Improving multiplication fact fluency by choosing between competing answers

Abstract

Developing fluency in arithmetic facts is instrumental to mathematics learning. This study compares the effects of two practice conditions on children's fluency in simple multiplication facts. Third and fourth graders in the Netherlands (N = 282) practised in either a conventional recall condition where they produced answers to problems, or a choice condition where they had to choose between competing answers that included common multiplication errors. Practice in the choice condition was faster and as accurate as recall practice but was not more beneficial to performance on speed tests of practised facts. For more experienced students, recall practice led to greater improvement on a conventional recall fluency test. Differential effects of practice conditions on test performance are explained in terms of practice-to-test transfer demands. The relative merits of recall and choice tasks in multiplication fact learning are discussed.

Children's Strategy Choices on Complex Subtraction Problems: Individual Differences and Developmental Changes

“…These findings extend results reported in previous studies, encompassing a wider range of subtraction problems. Previous research on simple addition problems indicated that children tend to shift from counting (an inefficient procedural strategy) to more efficient memory-based retrieval with increased age (Widaman et al, 1992 ; Lemaire and Siegler, 1995 ; Geary, 2004 ; Reed et al, 2015 ). The present results support a similar pattern for complex subtraction, but show that shifts are related to problem features and that there is also considerable persistence in strategy availability with development from grades three to five.…”

“…To address some of the limitations of free-choice retrospective reports, Siegler and Lemaire ( 1997 ) developed a modified method, known as the choice/no-choice paradigm. This method consists of a forced choice condition, where individuals apply a preferred strategy (chosen from a restricted set of two or three options), and two or more no-choice conditions, where they are required to solve all problems with a single strategy; thus, the number of no-choice conditions corresponds to the number of options in the forced-choice condition (e.g., Imbo and Vandierendonck, 2007a , b , c ; Reed et al, 2015 ). The choice/no-choice paradigm provides information on strategy efficiency from the no-choice condition, independently of the choice process, whereas the comparison of performance in the no-choice and the choice condition gives an indication of people's strategy adaptivity (i.e., the selection of the most efficient procedure from the limited set provided).…”