A study of teaching and learning number sense for sixth grade students in Taiwan

International Journal of Science and Mathematics Education

Volumn 2, Issue 3, 2004, Pages 407-430

  Yang, Der Ching ^a   Hsu, Chun Jen ^a   Huang, Ming Chiang ^a  

^a NATIONAL CHIAYI UNIVERSITY   (Taiwan)

Author keywords

Age group; Number sense; Post test; Pre test; Process oriented teaching model; Retention test

Indexed keywords

EID: 33544456178     PISSN: 15710068     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10763-004-6486-9     Document Type: Article

References (43)

1. Anghileri, J. (2000). Teaching number sense. Trowbridge, Wiltshire: Cromwell Press.
2. Australian Education Council (1991). A national statement on mathematics for Australian school. Melbourne: Curriculum Corporation.
3. Behr, M.J., Wachsmuth, I., Post, T.R. & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15, 323-341.
4. Burns, M. (1994). Arithmetic: The last holdout. Phi Delta Kappan, 411-416.
5. Case, R. (1989). Fostering the development of children's number sense. In J.T. Sowder & B.P. Schappelle (Eds.), Establishing foundations for research on number sence and related topics: Report of a conference (pp. 57-64). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
6. Case, R. & Griffin, S. (1990). Child cognitive development: The role of central conceptual structures in the development of scientific and social thought. In C.A. Hauert (Ed.), Cognitive, perceptuo-motor, and neuropsychological perspectives (pp. 193-230). Amsterdam, The Netherlands: Elsevier Science Publishers.
7. Cockcroft, W.H. (1982). Mathematics counts. London: HMSO.
8. Cramer, K.A., Post, T.R. & delMas, R.C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal of Research in Mathematics Education, 33(2), 111-144.
9. Ekenstam, A. (1977). On children's quantitative understanding of numbers. Educational Studies in Mathematics, 8, 317-332.
10. Graeber, A.O. & Tirosh, D. (1990). Insights fourth and fifth grades bring to multiplication and division with decimals. Educational Studies in Mathematics, 21, 565-588.
11. Greeno, J.G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22, 170-218.
12. Greer, B. (1987). Nonconservation of multiplication and division involving decimals. Journal for Research in Mathematics Education, 18, 37-45.
13. Hiebert, J. (1989). Reflections after the conference on number sense. In J.T. Sowder & B.P. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 82-84). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
14. Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics, 30, 3-19.
15. Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36, 6-11.
16. Kamii, C., Lewis, B.A. & Livingston, S.J. (1993). Primary arithmetic: Children inventing their own procedures. Arithmetic Teacher, 41, 200-203.
17. Markovits, Z. & Sowder, J.T. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), 4-29.
18. McIntosh, A., Reys, B.J. & Reys, R.E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-8.
19. McIntosh, A., Reys, B.J. & Reys, R.E. (1997). Number sense grades 6-8. Palo Alto: Dale Seymour Publications.
20. McIntosh, A., Reys, B.J., Reys, R.E., Bana, J. & Farrel, B. (1997). Number sense in school mathematics: Student performance in four countries. Mathematics, Science, and Technology Education Centre, Edith Cowan University.
21. Ministry of Education in Taiwan (2000). 9-year-integrated mathematics curriculum standards for national schools from grade 1 to 9 in Taiwan (pp. 19-86) (in Chinese). Taiwan: Ministry of Education in Taiwan.
22. National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
23. National Council of Teachers of Mathematics (NCTM) (2000). The principles and standards for school mathematics. Reston, VA: NCTM.
24. National Research Council (1989). Everybody counts. A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.
25. Resnick, L.B. (1989). Defining, assessing and teaching number sense. In Sowder & Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference. San Diego, CA: San Diego State University, Center for Research in Mathematics and Science Education.
26. Reys, B.J. (1994). Promoting number sense in middle grades. Teaching Mathematics in the Middle School, 1(2), 114-120.
27. Reys, B.J., Barger, R., Dougherty, B., Hope, J., Markovits, Z., Parnas, A., Reehm, S., Sturdevant, R., Weber, M. & Bruckheimer, M. (1991). Developing number sense in the middle grades. Reston, VA: NCTM.
28. Reys, R.E. & Yang, D.C. (1998). Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29, 225-237.
29. Skemp, R.R. (1982). Understanding the symbolism of mathematics (Special Issue). Visible Language, 16(3).
30. Sowder, J. (1992a). Estimation and number sense. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371-389). New York: Macmillan.
31. Sowder, J. (1992b). Making sense of numbers in school mathematics. In G. Leinhardt & R. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 1-51). Hillsdale, NJ: Erlbaum.
32. Sowder, L. (1988). Children's solution of story problems. Journal of Mathematical Behavior, 7, 227-238.
33. Steffe, L.P. & Cobb, P. (1988). Construction of arithmetical meanings and strategies. New York: Springer.
34. Treffers, A. (1991). Meeting innumeracy at primary school. Educational Studies in Mathematics, 26(1), 333-352.
35. Von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. London: The Falmer Press.
36. Wearne, D. & Hiebert, J. (1988). Constructing and using meaning for mathematical symbols: The case of decimal fractions. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 220-235). Hillsdale, NJ: Erlbaum.
37. Yang, D.C. (2000). Developing number sense for sixth grade students in Taiwan. A Number Sense Project supported by the National Science Council in Taiwan with grant no. NSC 89-2511-S-415-001.
38. Yang, D.C. (2001). Developing number sense for fifth grade students in Taiwan. A Number Sense Project supported by the National Science Council in Taiwan with grant no. NSC 90-2521-S-415-001.
39. Yang, D.C. (2002). Teaching and learning number sense: One successful process-oriented activity with six grade students in Taiwan. School Science and Mathematics, 102(4), 152-157 (NSC 89-2511-S-415-001).
40. Yang, D.C. (2003). Teaching and learning number sense - an intervention study of fifth grade students in Taiwan. International Journal of Science and Mathematics Education, 7(1), 115-134 (NSC 90-2521-S-415-001).
41. Yang, D.C. & Keys, R.E. (2001a). Developing number sense. Mathematics Teaching, 176, 39-41 (NSC 89-2511-S-415-001).
42. Yang, D.C. & Reys, R.E. (2001b). One fraction problem: Many solution paths. Mathematics Teaching in the Middle School, 7(3), 164-166 (NSC 89-2511-S-415-001).
43. Yang, D.C. & Reys, R.E. (2002). Fractional number sense strategies possessed by sixth grade students in Taiwan. Hiroshima Journal of Mathematics Education, 10(December), 53-70.