring to a 4-year institution within 1 year, compared with full-term concurrent dev-ed.

We also examined whether developmental course instructor characteristics were associated with the probabilities of persistence and transfer, but the results yielded no notable significant patterns. In Appendix B we present results for additional outcomes, including developmental course outcomes, math course taking, and major choice.

Discussion

Over the past few years, colleges across the country began to revise decades-old approaches to dev-ed. Faced with pressure to implement corequisite reforms, college administrators and faculty need evidence for how to build effective course pairings of introductory college-level math and corequisite developmental support. In this article, we used administrative data from Texas to illustrate how colleges structured corequisite coursework in response to a statewide mandate and how different corequisite course characteristics and structures predict student outcomes.

For the most part, our results suggest that, among students taking corequisite coursework, some course design decisions moderately improve passing rates of college-level math but do not trickle down to longer-term outcomes, like persistence and transfer. Our results suggest that mixed-ability college-level math classes boost pass rates for students who tested as not college ready, which presents an actionable approach colleges might consider when designing corequisite coursework. Other characteristics, like course modality, are also linked improvements in course outcomes, though it is unclear whether those results are driven by selection (i.e., students in face-to-face vs. online courses, or in different math pathways, likely differ systematically in a way that may not be captured in our models). Experiencing the college-level math course face-to-face is associated with higher pass rates than taking the course online, although hybrid modality may boost course retention (though we should note that hybrid courses made up a very small proportion in our sample and may not be representative of hybrid courses generally).

The math pathway of the college-level course significantly predicts course outcomes and subsequent college outcomes, whereas other college-level course characteristics do not appear to explain the longer-term college outcomes, but we anticipate that students’ differential selection into math pathway may also play a role in these observed relationships. Taking QR, compared with taking algebra, is positively associated with passing college math but negatively associated with persistence and vertical transfer. Taking statistics is also associated with a decrease in the probability of persistence into the subsequent year. Students in math for business, however, are more likely to persist into the next term than those who take algebra, though the relationship diminishes by the subsequent term. Overall, our results suggest that students in the college algebra pathway are more likely to persist in college than those in other pathways. Our supplemental analyses (see Appendix B) suggest they are also more likely to switch into STEM majors and to enroll in advanced math coursework. Ran and Lin (2019) similarly reported that students in non-algebra corequisite coursework experienced a larger boost in passing college-level math than those in algebra, with minimal long-term impacts. In their study of corequisite statistics coursework, Logue and colleagues (2016, 2019) observed both greater short-term improvements in course outcomes and longer-term benefits for credit accrual and degree attainment than in the traditional prerequisite algebra course. Although our results suggest that non-algebra corequisite coursework is correlated with higher passing rates than algebra corequisites, it is possible that the statistical model does not fully capture selection into math pathways; we also expect there could be differences in student support structures and subsequent course sequences across math pathways that are correlated with persistence and transfer. Selection into and impacts of math pathways are beyond the scope of our study, but we hope these results spur relevant future research.

Our regression results suggest that developmental supports also shape student outcomes in the college-level course. The number of credits for the dev-ed support course is positively associated with passing the college-level course. Likewise, face-to-face instruction and taking a lecture-based course also appear to boost success in the college-level math course.

Structuring corequisite coursework to use the same instructor across both courses positively predicts passing and persisting in the college-level course. Although we cannot know the mechanism driving this result, it is possible that when the two courses have the same instructor, the content is better aligned (Daugherty et al., 2018). Taking the developmental course with a full-time NTT instructor appears to positively predict passing the college-level course and course retention. Although we cannot discern experience teaching dev-ed from the administrative data we have access to, prior research (e.g., Datray et al., 2014; Daugherty et al., 2018) and our ongoing interviews in the field suggest that NTT instructors, especially those appointed full-time, have historically taught dev-ed courses. We hope that future research can capture the role teaching experience plays in student outcomes and can delineate between how prior experience teaching dev-ed intersects with conditions of having paired instructors.

Corequisite course design decisions appear to shape immediate student outcomes, such as persisting in and passing their required college-level math course. Our study offers a first look at how Texas community colleges, which educate 12% of the nation’s public-2-year-college students (Snyder et al., 2019), implemented a statewide mandate for corequisites. By fall 2019 (the second fall cohort in our analytic sample), one half of all developmental math students were enrolled in the corequisite courses we examined. Our results suggest that some course design elements, such as mixed-ability classes for the college-level course, higher credit loads (as opposed to one-credit courses) for the dev-ed corequisite support course, and using the same instructor across both the college-level and dev-ed courses, improve immediate outcomes for students. The relationships we illuminate offer insights for policymakers, administrators, and practitioners seeking evidence for how to put corequisite models into practice.

Supplemental Material

sj-docx-1-ero-10.1177_23328584221086664 – Supplemental material for Constructing Corequisites: How Community Colleges Structure Corequisite Math Coursework and the Implicationsfor Student Success

Supplemental material, sj-docx-1-ero-10.1177_23328584221086664 for Constructing Corequisites: How Community Colleges Structure Corequisite Math Coursework and the Implicationsfor Student Success by Wonsun Ryu, Lauren Schudde and Kim Pack in AERA Open

Footnotes

Authors’ Note

The first two authors are equal authors (order is alphabetical). The research reported here was supported by the National Science Foundation through Grant 1856720 (EHR/IUSE) to the University of Texas at Austin (PI: Lauren Schudde) and by the Eunice Kennedy Shriver National Institute of Child Health and Human Development through Grant P2CHD042849 (Population Research Center) awarded to the Population Research Center at the University of Texas at Austin. The opinions expressed are those of the authors and do not represent views of the National Science Foundation or National Institutes of Health. All opinions and any errors are our own.

ORCID iDs

Wonsun Ryu

Lauren Schudde

Kim Pack

Open Practices

Information for how to access the data for this article can be found at .

Notes

Authors

WONSUN RYU is a postdoctoral scholar at the Population Research Center at the University of Texas at Austin. His research investigates how higher education policies work and their impact on student outcomes. He holds a PhD in educational leadership and policy and an MS in statistics from the University of Texas at Austin.

LAUREN SCHUDDE is an associate professor of educational leadership and policy at the University of Texas at Austin. Her research examines the impact of educational policies and practices on college student outcomes, with a primary interest in how higher education can be better leveraged to ameliorate socioeconomic inequality in the United States. She earned her PhD in sociology from the University of Wisconsin-Madison.

KIM PACK is a doctoral student in educational leadership and policy at the University of Texas at Austin. Her research focuses on policies and practice that impact student success outcomes and alleviate socioeconomic disparities in postsecondary education, with particular emphasis on community college degree pathways.

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Supplementary Material

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Constructing Corequisites: How Community Colleges Structure Corequisite Math Coursework and the Implications for Student Success

Abstract

Keywords

Literature Review

Background on Corequisites

The Role of Varied Course Designs

Timing of developmental support

Instructor structure and characteristics

Instruction modality and type

Class composition and size

Math pathways

Research Questions

Policy Contexts

Method

Data

Variables

Analytic Approach

Results

Description of Corequisite Math Coursework

Regression Results: Course and College Outcomes

Predictors of college-level math course passing and withdrawal

Predictors of persistence and transfer

Discussion

Supplemental Material

sj-docx-1-ero-10.1177_23328584221086664 – Supplemental material for Constructing Corequisites: How Community Colleges Structure Corequisite Math Coursework and the Implicationsfor Student Success

Footnotes

Authors’ Note

ORCID iDs

Open Practices

Notes

Authors

References

Supplementary Material