Abstract
This study explored the mathematical problem posing and problem solving of 181 U.S. and 223 Chinese sixth-grade students. It is part of a continuing effort to examine U.S. and Chinese students’ performance by conducting a cognitive analysis of student responses to mathematical problem-posing and problem-solving tasks. The findings of this study provide further evidence that, while Chinese students outperform U.S. students on computational tasks, there are many similarities and differences between U.S. and Chinese students in performing relatively novel tasks. Moreover, the findings of this study suggest that a direct link between mathematical problem posing and problem solving found in earlier studies for U.S. students is true for Chinese students as well.
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References
Becker, J. P. (Ed.). (1992).Report of U.S.-Japan cross-mtional research on students’ problem solving behaviors. Columbus, OH: ERIC/SMEAC Clearinghouse. (ERIC Document Reproduction Service No. ED 351 204)
Bradburn, M. B., & Gilford, D. M. (1990).A framework and principles for international comparative studies in education. Washington, DC: National Academic Press.
Brown, S. I., & Walter, M. (1983).The art of problem posing. Philadelphia, PA: Franklin Institute Press.
Cai, J. (1995).A cognitive analysis of U.S. and Chinese students’ mathematical performance on tasks involving computation, simple problem solving, and complex problem solving (Journal for Research in Mathematics Education Monograph No. 7). Reston, VA: National Council of Teachers of Mathematics.
Cai, J. (1997). Beyond computation and correctness: Contributions of open-ended tasks in examining U.S. and Chinese students’ mathematical performance.Educational Measurement: Issues and Practice, 26(1), 5–11.
Cai, J., Magone, M., Wang, N., & Lane, S. (1996). Assessment: Describing student performance qualitatively.Mathematics Teaching in the Middle School, 1, 828–835.
Cai, J., & Silver, E. A. (1994). A cognitive analysis of Chinese students’ mathematical problem solving: An exploratory study. In D. Kirshner (Ed.),Proceedings of the Sixteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 3–9). Baton Rouge, LA: Louisiana State University.
Cai, J., & Silver, E. A. (1995). Solution processes and interpretations of solutions in solving a division-with-remainder story problem: Do Chinese and U.S. students have similar difficulties?Journal for Research in Mathematics Education, 26, 491–497.
Ellerton, N. F. (1986). Children’s made-up mathematics problems: A new perspective on talented mathematicians.Educational Studies in Mathematics, 17, 267–271.
Husen, T. (1967).International study of achievement in mathematics: A comparison of twelve countries (Vols. 1–2). New York: John Wiley & Sons.
Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.),Cognitive science and mathematics education (pp. 123–147). Hillsdale, NJ: Lawrence Erlbaum.
Lapointe, A. E., Mead, N. A., & Askew, J. M. (1992).Learning mathematics. Princeton, NJ: Educational Testing Service.
National Council of Teachers of Mathematics (1989).Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (1991).Professional standards for teaching mathematics. Reston, VA: Author.
Robitaille, D. F., & Garden, R. A. (1989).The IEA study of mathematics II: Contexts and outcomes of school mathematics. New York: Pergamon Press.
Silver, E. A. (1994). On mathematical problem posing.For the Learning of Mathematics, 14(1), 19–28.
Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students.Journal for Research in Mathematics Education, 27, 521–539.
Silver, E. A., Leung, S. S., & Cai, J. (1995). Generating multiple solutions for a problem: A comparison of the responses of U.S. and Japanese students.Educational Studies in Mathematics, 28, 35–54.
Silver, E. A., Shapiro, L. J., & Deutsch, A. (1993). Sense-making and the solution of division problems involving remainders: An examination of students’ solution processes and their interpretations of solutions.Journal for Research in Mathematics Education, 24, 117–135.
Simon, H. A. (1989).Models of Thought (Vol. 2). New Haven: Yale University Press.
Stevenson, H. W, Lee, S., Chen, C, Lummis, M., Stigler, J. W, Liu, F., & Fang, G. (1990). Mathematics achievement of children in China and the United States.Child Development, 61, 1053–1066.
Stevenson, H. W, & Stigler, J. W (1992).The learning gap. New York: Summit.
Stigler J. W, Lee, S., & Stevenson, H. W (1990).Mathematical knowledge of Japanese, Chinese, and American elementary school children. Reston, VA: National Council of Teachers of Mathematics.
U.S. Department of Education and National Center for Education Statistics (1996).Pursuing excellence (NCES Publication No. 97-198). Washington, DC: U.S. Government Printing Office.
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Cai, J. An investigation of U.S. and Chinese students’ mathematical problem posing and problem solving. Math Ed Res J 10, 37–50 (1998). https://doi.org/10.1007/BF03217121
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DOI: https://doi.org/10.1007/BF03217121