Development of fraction concepts and procedures in U.S. and Chinese children

•We assessed fraction knowledge in Chinese and U.S. 6th and 8th graders.•Chinese children had higher procedural and conceptual knowledge than U.S. children.•Differences in conceptual knowledge were fully mediated by procedural knowledge.•We propose a model of mutually facilitative interaction between conceptual and procedural knowledge of fractions.

We compared knowledge of fraction concepts and procedures among sixth and eighth graders in China and the United States. As anticipated, Chinese middle school children had higher knowledge of fraction concepts and procedures than U.S. children in the same grades, and the difference in procedural knowledge was much larger than the difference in conceptual knowledge. Of particular interest, national differences in knowledge of fraction concepts were fully mediated by differences in knowledge of fraction procedures, and differences between the knowledge of Chinese and U.S. children were most pronounced among the lowest achieving children within each country. Based on these and previous results, a theoretical model of the mutually facilitative interaction between conceptual and procedural knowledge of fractions is proposed and discussed.