Study sequence matters for the inductive learning of cognitive concepts.

Abstract

The sequence in which problems of different concepts are studied during instruction impacts concept learning. For example, several problems of a given concept can be studied together (blocking) or several problems of different concepts can be studied together (interleaving). In the current study, we demonstrate that the 2 sequences impact concept induction differently as they differ in the temporal spacing and the temporal juxtaposition of to-be-learned concept problems, and in the cognitive processes they recruit. Participants studied 6 problems of 3 different statistical concepts, and then were tested on their ability to correctly classify new problems on a final test. Interleaving problems of different to-be-learned concepts, rather than blocking problems by concept, enhanced classification performance, replicating the interleaving effect (Experiment 1). Introducing temporal spacing between successive problems decreased classification performance in the interleaved schedule-consistent with the discriminative-contrast hypothesis that interleaving fosters between-concept comparisons-and increased classification performance in the blocked schedule-consistent with the study-phase retrieval hypothesis that temporal spacing causes forgetting and subsequent retrieval enhances memory (Experiment 2). Temporally juxtaposing problems of concepts 3-at-a-time rather than 1-at-a-time improved overall classification performance, particularly in a blocked schedule-consistent with the commonality-abstraction hypothesis that blocking fosters within-concept comparisons (Experiment 3). All participants also completed a working memory capacity (WMC) task, findings of which suggest that the efficacy of the above study sequences may be related to individual differences in WMC.

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

“…We observed benefits of interleaving practice on formula retrieval and on final test performance of geometric shapes in Experiments 1 and 2. These results replicate research showing benefits of interleaving for math materials (Rohrer & Taylor, 2007;Taylor & Rohrer, 2010;Rohrer, 2012;Sana et al, 2017). Most important, relevant to explaining such interleaving effects, evidence from the current experiments provides more support for the distributed-practice hypothesis than for the discriminative-contrast hypothesis.…”

“…Interleaving practice of tobe-learned information is a promising strategy for improving learning of various kinds of material (for reviews, see Dunlosky, Rawson, Marsh, Nathan, & Willingham, 2013;Rohrer, 2012). Relative to blocked practice, interleaving has been shown to improve learning of different mathematics materials, including permutation calculations (Rohrer & Taylor, 2007;Taylor & Rohrer, 2010), identifying the number of faces, corners, edges, and angles of prism shapes (Taylor & Rohrer, 2010), calculating the volume of geometric shapes using task-relevant formulas (Rohrer, 2012;Rohrer & Taylor, 2007), and applying statistical tests to different word problems (Sana, Yan, & Kim, 2017).…”

Pan, Tajran, Lovelett, Osuna, and Rickard (2018) Interleaved practice and foreign language learning (preprint)

“…Phase 3 in the interleaved group also resembled that in the blocked group but with the following exceptions: (a) the phase began with two summary slides, one per tense; (b) the instructions stated that the practice trials would involve both tenses; and (c) 18 practice trials were presented consecutively (i.e., 9 per tense x 2 tenses) using the same general "I"-"you"-"we" pronoun order as in Phase 2 but with the tense changing every 3 trials and the pronoun changing every 6 trials (e.g., 3 "I"-preterite trials, then 3 "I"-imperfect trials, then 3 "You"-preterite trials, then 3 "You"-imperfect trials, and so on). This pattern, which was also unique to Experiment 1, maintained a consistent rate of switching between tenses and is comparable to the fixed patterns used in several prior interleaving studies (e.g., Kang & Pashler, 2012;Sana et al, 2017;Taylor & Rohrer, 2010), albeit with a more complex nested structure. Once participants completed Phase 3, they provided the same metacognitive judgment as in the blocked group and were dismissed.…”

“…This hypothesis posits that the interleaving effect is due to the juxtaposition of items from different categories on successive trials (Kang & Pashler, 2012). As such, it predicts that interleaving's benefits are likeliest when categories have high between-category similarity (i.e., Birnbaum, Kornell, Bjork, & Bjork, 2013;Rohrer, 2012;Sana, Yan, & Kim, 2017). For example, the simple past and the present perfect tenses in English both refer to relatively subtle differences in past actions that can be difficult to discriminate between (e.g., "I went to the store yesterday" vs. "I have gone to the store many times").…”

“…The fact that the interleaved group's test results were on par with or better than the blocked group in Experiments 2-4 is consistent with this possibility. Trial-level randomization might also have constraints in that specific category changes occur on successive trials (e.g., Sana et al, 2017). In particular, a random schedule that guarantees a pronoun change on each successive trial might yield even larger benefits.…”