Relationships among computational performance, pictorial representation, symbolic representation and number sense of sixth-grade students in Taiwan

Educational Studies

Volumn 30, Issue 4, 2004, Pages 373-389

  Yang, Der Ching ^a   Huang, Fang Yu ^b  

^a NATIONAL CHIAYI UNIVERSITY   (Taiwan)

^b Elementary School Teacher   (Taiwan)

Author keywords

Number sense; Pictorial representation; Symbolic representation; Written computation

Indexed keywords

EID: 10044227033     PISSN: 03055698     EISSN: None     Source Type: Journal    
DOI: 10.1080/0305569042000310318     Document Type: Article

References (43)

1. Alitzer-Tuning, C. (1984) One point of view: crisis in arithmetic teaching: the future is here, Arithmetic Teacher, 32(1), 2.
2. Australian Education Council (1991) A national statement on mathematics for Australian schools (Melbourne, Curriculum Corporation).
3. Beaton, A. E., Mullis, I., Martin, M. O., Gonzalez, E. J., Kelly, D. E. & Smith, T. A. (1997) Mathematics achievement in the middle school years: IEA's Third International Mathematics and Science Study (Chestnut Hill, MA, Boston College, Center for the Study of Testing, Evaluation and Educational Policy).
4. Boerst, T. A. & Schielack, J. F. (2003) Toward understanding of 'computational fluency', Teaching Children Mathematics, 9(6), 292-293.
5. Brenner, M. E., Herman, S., Ho, H. Z. & Zimmer, J. M. (1999) Cross-national comparison of representational competence, Journal for Research in Mathematics Education, 30(5), 541-547.
6. Brunner, J. S. (1966) Toward a theory of instruction (Cambridge, MA, Harvard University Press).
7. Burn, M. (1994) Arithmetic: the last holdout, Phi Delta Kappan, 75(6), 471-476.
8. Cai, J. (2001) Improving mathematics: learning lessons from cross-national studies of Chinese and US students, Phi Delta Kappan, 83, 400-404.
9. Cockroft, W. H. (1982) Maths counts (Lodon, HMSO).
10. 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 for Research in Mathematics Education, 33(2), 111-144.
11. Dreyfus, T. & Eisenberg, T. (1996) On different facets of mathematical thinking, in: R. J. Sternberg & T. Ben-Zeev (Eds) The nature of mathematical thinking (Mahwah, NJ, Erlbaum).
12. Emanuelsson, G. & Johansson, B. (1996) Kommentarer till kursplan I matematik Lpo 94
13. Fennell, F. & Rowan, T. (2001) Representation: an important process for teaching and learning mathematics, Teaching Children Mathematics, 7(5), 288-292.
14. Gonzales, P., Calsyn, C., Jocelyn, L., Mark, K., Kastberg, D., Arafeh, S., Williams, T. & Tsen, W. (2000) Highlights from TIMSS-R. Available online at: http://nces.ed.gov/pubsearch/ pubsinfo.asp?pubid=2001027 (accessed December 2000).
15. Greeno, J. G. & Hall, R. B. (1997) Practicing representation: learning with and about representation forms, Phi Delta Kappan, 79, 361-367.
16. Hiebert, J. (1984) Children's mathematical learning: the struggle to link form and understanding, Elementary School Journal, 84(5), 497-513.
17. Hiebert, J. (1999) Relationship between research and the NCTM standards, Journal for Research in Mathematics Education, 30(1), 3-19.
18. Hiebert, J. & Lindquist, M. (1990) Developing mathematical knowledge in the young child, in: J. N. Payne (Ed.) Mathematics for the young child (Reston, VA, NCTM).
19. Howden, H. (1989) Teaching number sense, Arithmetic Teacher, 36, 6-11.
20. Kamii, C. (1989) Young children continue to reinvent arithmetic, second grade: implications of Piaget's theory (New York, Teachers College Press).
21. Kamii, C., Lewis, B. A. & Livingston, S. J. (1993) Primary arithmetic: children inventing their own procedures, Arithmetic Teacher, 41, 200-203.
22. Lesh, R., Post, T. & Behr, M. (1987) Representation and translation among representation in mathematics learning and problem solving, in: C. Janvier (Ed.) Problem of representation in teaching and learning of mathematics (Hillsdale, NJ, Erlbaum).
23. Markovits, Z. & Sowder, J. T. (1991) Students' understanding of the relationship between fractions and decimals, Focus on Learning Problems in Mathematics, 13(1), 3-11.
24. 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.
25. 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.
26. McIntosh, A., Reys, B. J., Reys, R. E., Bana, J. & Farrel, B. (1997) Number sense in school mathematics: student performance in four countries (Perth, Edith Cowan University).
27. National Council of Teachers of Mathematics (1989) Curriculum and evaluation standards for school mathematics (Reston, VA, NCTM).
28. National Council of Teachers of Mathematics (2000) The principles and standards for school mathematics (Reston, VA, NCTM).
29. Piaget, J. (1971) Biology and knowledge (Chicago, IL, University of Chicago Press).
30. Piaget, J. (1977) Recherches sur 'abstraction réfléchissante, Vol. 1 (Paris, Presses Universitaires de France).
31. Reys, B. J. (1994) Promoting number sense in middle grades, Teaching Mathematics in the Middle School, 1(2), 114-120.
32. 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.
33. Reys, R. E., Reys, B. J., McIntosh, A., Emanuelsson, G., Johansson, B. & Yang, D. C. (1999) Assessing number sense of students in Australia, Sweden, Taiwan and the United States, School Science and Mathematics Journals, 99(2), 61-70.
34. Stevenson, H. W., Chen, C. & Lee, S. Y. (1993) Mathematical achievement of Chinese, Japanese, and American children: ten years later, Science, 259, 53-58.
35. Stevenson, H. W., Lee, S. Y. & Stigler, J. W. (1986) Mathematical achievement of Chinese, Japanese, and American children, Science, 231, 693-699.
36. Sowder, L. (1988) Children's solution of story problems, Journal of Mathematical Behavior, 7, 227-238.
37. Sowder, J. (1992a) Estimation and number sense, in: D. A. Grouws (Ed.) Handbook of research on mathematics teaching and learning (New York, Macmillan).
38. Sowder, J. (1992b) Making sense of numbers in school mathematics, in: G. Leinhardt & R. Hattrup (Eds) Analysis of arithmetic for mathematics teaching (Hillsdale, NJ, Erlbaum).
39. Stigler, J. W., Lee, S. Y. & Stevenson, H. W. (1991) Mathematical knowledge of Japanese, Chinese, and American elementary school children (Reston, VA, NCTM).
40. Yang, D. C. (2002) Teaching and learning number sense: one successful process-oriented activity with sixth grade students in Taiwan, School Science and Mathematics Journal, 102(4), 152-157.
41. 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, 1(1), 115-134.
42. 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.
43. Yerushalmy, M. (1997) Designing representations: reasoning about functions of two variables, Journal for Research in Mathematics Education, 28, 431-466.