The Benefits of Interleaving Different Kinds of Mathematics Practice Problems

2008

Dissertation

Ph.D.

Psychology

Major Professor

Doug Rohrer, Ph.D.

Committee Member

Michael Coovert, Ph.D.

Committee Member

James Eison, Ph.D.

Committee Member

Kristin Salomon, Ph.D.

Committee Member

Toru Shimizu, Ph.D.

Keywords

Mixture, Mixed practice, Children, Practice sets, Textook design

Abstract

In most mathematics textbooks, virtually all of the problems in each set of practice problems, or in each practice set, relate to the immediately preceding lesson - an arrangement described here as the standard format of practice. Alternatively, the problems within a shuffled practice set are drawn from numerous lessons. With the shuffled format, each practice set has two distinguishing features: within-session spacing, in which problems of the same kind appearing in a single practice set are separated by some period of time, and mixed practice, in which different types of problems are interleaved. Although previous studies have assessed the combined effects of within-session spacing and mixed practice, the experiment presented here is the first to examine the effect of mixture while holding fixed the effect of within-session spacing in order to determine whether there is a benefit of mixture above and beyond the well-documented benefits of within-session spacing.

Fifth-grade students attended two sessions, a practice session and a test session, spaced one day apart. All students were taught how to solve four kinds of problems, and every student received the same tutorials and the same practice problems.

Students were randomly assigned to receive one of two kinds of practice: mixed practice, in which all four types of problems were interleaved, or unmixed practice, in which all the problems of each type appeared in a block. Critically, in the unmixed practice condition, problems were separated by unrelated filler tasks so that the duration between each problem and the next problem of the same kind was equated for the mixed and unmixed conditions (i.e., the amount of spacing between two problems of the same kind was held constant). One day later, students returned for a test that included one novel problem of each kind, and, on average, the mixed practice group outscored the unmixed practice group by a large margin (77% vs. 38%). Thus, although there are limitations on the generalizability of the data, these findings nevertheless suggest that mixed practice, an important feature of shuffled practice sets, might boost mathematics proficiency.

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