Why does interleaving improve math learning? The contributions of discriminative contrast and distributed practice

Abstract

Interleaved practice involves studying exemplars from different categories in a non-systematic, pseudorandom order under the constraint that no two exemplars from the same category are presented consecutively. Interleaved practice of materials has been shown to enhance test performance compared to blocked practice in which exemplars from the same category are studied together. Why does interleaved practice produce this benefit? We evaluated two non-mutually exclusive hypotheses, the discriminative-contrast hypothesis and the distributed-practice hypothesis, by testing participants' performance on calculating the volume of three-dimensional geometric shapes. In Experiment 1, participants repeatedly practiced calculating the volume of four different-sized shapes according to blocked practice, interleaved practice, or remote-interleaved practice (which involved alternating the practice of volume calculation with non-volume problems, like permutations and fraction addition). Standard interleaving enhanced performance compared to blocked practice but did not produce enhanced performance compared to remote interleaving. In Experiment 2, we replicated this pattern and extended the results to include a remote-blocked group, which involved blocking volume calculation with non-volume problems. Performance on key measures was better for remoteinterleaved groups compared to remote-blocked groups, a finding that supports the distributed-practice hypothesis.

Pan, Lovelett, Phun, and Rickard (2019) Systematic and random interleaving for second language learning (preprint)

“…In multiple domains, a prominent precondition for interleaving effects is that the to-belearned categories have high between-category similarity wherein it is difficult to discriminate one category from the other (e.g., Carvalho & Goldstone, 2014;Rohrer, 2012;Sana et al, 2017; but see also Foster, Mueller, Was, Rawson, & Dunlosky, 2019;Rohrer, Dedrick, & Burgess, 2014). That high similarity held for the materials in this study.…”

Samani and Pan (2021) Interleaving enhances memory and problem-solving skills in physics

“…45 There is evidence in the interleaving literature to support both minimal and major roles of distributed practice; in the case of perceptual category learning, conditions that feature extensive amounts of distributed practice in the absence of interleaving have failed to yield similar learning benefits, 13,15 which suggests a minimal role, whereas in studies involving mathematics or second language learning, interleaving schedules that incorporate substantial amounts of distributed practice have yielded larger benefits, which suggests a major role. 2,24 Given the greater similarity in materials and task structure between those latter studies and the present research, it is plausible in our view that, as in those studies, distributed practice was a major contributing factor. Further research is needed however to verify that possibility.…”

“…8,21 Mechanistically, benefits of interleaving for perceptual category learning have been attributed to the temporal spacing between category exemplars that occurs during such interleaving, which constitutes a form of distributed practice (which over a century of research has established can improve memory 22 ), as well as learners' attention being focused on differences between categories (i.e., the attention bias and discriminative contrast framework, wherein interleaving-induced focused attention may yield improvements in the ability to discriminate between perceptually similar categories). 12,13,23,24 Based on the aforementioned research, recent reviews have defined the "interleaving effect" as improved inductive learning-that is, the mental process of constructing general categories from a finite sample of instances-that stems from interleaving exemplars of visual or other perceptual categories. 8,11,25 A question left largely unanswered, however, is whether the interleaving effect extends beyond inductive learning tasks wherein only determination of category membership is needed.…”

Transfer: A Review for Biology and the Life Sciences

“…For blocked practice, however, the learner simply needs to apply the previously used procedure to all problems within a block-without further reflecting on each item and retrieving the procedure from memory. Spaced practice (Cepeda et al 2006) further contributes to the benefits of interleaving (Foster et al 2019), because interleaving naturally introduces spacing between solving one type of problem and solving it again after other problem types have been worked on. Taken together, the mechanisms promoted by interleaved practice allow students to obtain a better understanding of the underlying principles of the material, which equips them to recall, select, and apply the correct procedures to tasks in novel contexts.…”