Prospective teachers' knowledge: Concept of division

International Education Journal

Volumn 8, Issue 2, 2007, Pages 377-392

  Rizvi, Nusrat Fatima ^a   Lawson, Michael J ^a  

^a School of Education   (Australia)

Author keywords

Concept of division; Conceptual knowledge of mathematics; Multiplicative thinking; Pedagogical content knowledge of mathematics

Indexed keywords

EID: 75349091681     PISSN: 14431475     EISSN: 14431475     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Anderson, J. R. (2000). Cognitive psychology and its implications. (5th ed.) New York: Worth.
2. Ball, D.L. (1990).The mathematical understanding that preservice teachers bring to teacher Education. Elementary School Journal, 90, 449-466.
3. Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.
4. Bell, A., Swan, M., & Taylor, G. (1981). Choice of the operations in verbal problems with decimal numbers. Educational Studies in Mathematics, 12, 399-420.
5. Bell, A., Fischbein, E., & Greer, B. (1984). Choice of operation in verbal arithmetic: The effect of number size, problem structure and context. Educational Studies in Mathematics, 15, 129-147.
6. Brown, S. I., Cooney, T. J., and Jones, D. (1990). Mathematics Teacher Education. In W.R.Houston (Ed.), Handbook of research on teacher education (pp. 639-659). New York: Macmillan.
7. Dooren, W.V., Verschaffel, L. & Onghena, P (2002). The impact of preservice teachers' content knowledge on their evaluation of students' strategies for solving Arithmetic and Algebra words problems. Journal for Research in Mathematics Education, 33 (5),319-351.
8. Dooren, W.V., Bock, D.D., Verschaffel, L. and Janssens, D. (2003). Improper application of proportional reasoning. Mathematics Teaching in the Middle School. 9 (4) 205-209.
9. Ericsson, K. A., & Simon, H. A. (1993). Protocol analysis: Verbal reports as data. Cambridge, MA: MIT Press.
10. Fendel, D.M. (1987). Understanding the structure of elementary school mathematics. Newton, MA: Allyn & Bacon.
11. Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed), Handbook of research on mathematics teaching and learning. NewYork: National Council of Teachers of Mathematics.
12. Fischbein, E., M. Deri, M. Nello, and M. Mario. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal of Research in Mathematics Education 16(1), 3-17.
13. Flores, A., (2002). Profound understanding of division of fractions In Bonnie Litwiller (Eds.), Making sense of Fraction, Ratios, and proportions. National Council of Teachers of Mathematics Reston, Virginia.
14. 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).NewYork: Macmillan.
15. Haswesh, M.Z. (1986) Effect of subject matter knowledge in the teaching of biology and physics. Greenwich, CT: JAI Press.
16. Marshel, S. P., Barthuli, K. E., Brewer, M. A., and Rose, F. E. (1989). Story problem solver: A schema-based system of instruction (Tech. Rep. No. 89-01). San Diego: San Diego State University, Centre of research in Mathematics and Science Education.
17. McSeveny, A., Conway. R. & Wikes, S.(2000). Signpost mathematics. Melbourne:Pearson Education Australia Pty Limited.
18. Perkins, D. N. and Simmons, R. (1988). Pattern of misunderstanding: An integrated model for science, Math, and programming. Review of Educational Research 58, (3). Pp. 303-326.
19. Payne, J. N. (1976). Review of research on fractions. In R. Lesh (Ed.), Number and measurement (pp.145-188). Athens: University of Georgia.
20. Rizvi, N.F. (2004). Prospective teachers' ability to pose word problems. International Journal for Mathematics Teaching and Learning.
21. Sellke, D. H, Behr, M. J & Voleker, A.M. (1991) Using data tables to represent and solve multiplicative story problems. Journal for Research in Mathematics Education 22. (1), 30-38.
22. Shulman, L.S. (1987). Those who understand: knowledge growth in teaching. Educational Researcher, 15 (2), 4-14.
23. Siebert, D. (2002). Connecting informal thinking and algorithms: The case of division of fraction. In Bonnie Litwiller (Eds.), Making sense of Fraction, Ratios, and proportions National Council of Teachers of Mathematics Reston, Virginia.
24. Squire, S., & Bryant, P. (2002). The influence of sharing on children's initial concept of division. Journal of Experimental Child Psychology. 81,1-43.
25. Thompson, C.S. & Bush, WS. (2003). Improving middle school teachers' reasoning about proportional reasoning. Mathematics Teaching in the Middle School. 8 (8) 398-403.
26. Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conception: The case of division of fraction. Journal for Research in Mathematics Education 31 (1) 5-25.
27. Vergnaud, G. (1983). Multiplicative structure. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes .127-174. New York: Academic Press.
28. Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.) Number concepts and operations in the middle grades 141-161. Reston: NCTM.