Abstract
Relations among patterns of conceptual and procedural knowledge and grade were examined in 90 six- to eight-year-olds in order to explore addition and subtraction development. Conceptual knowledge was assessed by examining children’s responses to pairs of problems reflecting various part–whole relations. Children solved related problems as part of a Problem-solving Task, judged, and explained part–whole relations in a Judgement Task. Children also solved a random set of addition and subtraction problems. Distinct profiles of problem-solving were derived from an analysis of children’s speed, accuracy and self-reported problem-solving procedures on unrelated problems. Problem-solving profiles were associated with individual differences in part–whole knowledge and grade level but grade and part–whole knowledge were not related. Findings suggest that identifying profiles of procedural and conceptual knowledge is important for understanding children’s mathematical development.
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