Mathematical Thinking Involved in U.S. and Chinese Students' Solving of Process-Constrained and Process-Open Problems

This study examined U.S. and Chinese 6th-grade students' mathematical thinking and reasoning involved in solving 6 process-constrained and 6 process-open problems. The Chinese sample (from Guiyang, Guizhou) had a significantly higher mean score than the U.S. sample (from Milwaukee, Wisconsin) on the process-constrained tasks, but the sample of U.S. students had a significantly higher mean score than the sample of the Chinese students on the process-open tasks. A qualitative analysis of students' responses was conducted to understand the mathematical thinking and reasoning involved in solving these problems. The qualitative results indicate that the Chinese sample preferred to use routine algorithms and symbolic representations, whereas the U.S. sample preferred to use concrete visual representations. Such a qualitative analysis of students' responses provided insights into U.S. and Chinese students' mathematical thinking, thereby facilitating interpretation of the cross-national differences in solving the process-constrained and process-open problems.