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The purpose of this paper is to illustrate how to examine the effectiveness of a pilot summer bridge program for elementary algebra using propensity scores. Typically, selection into treatment programs, such as summer bridge programs, is based on self-selection. Self-selection makes it very difficult to estimate the true treatment effect because the selection process itself often introduces a source of bias.

By using propensity scores, the authors can match students who participated in the summer bridge program with equivalent students who did not participate in the summer bridge program. By matching students in the treatment group to equivalent students who do not participate in the treatment, the authors can obtain an unbiased estimate of the treatment effect. The authors also describe a method to conduct a sensitivity analysis to estimate the amount of hidden bias generated from unobserved factors that would be needed to alter the inferences made from a propensity score matching analysis.

Findings suggest there is no significant difference in the pass rates of the subsequent intermediate algebra course for students who participated in the summer bridge program when compared to matched students who did not participate in the summer bridge program. Thus, students who participate in the summer bridge program fared no better or worse when compared to similar students who do not participate in the program. These findings also appear to be robust to hidden bias.

This study describes a unique way to estimate the causal effect of participating in a treatment program when there is self-selection into the treatment program.

This paper aims to describe how a fuzzy qualitative comparative analysis can be used to describe which combinations of academic factors are most influential for achieving success in college‐level mathematics. Using a fuzzy qualitative comparative analysis allows for the comparison of all possible combinations for a collection of predictor variables, as well as strategies for determining which configurations of these sets of variables are the most consistent with success in college‐level mathematics. Recent advances in fuzzy qualitative comparative analysis techniques have now integrated traditional qualitative comparative analysis strategies with formal statistical tests, thus allowing for the analysis and comparison of complex relationships that are difficult to describe with more traditional statistical methods such as regression analysis.

Data were collected from 259 full‐time, first‐time freshmen at a large state university in the USA. They were analysed using fuzzy‐set qualitative comparative analysis (FQCA).

Findings from this study suggest that the most parsimonious configuration of college remediation status, spending less time away from mathematics, and doing better in high school mathematics are key to success in college‐level mathematics.

Although numerous studies have made great progress in describing the complex relationship between prior mathematics exposure in high school with success in college‐level mathematics, one limitation of many studies is that they rely on analytic methods that only estimate the net effect of a single predictor variable, or a very small collection of predictor variables. This study utilises fuzzy‐set qualitative comparative analysis (FQCA) which can be used to analyze more complex interrelationships among a collection of predictor variables.