Promoting mathematical understanding: Number sense in action

Mathematics Education Research Journal

Volumn 14, Issue 2, 2002, Pages 133-149

  Kaminski, Eugene ^a  

^a AUSTRALIAN CATHOLIC UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17444370977     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03217358     Document Type: Article

References (42)

1. Askew, M., Brown, M., Rhodes, V., William, D., & Johnson, D. (1997). Effective teachers of numeracy in UK primary schools: Teachers' beliefs, practices and pupils' learning. In E. Pehkonen (Ed.), Proceedings of the 21 st annual conference of the International Group for the Psychology of Mathematics Education (Vol 2, pp. 25-32). Lahti, Finland: PME Program Committee.
2. Australian Council for Educational Research. (1997). Reading comprehension and numeracy among junior secondary school students in Australia. Melbourne: ACER.
3. Ball, D. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90(4), 449-466.
4. Bay, J. (2000). Bingo games: Turning student intuitions into investigations in probability and number sense. Mathematics Teacher, 93(3).
5. Brown, C., Carpenter, T., Kouba, V., Lindquist, M., Silver, E., & Swafford, J. (1988). Secondary school results for the fourth NAEP mathematics assessment: Discrete mathematics, data organization and interpretation, measurement, number and operations. Mathematics Teacher, 81(4), 241-249.
6. Carpenter, T., Moser, M., & Romberg, T., (Eds.) (1982). Addition and subtraction: A cognitive approach. Hillsdale, NJ: Erlbaum.
7. Carter, J. (1990). Teachers' knowledge and learning to teach. In W. Houston (Ed.), Handbook of research on teacher education (pp. 291-310). New York: Macmillan.
8. Case, R. (1989). Fostering the development of children's number sense: Reflections on the conference. In J. Sowder & B. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 57-64). San Diego, CA: San Diego State University.
9. Cobb, P., Yackel, E., & Wood, T. (1988). Curriculum and teacher development: Psychological and anthropological perspectives. In E. Fennema, T. Carpenter, & S. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 44-54). Madison: Wisconsin Centre for Educational Research, University of Wisconsin.
10. Department of Education, Training and Youth Affairs. (2000). Numeracy: A priority for all: Challenges for Australians schools. Canberra: McMillan.
11. Dossey, J., Mullis, I., Linquist, M., & Chambers, D. (1988). The mathematics report card: Are we measuring up? Trends and achievements based on the 1986 national assessment. Princeton, NJ: Educational Testing Service.
12. Ernest, P. (1994). Varieties of constructivism: Their metaphors, epistemologies and pedagogical implications. Hiroshima Journal of Mathematics Education, 2, 1-14.
13. Gagatsis, A., & Petronis, T. (1990). Using geometrical models in a process of reflective thinking in learning and teaching mathematics. Educational Studies in Mathematics, 21(1), 29-54.
14. Greeno, J. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170-218.
15. Hiebert, J. (1988). A theory of developing competence with written mathematical symbols. Educational Studies in Mathematics, 19, 333-355.
16. Hogan, K. (1997). Introduction. In K. Hogan & M. Pressley (Eds.), Scaffolding student learning: Instructional approaches and issues (pp. 1-5). Cambridge, MA: Brookline Books.
17. Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11.
18. Kagan, S. (1990). The structural approach to co-operative learning. Educational Leadership, 47(4), 12-15.
19. Lampert, M. (1986). Teaching multiplication. Journal of Mathematical Behavior, 5, 241-280.
20. Lindquist, M., Carpenter, T., Silver, E., & Matthews, W. (1983). The third national mathematics assessment: Results and implications for elementary and middle schools. Arithmetic Teacher, 31, 14-19.
21. Louden, W., Chan, L. K. S., Elkins, J., Greaves, D., House, H., Milton, et al. (2000). Mapping the territory, primary students with learning difficulties: Literacy and numeracy (Vols. 1-3). Canberra: DETYA.
22. McIntosh, A. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-8.
23. Mason, K. (1986). Decimals: Assessment at age 11 and 15. Windsor, Berkshire: NFER, Nelson.
24. National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The Council.
25. Resnick, L. (1987). Education and learning to think. Washington, DC: National Academic Press.
26. Resnick, L. (1989). Defining, assessing and teaching number sense. In J. Sowder & B. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 35-39). San Diego, CA: San Diego State University.
27. Reys, B. (1991). Number sense: Building on student's intuitive knowledge. In C. J. Irons (Ed.), Challenging children to think when they compute: Developing number sense, mental computation and computational estimation, Proceedings of the 1 annual conference on Mathematics Teaching and Learning presented by The Centre for Mathematics and Science Education, Queensland University of Technology, Brisbane.
28. Reys, R., Reys, B., Mclntosh, A., Emanuelsson, G., Johnsson, B., & Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan, and the United States. School Science and Mathematics, 99(2), 61-70.
29. Slesnick, T. (1982). Algorithmic skill vs conceptual understanding. Educational Studies in Mathematics, 13, 143-154.
30. Sowder, J. (1989). Introduction. In J. Sowder & B. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 1-5). San Diego, CA: San Diego State University.
31. Sowder, J. (1991). Teaching computation in ways that promote number sense. In C. J. Irons (Ed.), Challenging children to think when they compute: Developing number sense, mental computation and computational estimation, Proceedings of the 1st annual conference on Mathematics Teaching and Learning presented by The Centre for Mathematics and Science Education, Queensland University of Technology, Brisbane.
32. Sowder, J., & Markovits, Z. (1989). Effects of instruction on number magnitude. In C. Maher, G. Goldin, & R. Davis (Eds.), Proceedings of the eleventh annual meeting: North American Chapter of the International Group for the Psychology of Mathematics Education. New Brunswick, NJ: Centre for Mathematics, Science and Computer Education, Rutgers-The State University of New Jersey.
33. Sowder, J., & Schappelle, B. (1994). Number sense making. Arithmetic Teacher, 41(6), 342-345.
34. Trafton, P. (1986). Computation-It's time for a change. Arithmetic Teacher, 34(3), 2.
35. Trafton, P. (1989). Reflections on the number sense conference. In J. Sowder & B. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report on a conference. San Diego, CA: San Diego State University.
36. Turkel, S., & Newman, C. (1988). What's your number? Developing number sense. Arithmetic Teacher, 36(6), 53-55.
37. van Kraayenoord, C., Elkins, J., Palmer, C., & Rickards, F. (2000). Literacy, numeracy and students with disabilities. Canberra: McMillan.
38. von Glasersfeld, E. (1995). A constructivist approach to teaching. In L. Steffe & J. Cole (Eds.), Constructivism in education (pp. 3-15). Hillside, NJ: Lawrence Erlbaum.
39. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
40. Walkerdine, V. (1989). Counting girls out. London: Virago.
41. Weinstein, C., & Mayer, R. (1986). The teaching of learning strategies. In M. Wittrock (Ed.), Handbook ofresearch on teaching (3rd ed., pp. 315-327). New York: Macmillan.
42. Yackel, E., Cobb, P., & Wood, T. (1992). Instructional development and assessment from a socioconstructivist perspective. In G. Leder (Ed.), Assessment and learning of mathematics (pp. 63-80). Melbourne: The Australian Council for Educational Research.