Affordances of fractions and decimals for arithmetic among middle school students in the United States and China

Abstract

Recent research by Liu and Braithwaite (2023; Journal of Experimental Psychology: Learning, Memory, and Cognition, Vol. 49, pp. 1459–1470) revealed differential affordances of fractions and decimals for arithmetic. Specifically, adults preferred to solve addition problems in decimal form rather than fraction form and preferred to solve multiplication problems in fraction form rather than decimal form. The current study tested whether similar preferences would appear among middle school children in the United States (N = 84) and China (N = 88) and whether analogous patterns would appear in children’s calculation performance. Like adults in Liu and Braithwaite’s study, children in both countries preferred decimals more for addition and preferred fractions more for multiplication. Furthermore, calculation accuracy was relatively higher with decimals for addition and with fractions for multiplication, and calculation was perceived to be relatively less effortful with decimals for addition and with fractions for multiplication. We consider both conceptual and procedural explanations for the findings, based respectively on semantic alignment theory and strategy choice theory, and conclude that a procedural perspective offers the more complete and parsimonious explanation. Educational implications of the findings are discussed.