Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing

Abstract

This study examined US and Chinese 6th grade students’ generalization skills in solving pattern-based problems, their generative thinking in problem posing, and the relationships between students’ performance on problem solving and problem posing tasks. Across the problem solving tasks, Chinese students had higher success rates than US students. The disparities appear to be related to students’ use of differing strategies. Chinese students tend to choose abstract strategies and symbolic representations while US students favor concrete strategies and drawing representations. If the analysis is limited to those students who used concrete strategies, the success rates between the two samples become almost identical. With regard to problem posing, the US and Chinese samples both produce problems of various types, though the types occur in differing sequences. Finally, this study revealed differential relationships between problem posing and problem solving for US and Chinese students. There was a much stronger link between problem solving and problem posing for the Chinese sample than there was for the US sample.