Why do U.S. and Chinese students think differently in mathematical problem solving? Impact of early algebra learning and teachers' beliefs

Journal of Mathematical Behavior

Volumn 23, Issue 2, 2004, Pages 135-167

  Cai, Jinfa ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942618187     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2004.03.004     Document Type: Article

References (28)

1. Becker J.P. Sawada T. & Shimizu Y. (1999). Some findings of the U.S.-Japan cross-cultural research on students' problem-solving behaviors. In: G. Kaiser, E. Luna, & I. Huntley (Eds.), International comparisons in mathematics education (pp. 121-139). London: Falmer Press.
2. Bolster L.C. Boyer C. Butts T. Cavanagh M. Channel M.W. Warren D. et al. (1997). Exploring mathematics. Glenview, IL: Scott Foresman.
3. Bradburn M.B. & Gilford D.M. (1990). A framework and principles for international comparative studies in education. Washington, DC: National Academic Press.
4. Bruner J.S. (1990/1998). Acts of meaning. Cambridge, MA: Harvard University Press.
5. Bruner J. (1996). The culture of education. Cambridge, MA: Harvard University Press.
6. 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 Series No. 7).
7. Cai J. Mathematical thinking involved in U.S. and Chinese students' solving process-constrained and process-open problems Mathematical Thinking and Learning 2 2000a 309-340
8. Cai J. Understanding and representing the arithmetic averaging algorithm: an analysis and comparison of U.S. and Chinese students' responses International Journal of Mathematical Education in Science and Technology 31 6 2000b 839-855
9. Cai J. Hwang S.U.S. and Chinese students' generalized and generative thinking in mathematical problem solving and problem posing Journal of Mathematical Behavior 21 2002 401-421
10. Cooney T.J. Shealy B.E. Arvold B. Conceptualizing belief structures of preservice secondary mathematics teachers Journal for Research in Mathematics Education 29 1998 306-333
11. Detterman D.K. (Ed.). (1993). Individual differences and cognition. Norwood, NJ: Ablex.
12. Division of Elementary Mathematics. (1996). Mathematics: elementary school textbook. Beijing, China: People's Education Press.
13. Dreyfus T. & Eisenberg T. (1996). On different facets of mathematical thinking. In: R. J. Sternberg, & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 253-284). Hillsdale, NJ: Erlbaum.
14. Freeman D.J. Porter A.C. Do textbooks dictate the content of mathematics instruction in elementary school? American Educational Research Journal 26 1989 403-421
15. Gardner H. (1991). The unschooled mind: how children think and how schools should teach. Basic Books.
16. Greeno J.G. (1987). Instructional representations based on research about understanding. In: A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 61-88). New York: Academic Press.
17. Harmon M. Smith T.A. Martin M.O. Kelly D.L. Beaton A.E. Mullis I.V.S. et al. (1997). Performance assessment in IEA's Third International Mathematics and Science Study (TIMSS). Chestnut Hill, MA, Boston College: TIMSS International Study Center.
18. Lave J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge: Cambridge University Press.
19. Lee P.Y. Zhang D. Zheng Z. Examination culture and mathematics education EduMath 4 1997 96-103
20. Ma L. (1999): Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Hillsdale, NJ: Erlbaum.
21. Mathematical Sciences Education Board. (1998). The nature and role of algebra in the K-14 curriculum: Proceedings of a national symposium. Washington DC: National Research Council.
22. Resnick L.B. Learning in school and out Educational Researcher 16 1987 13-19
23. Rogoff B. Chavajay P. What's become of research on the cultural basis of cognitive development? American Psychologist 50 10 1995 859-877
24. Silver E.A. Leung S.S. Cai J. Generating multiple solutions for a problem: a comparison of the responses of U.S. and Japanese students Educational Studies in Mathematics 28 1 1995 35-54
25. Stigler J.W. & Hiebert J. (1999). The teaching gap: best ideas from the world's teachers for improving education in the classroom. New York: The Free Press.
26. Thompson A.G. (1992). Teachers' beliefs and conceptions: a synthesis of the research. In: D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.
27. Wozniak R.H. & Fischer K.W. (Eds.). (1993). Development in context: acting and thinking in specific environments. Hillsdale, NJ: Erlbaum.
28. Usiskin Z. Flanders J. Hynes C. Polonsky L. & Porter S. (1997). Transition mathematics. Glenview, IL: Scott Foresman.