Discerned Aspects of Multiplicative Structures Explaining Differences in 6-yearolds’ Arithmetic Skills

Abstract

Critical for developing multiplicative reasoning skills is recognizing the multiplicative structure in the problem. In this study, we investigate which discerned and undiscerned aspects explain differences in 6 yearolds’ ways of solving a task with a multiplicative structure. Drawing on variation theory of learning, qualitative analyses were conducted of interview data from 199 students solving an arithmetic task with a multiplicative structure. Four critical aspects were identified: the size of the unit, its iteration, the number of iterations, and the relation between iterations and the whole. Results show that learning to handle multiplicative structures requires discernment and coordination of all four aspects simultaneously.

Keywords

multiplicative structuremultiplicative reasoningyoung learnerscritical aspects

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