The shuffling of mathematics problems improves learning

Abstract

In most mathematics textbooks, each set of practice problems is comprised almost entirely of problems corresponding to the immediately previous lesson. By contrast, in a small number of textbooks, the practice problems are systematically shuffled so that each practice set includes a variety of problems drawn from many previous lessons. The standard and shuffled formats differ in two critical ways, and each was the focus of an experiment reported here. In Experiment 1, college students learned to solve one kind of problem, and subsequent practice problems were either massed in a single session (as in the standard format) or spaced across multiple sessions (as in the shuffled format). When tested 1 week later, performance was much greater after spaced practice. In Experiment 2, students first learned to solve multiple types of problems, and practice problems were either blocked by type (as in the standard format) or randomly mixed (as in the shuffled format). When tested 1 week later, performance was vastly superior after mixed practice. Thus, the results of both experiments favored the shuffled format over the standard format.

How experts practice: A novel test of deliberate practice theory.

“…A random practice schedule has been shown to facilitate motor learning more so than a blocked one (Goode & Magill, 1986;Holladay & Quiñones, 2003;Rohrer & Taylor, 2007;Shea & Morgan, 1979;Ste-Marie et al, 2004) and to increase mental effort (Lee & Magill, 1983;Lee et al, 1994). There was some This document is copyrighted by the American Psychological Association or one of its allied publishers.…”

The effects of interleaving versus blocking on foreign language pronunciation learning

“…However, recent evidence suggests that it may be more beneficial to present different concepts in an order that is shuffled and less predictable (e.g., practicing a present-tense conjugation followed by a past-tense conjugation, followed by more present-tense conjugations, etc.). For example, Rohrer and Taylor (2007) taught students to calculate the volume of 4 different types of solid figures. Students worked through practice problems in an order that was either blocked by type of figure (i.e., all problems pertaining to one type of figure were finished before the student moved on to the next type of figure) or interleaved such that the same problems appeared in an order that was shuffled and unpredictable.…”

“…For example, in Rohrer and Taylor's (2007) study, interleaving the types of solid figures affords students the opportunity to compare the solution for the current problem (e.g., calculating the volume of a wedge) with the solution for the previously presented problem (e.g., calculating the volume of a spheroid), allowing an opportunity to compare key differences between the solutions. Calculating the volume for the same type of figure in back-to-back blocked fashion provides less of an opportunity to notice these differences and may render it harder to distinguish between the different solutions later on.…”

Learning from graphically integrated 2D and 3D representations improves retention of neuroanatomy.

“…This approach to learning provides multiple opportunities for the participants to transfer their whole anatomy knowledge to learning sectional anatomy, and sectional anatomy knowledge to learning whole anatomy. Evidence from the literature on interleaved learning suggests that although learning from an interleaved presentation is more difficult than learning from blocked presentation, it leads to better learning outcomes (KorneH & Bjork, 2008;Rohrer & Taylor, 2007;Taylor & Rohrer, 2010). Learning from a sequential (blocked) presentation of whole and sectional anatomy (Whole then Sections) was compared with learning from an interleaved presentation of whole and sectional anatomy (Alternation).…”