NUMBER SENSE-BASED STRATEGIES USED BY HIGH-ACHIEVING SIXTH GRADE STUDENTS WHO EXPERIENCED REFORM TEXTBOOKS

International Journal of Science and Mathematics Education

Volumn 10, Issue 5, 2012, Pages 1071-1097

  Alsawaie, Othman N ^a  

^a UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

Author keywords

mathematical thinking; mathematics curriculum; number sense; problem solving strategies; reform textbooks

Indexed keywords

EID: 84866898249     PISSN: 15710068     EISSN: 15731774     Source Type: Journal    
DOI: 10.1007/s10763-011-9315-y     Document Type: Article

References (50)

1. Baroody, A. J. & Coslick, R. T. (1998). Fostering children's mathematical power: An investigative approach to K-8 mathematics instruction. Mahwah, NJ: Erlbaum.
2. Behr, M., Harel, G., Post, T. & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York, NY: Macmillan Publishing.
3. Burns, M. (1989). Teaching for understanding: A focus on multiplication. In P. R. Trafton & A. P. Shulte (Eds.), New directions for elementary school mathematics (pp. 123-134). Reston, VA: NCTM.
4. Faulkner, V. N. (2009). Components of number sense: An instructional model for teachers. Teaching Exceptional Children, 41(5), 24-30.
5. Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F. & Suk Yoon, K. (2001). What makes professional development effective: Results from a national sample of teachers. American Educational Research Journal, 38(4), 915-945.
6. Garner, R. (1992). Learning from school texts. Educational Psychologist, 27, 53-63.
7. Ghazali, M., Abdul Rahman, S., Ismail, Z., Sharifah Norhaidah Idros, S. N., & Salleh, F. (2003). Development of a framework to assess primary students' number sense in Malaysia. Proceedings of the International Conference, the Decidable and the Undecidable in Mathematics Education, Brno, Czech Republic. The Mathematics Education into the 21st Century Project.
8. Greenes, C., Schulman, L. & Spungin, R. (1993). Developing sense about numbers. Arithmetic Teacher, 40(5), 279-284.
9. Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22, 170-218.
10. Greer, B. (1992). Multiplication and division as models of situations. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276-295). New York, NY: Macmillan.
11. Hiebert, J. C. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics Education, 30, 3-19.
12. Hiebert, J. & Lindquist, M. M. (1990). Developing mathematical knowledge in the young child. In J. N. Payne (Ed.), Mathematics for the young child (pp. 17-36). Reston, VA: National Council of Teachers of Mathematics.
13. Hiebert, J. & Stigler, J. W. (2000). A proposal for improving classroom teaching: Lessons from the TlMSS video study. The Elementary School Journal, 101l, 3-20.
14. Hiebert, J. & Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 199-223). Hillsdale, NJ: Erlbaum.
15. Hill, H. C., Rowan, B. & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
16. Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11.
17. Jones, G. A., Langrall, C. W., Thornton, C. A. & Nisbet, S. (2002). Elementary students' access to powerful mathematical ideas. In L. English, M. B. Bussi, G. A. Jones, R. A. Lesh & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 113-141). Mahwah, NJ: Erlbaum.
18. Kamii, C. (1989). Young children reinvent arithmetic: Implications of Piaget's theory. New York, NY: Teachers College Press.
19. Kamii, C., Lewis, B. A. & Livingston, S. J. (1993). Primary arithmetic: Children inventing their own procedures. Arithmetic Teacher, 41(4), 200-203.
20. Kerslake, D. (1986). Fractions: Children's strategies and errors: A report of the Strategies and Errors in Secondary Mathematics Project. Windsor, England: NFER-Nelson.
21. Knuth, E. (2002). Teachers' conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5(1), 61-88.
22. Markovits, Z. (1989). Reactions to the number sense conference. In J. T. Sowder & B. P. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 78-81). San Diego, CA: San Diego University, Center for Research in Mathematics and Science Education.
23. 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.
24. McIntosh, A., Reys, B. J. & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12, 2-8.
