Spaced Retrieval Practice Imposes Desirable Difficulty in Calculus Learning

Abstract

After being taught how to perform a new mathematical operation, students are often given several practice problems in a single set, such as a homework assignment or quiz (i.e., massed practice). An alternative approach is to distribute problems across multiple homeworks or quizzes, increasing the temporal interval between practice (i.e., spaced practice). Spaced practice has been shown to increase the long-term retention of various types of mathematics knowledge. Less clear is whether spacing decreases performance during practice, with some studies indicating that it does and others indicating it does not. To increase clarity, we tested whether spacing produces long-term retention gains, but short-term practice costs, in a calculus course. On practice quizzes, students worked problems on various learning objectives in either massed fashion (3 problems on a single quiz) or spaced fashion (3 problems across 3 quizzes). Spacing increased retention of learning objectives on an end-of-semester test but reduced performance on the practice quizzes. The reduction in practice performance was nuanced: Spacing reduced performance only on the first two quiz questions, leaving performance on the third question unaffected. We interpret these findings as evidence that spacing led to more protracted, but ultimately more robust, learning. We, therefore, conclude that spacing imposes a desirable form of difficulty in calculus learning.

Analysis of the Deep Learning Strategies Questionnaire with Ecuadorian students

“…Future studies should replicate this study by controlling performance on learning tasks (i.e., with pre and post-test) and including mediating factors (e.g., self-efficacy and effort; Panadero et al, 2021). Further, as the parallel analysis suggested three factors and the exploratory analysis found four, more studies should confirm the internal structure of the questionnaire and consider whether deep information processing strategies can be better identified when associated with strategies that explicitly evoke prior knowledge and foster long retention (e.g., spacing and retrieval practice; Carpenter et al, 2022;Lyle et al, 2022).…”