No Robust Effect of Distributed Practice on the Short- and Long-Term Retention of Mathematical Procedures

Abstract

We investigated the effect of distributed practice and more specifically the "lag effect" concerning the retention of mathematical procedures. The lag effect implies that longer retention intervals benefit from longer inter-study intervals (ISIs). University students (N = 235) first learned how to solve permutation tasks and then practiced this procedure with an ISI of zero (i.e., massed), one, or 11 days. The final test took place after one or five weeks. All conditions were manipulated between-subjects. Contrary to our expectations, the analyses revealed no effect of distributed practice and therewith also no lag effect, even though the sample size was sufficiently large. The only significant effect was that test performance was poorer after 5 weeks than after 1 week. In view of the present results and those of other studies, we assume that distributed practice works differently for declarative and procedural knowledge, with less robust of even absent effects when procedural skills are practiced with ISIs compared to massed practice.

Spaced mathematics practice improves test scores and reduces overconfidence

“…Some indirect evidence suggests that the mathematics spacing effect can shrink or disappear if the spacing gap is much shorter than the test delay, as is the case with non‐mathematics materials (e.g., see meta‐analysis by Cepeda et al, 2006). This possibility also is consistent with the results of the mathematics spacing study that found null effects when the test delay was rather long (Ebersbach & Barzagar Nazari, 2020a). Students in that study either massed their practice or spaced their practice across two sessions separated by 1 or 11 days before taking a test 5 weeks later, and the larger spacing gaps produced larger test scores: about 25% after massed practice, about 30% after a 1‐day spacing gap, and nearly 40% after an 11‐day spacing gap.…”

“…This potential caveat is only conjecture, however, because the nature or degree of feedback has not been manipulated in a mathematics spacing study. However, feedback was provided after only one half of the practice problems in the aforementioned study finding only null effects (Ebersbach & Barzagar Nazari, 2020a).…”

“…Might the mathematics spacing effect be moderated by the nature of the mathematics task? This possibility was raised by Ebersbach and Barzagar Nazari 2020a to account for the null effects observed in every condition of their laboratory study. Yet we are not aware of any evidence for this claim.…”

“…Fewer studies have examined the effect of spacing on mathematics learning, though the available data suggest that spacing can boost mathematics learning, too. Mathematics spacing effects were first found in laboratory studies with college students (Gay, 1973;Rohrer & Taylor, 2006;Rohrer & Taylor, 2007), though one recent lab experiment found only null effects (Ebersbach & Barzagar Nazari, 2020a). Spacing also improved test scores in each of several non-randomized classroom studies, including studies with students in high school geometry (Yazdani & Zebrowski, 2006), college statistics (Budé et al, 2011), and year four mathematics (Chen et al, 2018).…”

“…For instance, one of the laboratory studies cited above found that the spacing effect disappeared entirely when the test delay was shortened from 4 weeks to 1 week, suggesting that short test delays might reduce or eliminate the spacing effect (Rohrer & Taylor, 2006). Yet a recent laboratory experiment found null effects after both a one‐week and five‐week test delay, leading the authors to speculate that the nature of the mathematics task might moderate the size of the spacing effect (Ebersbach & Barzagar Nazari, 2020a). The present studies were not designed to test the plausibility of any particular boundary condition, but the results of our studies are incidentally inconsistent with certain possibilities, as we detail in the Discussion.…”