Third graders’ verbal reports of multiplication strategy use: How valid are they?

This study investigates whether children’s verbal reports accurately represent their thinking processes when solving simple multiplication problems. A total of 106 third graders in Dutch mainstream primary schools solved simple multiplication problems and retrospectively reported how they had done this. The degree to which verbal reports predict children’s problem-solving performance in ways that correspond to known patterns of response latency, accuracy, errors and strategy choice was assessed. The analyses took account of relevant problem characteristics and child cognitive characteristics (i.e., math ability, verbal ability, phonological decoding speed) known to affect the relation between strategy use and multiplication performance. The verbal reports were largely consistent with known patterns, supporting the use of verbal reports in assessing multiplication strategy use. Moreover, verbal reports provide valuable information that can alert teachers and educational researchers to specific issues that students face when solving simple multiplication problems. Considerations for soliciting reliable verbal reports are suggested

Improving multiplication fact fluency by choosing between competing answers

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