Children’s Spontaneous Additive Strategy Relates to Multiplicative Reasoning

Abstract

We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's spontaneous additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses during clinical, task-based interviews. All participants spontaneously used one of three additive strategies-counting-on, doubling, or break-apart-make-ten (BAMT)-to correctly solve an addition word problem (8 þ 7). We found between-group differences, with asymmetric association of those ordinal variables. We found counting-on to be mainly related to premultiplicative reasoning and BAMT to mDC reasoning. We discuss the theoretical significance and implications of this corroboration of Steffe's model. Children's spontaneous additive strategy relates to multiplicative reasoningPart of the attraction of qualitative, noncomparative methods … was that they promised to generate hypotheses that could then be tested. That promise has gone largely unmet. … The field needs to return more of its energies to conducting hypothesis-testing studies. (Kilpatrick, 2001, pp. 424-425) Children's development of multiplicative reasoning has long been a major concern for mathematics educators (