25. McIntosh, A., Reys, B. J., Reys, R. E., Bana, J. & Farrell, B. (1997). Number sense in school mathematics: Student performance in four countries. Perth, Australia: Edith Cowan University.
26. Ministry of Education (2001). The national document for mathematics curriculum in public education. Dubai, UAE: Ministry of Education.
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. Norul Akmar, S. (1997). Two students subtraction of integers schemes. Journal of Education, 18, 75-96.
30. Peck, D. M. & Jencks, S. M. (1981). Conceptual issues in the teaching and learning of fractions. Journal for Research in Mathematics Education, 12(5), 339-348.
31. Post, T. R., Cramer, K. A., Behr, M., Lesh, R. & Harel, G. (1993). Curriculum indications from research on the learning, teaching and assessing of rational number concepts: Multiple research perspective. In T. Carpenter & E. Fennema (Eds.), Learning, teaching and assessing rational number concepts: Multiple research perspective. Madison: University of Wisconson.
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, 29, 225-237.
33. Sackur-Grisvad, C. & Leonard, F. (1985). Intermediate cognitive organizations in the process of learning a mathematical concept: The order of positive decimal numbers. Cognition and Instruction, 2, 157-174.
34. Schmidt, W. H., Jakwerth, P. M. & McKnight, C. C. (1998). Curriculum-sensitive assessment: Content does make a difference. International Journal of Educational Research, 29, 503-527.
35. Schneider, S. B. & Thompson, C. S. (2000). Incredible equations develop incredible number sense. Teaching Children Mathematics, 7(3), 146-148.
36. Sheetal Sood, S. & Jitendra, A. K. (2007). A comparative analysis of number sense instruction in reform-based and traditional mathematics textbooks. The Journal Of Special Education, 41(3), 145-157.
37. Sowder, J. (1992). Estimation and number sense. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371-389). New York, NY: Macmillan.
38. Sowder, J. T. & Markovits, Z. (1989). Effects of instruction on number magnitude. In C. A. Maher, G. A. Goldin & R. B. Davis (Eds.), Proceedings of Eleventh Annual Meeting: North American Charter of the International Group far the Psychology o f Mathematics Education (pp. 105-110). New Brunswick, NJ: Rutgers University Center for Mathematics, Science, and Computer Education.
39. Sowder, J. T. & Markovits, Z. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), 4-29.
40. Sowder, J. T. & Schappelle, B. P. (Eds.). (1989). 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.
41. Sowder, J. T. & Wheeler, M. M. (1987). The development of computational estimation and number sense: Two exploratory studies. San Diego, CA: San Diego State University Center for Research in Mathematics and Science Education.
42. Stigler, J. W. & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 61(5), 12-17.
43. Stigler, J. W., Lee, S. Y. & Stevenson, H. W. (1991). Mathematical knowledge of Japanese, Chinese, and American elementary school children. Reston, VA: NCTM.
44. Suter, L. E. (2000). Is student achievement immutable? Evidence from international studies on schooling and student achievement. Review of Educational Research, 70, 529-545.
45. Threadgill-Sowder, J. (1984). Computational estimation procedures of school children. The Journal of Educational Research, 77, 332-336.
46. Trafton, P. R. (1989). Reflections on the number sense conference. In J. T. Sowder & B. P. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 74-77). San Diego, CA: San Diego University, Center for Research in Mathematics and Science Education.
47. Tsao, Y. L. (2005). The number sense of preservice elementary school teachers. College Student Journal, 39(4), 647-679.
48. van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). New York, NY: Longman.
49. Yang, D. C. (2005). Number sense strategies used by sixth grade students in Taiwan. Educational Studies, 31(3), 317-333.
50. Yang, D. C. & Huang, F. Y. (2004). Relationships among computational performance, pictorial representation, symbolic representation and number sense of sixth-grade students in Taiwan. Educational Studies, 30, 373-389.