Examining the causal effects of the foundations of college math program in Delaware: an application of regression discontinuity and propensity score matching analysis
Date
2020
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Delaware
Abstract
Remedial education, also known as developmental education, college preparation courses, or skills courses, are usually offered by two-year and four-year colleges and universities in the United States to students deemed underprepared for college-level coursework. In sharp contrast with the prevalent offering of remedial courses in post-secondary education, research on the causal effects of placement in remedial courses is both mixed and limited, largely due to the failure to control for important selection biases. This dissertation seeks to address this gap in the literature through a partnership with the Delaware Department of Education (DDOE), which has taken action to intervene at an earlier stage by providing a Foundations of College Mathematics (FCM) course in twelfth grade to better prepare graduates for college-level math courses. ☐ In this dissertation, I apply two causal research designs to examine the impact of the FCM course offered to high school seniors who did not meet the College and Career Ready target score on the SAT Math test. The results suggest that a regression discontinuity (RD) design is not applicable to the program due to lack of sufficient “discontinuity” at the cut-score. However, a propensity score (PS) design using matched samples based on single-level (SL), multi-level (ML) and neural network (NN) models shows that the FCM course produced a significant reduction in students’ probability of taking a remedial math course in a DE college. Students who participated in the FCM courses in the twelfth grade and then enrolled in a DE college were 63% to 70% less likely to take a remedial math course during their first year in college. While there were no significant impacts on the probability of enrolling in a college in general, the FCM course may have had significant impacts on students’ likelihood of enrolling in a Delaware college. However, it is unclear whether students who enrolled in the FCM course do so because they had preexisting aspirations to enroll at a DE college, and thus the difference in enrollment rates may not be due to the FCM course. One model also showed a significant increase in students’ probability of earning a C or higher grade in a non-remedial math course during their first year in college, suggesting that the impact of FCM was not simply a reduction in remediation but improvement in college-level math skills. ☐ Additionally, I discuss implications of the findings and the application of RD and PS designs in similar pilot programs with limited sample sizes of students and schools in the treatment group. Considering the promising results from this study, future research on the FCM course should include a greater number of schools and eligible students enrolled in the FCM course in the twelfth grade. Long-term effects, and differential treatment impacts across different groups of students should also be investigated. In terms of methodology, this study also has implications for simulation studies examining best practices for utilizing NN in estimating PS.
Description
Keywords
Causal effects, Foundations of college mathematics, Neural network, Propensity score matching, Regression discontinuity, Remedial education