Retrieval practice in higher education: Causality and content transfer effects in a gateway math course.

What is it about?

Many students struggle in introductory university mathematics courses, and instructors are constantly looking for evidence-based strategies to help them succeed. One promising approach is retrieval practice — the idea that actively recalling information from memory, rather than simply rereading notes or worked solutions, leads to stronger and more durable learning. While this has been well-established in laboratory settings and for fact-based subjects, much less is known about whether it works in real university mathematics courses, and whether it helps students go beyond memorization to actually apply their knowledge to new problems. In this study, we embedded weekly online problem sets into a gateway mathematics course for first-year business students at a German university, following three consecutive cohorts of roughly 570 to 640 students each. The exercises required students to reconstruct previously taught procedures from scratch, without access to worked solutions or step-by-step guidance. Crucially, the study was designed to distinguish between students who happened to practice more because they were already motivated or able, and students whose behavior genuinely changed because of the intervention — a distinction that many prior studies have not been able to make. Using a randomized assignment combined with an instrumental variable approach, we estimated the causal effect of retrieval practice on performance across different types of problems and assessment timepoints, including both short-term quizzes and end-of-term exams.

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Photo by Compare Fibre on Unsplash

Photo by Compare Fibre on Unsplash

Why is it important?

Most existing research on retrieval practice in higher education relies on correlational designs, meaning it is difficult to tell whether students benefit from the practice itself or whether more motivated and able students simply tend to practice more. This study addresses that gap directly by estimating causal effects using a quasi-experimental design that explicitly accounts for noncompliance and self-selection — methods common in economics but rarely applied in educational psychology. The findings show that retrieval practice not only improves performance on practiced problem types, but also helps students solve structurally similar problems they have never seen before, providing some of the clearest evidence to date that retrieval practice in mathematics promotes genuine conceptual understanding rather than mere repetition. The study also demonstrates that these effects replicate across three independent cohorts, strengthening confidence in the results. For instructors and course designers, the findings offer practical, actionable guidance: structured, incentivized retrieval practice embedded into regular coursework is a scalable and cost-effective tool for improving student learning in mathematically demanding university courses.

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