A Cognitive Analysis of U. S. and Chinese Students' Mathematical Performance on Tasks Involving Computation, Simple Problem Solving, and Complex Problem Solving

The mathematical performance of 250 U.S. sixth-grade students from both private and public schools and 425 Chinese sixth graders from both key and common schools was examined on multiple-choice tasks assessing computation and simple problem solving and on open-ended tasks assessing complex problem solving. Chinese students performed significantly better than U.S. students on both computation and simple problem solving. The results were about the same for the two samples on complex problem solving. Moreover, when subsets of U.S. and Chinese students were matched on their computational performance, the U.S. students scored significantly higher than comparable Chinese students on the measures of both simple and complex problem solving. U.S. and Chinese students had similar overall performance on complex problem solving, but a detailed cognitive analysis of students' written responses revealed not only many similarities in the solutions but also many subtle differences. For example, the types of strategies employed and the types of errors made by the Chinese students were similar to those for the U.S. students, although the Chinese students' solutions tended to be more elegant. Also, U.S. students tended to use visual representation more frequently than Chinese students, who tended to use symbolic representation (e.g., algebraic equations) more frequently. The results of this study suggest not only the complexity of examining mathematical performance differences, but also the inadequacy of using a limited range of tasks to measure mathematical performance in cross-national studies. One of the main contributions of this study is its use of a variety of mathematical tasks to capture the thinking and reasoning of U.S. and Chinese students. Another contribution is the scheme used to analyze student performance, a scheme based not solely on the percentage correct or incorrect, but rather on a detailed analysis of students' strategies, representations, and errors. This range of tasks and the associated methodology supported the discovery of findings of similarities and differences between U.S. and Chinese students that have not been reported previously.