Teaching whole-number multiplication to promote children’s proportional reasoning: a practice-based perspective from Japan

Abstract

Whole-number arithmetic is a core content area of primary mathematics, which lays the foundation for children’s later conceptual development. This paper focuses on teaching whole-number multiplication (WNM) to build a stepping stone for children’s proportional reasoning. Our intention in writing this paper is to obtain a practice-based perspective on the teaching of WNM, given the growing attention being given to significant connections between children’s understanding of multiplication and their proportional reasoning. To this end, we review studies on teaching WNM that were conducted in Japan. Our review highlights several aspects of teaching WNM that are integral to building an initial understanding of proportional relationships. Linear representations such as tape diagrams and number lines are also found to help make explicit the important properties of proportional relationships that can be used progressively across grade levels.