Understanding and representing the arithmetic averaging algorithm: An analysis and comparison of US and Chinese students' responses

International Journal of Mathematical Education in Science and Technology

Volumn 31, Issue 6, 2000, Pages 839-855

  Cai, Jinfa ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85015293459     PISSN: 0020739X     EISSN: 14645211     Source Type: Journal    
DOI: 10.1080/00207390050203342     Document Type: Article

References (25)

1. Cai, J., 1998. Sch. Sci. Math., 98:93
2. Mokros, J., and Russell, S. J., 1995. J. Res. Math. Educ., 26:20
3. Pollatsek, A., Lima, S., and Well, A. D., 1981. Educ. Studies Math., 12:191
4. Becker, J. P., ed. 1992. Report of U.S.-Japan Cross-National Research on Students' Problem Solving Behaviors, ED 351/204 Columbus, OH:ERIC/SMEAC Clearing House.
5. Cai, J., 1995. A Cognitive Analysis of U.S. and Chinese Students' Mathematical Performance on Tasks Involving Computations, Simple Problem Solving, and Complex Problem Solving, J. for Res. In Math. Edu. monograph series #7 National Council of Teachers of Mathematics.
6. Cai, J., 1998. Math. Educ. Res. J., 10:37
7. Cai, J., and Silver, E. A., 1995. J. Res. Math. Educ., 26:491
8. Silver, E. A., Leung, S. S., and Cai, J., 1995. Educ. Studies Math., 28:35
9. Division of Mathematics. 1993. Mathematics, Beijing:People's Education Press.
10. Bolster, L. C., 1995. Exploring Mathematics, Glenview, IL:Scott Foresman.
11. Balch, K., 1995. Mathematics Application and Connections, Columbus, OH:Clencoe Division, Macmillan/McGraw Hill.
12. Glenda, L., 1995. The Connected Mathematics Project, Pola Alto, CA:Dale Seymour Publications.
13. Cai, J., Magone, M., Wang, N., and Lane, S., 1996. Res. Middle Level Educ. Quarterly, 19:63
14. Magone, M., Cai, J., Silver, E. A., and Wang, N., 1994. Int. J. Educ. Res., 12:317
15. Hiebert, J., ed. 1986. Conceptual and Procedural Knowledge:The Case of Mathematics, Hillsdale, NJ:Erlbaum.
16. Hiebert, J., and Carpenter, T. P., 1992. “ Learning and teaching with understanding ”. In Handbook of Research on Mathematics Teaching and Learning, Edited by:Grouws, D. A., 65–97. New York:Macmillan.
17. NCTM. 1989. Curriculum and Evaluation Standards for School Mathematics, National Council of Teachers of Mathematics.
18. Steen, L., 1988. Science, 240:61
19. Kamii, C., 1994. Young Children Continue to Reinvent Arithmetic (3rd grade):Implications of Piaget's Theory, New York:Teachers College Press.
20. Carpenter, T. P., 1998. J. Res. Math. Educ., 29:3
21. Dreyfus, T., and Eisenberg, T., 1996. “ On different facets of mathematical thinking ”. In The Nature of Mathematical Thinking, Edited by:Sternberg, R. J., and Ben-Zeev, T., 253–284. Hillsdale, NJ:Erlbaum.
22. Janvier, C., 1987. Problems of Representation in the Teaching and Learning of Mathematical Problem Solving, Hillsdale, NJ:Erlbaum.
23. Larkin, J. H., 1983. “ The role of problem representation in physics ”. In Mental Models, Edited by:Gener, D., and Stevens, A. L., 75–98. Hillsdale, NJ:Erlbaum.
24. Sweller, J., 1988. Cognitive Sci., 12:257
25. Cai, J., 1998. Teaching Children Math., 5:225