Investigating distributed practice as a strategy for school students learning mathematics

Spacing or distributed practice is a prominent learning strategy that is related to the so-called desirable difficulties. With distributed practice, a given learning duration is interrupted by at least one break of variable length. In contrast, with massed practice the same total time is spent learning, but without interruption. There is a rich body of empirical evidence proving the positive effect of distributed practice on the retention of verbal material. Beyond rote memory, however, the empirical grounds regarding the effect of distributed practice are sparse. In the present dissertation, this research gap was addressed and the effect of distributed practice on the mathematical performance of school students investigated. In the introductory sections (Chapter I) distinctive features of mathematical learning and practice are exposed and the few available studies on distributed practice with mathematical material are reviewed, especially considering their contribution to research on distributed practice that goes beyond rote memory. In the frame of the first study (Chapter II), two experiments were conducted in order to investigate whether distributed practice generally improves performance of school students learning mathematics. Students from Grade 3 (N = 95) and Grade 7 (N = 118) received an introduction to a mathematical topic, derived from the regular curriculum. Afterwards, they practiced the respective topics with three practice sets, either massed in one session or distributed on three consecutive days. Bayesian analyses of the performance in two follow-up tests, one and six weeks after the last practice set, revealed evidence for a positive effect of distributed practice as compared to massed practice in Grade 7. In Grade 3, evidence for a positive effect of distributed practice was supported by the data only in the test one week after the last practice set. In the frame of the second study (Chapter III) a similar experiment was conducted, again in Grade 7 (N = 81). This time, strong evidence for a positive effect of distributed practice was revealed only six weeks after the last practice set. Exploratory analyses indicated that especially students in the medium performance range benefitted from distributed practice. Within the third study (Chapter IV), one experiment in high school math courses was conducted (N = 88) with the aim to investigate whether distributed practice proves a successful learning strategy in a more self-regulated context, too. In this study, only the lecture sessions took place in school and the practice and test sets were worked online at home. Only 44 students finished the study, which hampered the analysis of the effect of distributed practice. Exploratory analyses were conducted to investigate the individual characteristics of those students who completed the exercises in the context of their self-regulated learning. The results indicated that only a small group of specific learners is capable of successfully realizing distributed practice within their individual learning time. Taken together, the results suggest that distributed practice can improve the mathematical performance of school students (Studies 1 and 2). Exploratory results indicated a particularly strong effect for students in a medium performance range (Study 2). Additionally, distributed practice should be implemented in the classroom or at least be guided externally, because students seem to fail when they are supposed to realize the distributed practice schedule individually at home (Study 3).