Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions

Journal for Research in Mathematics Education

Volumn 31, Issue 1, 2000, Pages 5-25

  Tirosh, Dina ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Fractions; Multiplication, division; Pedagogical knowledge; Preservice teacher education

Indexed keywords

EID: 22844453632     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: 10.2307/749817     Document Type: Article

References (33)

1. Ashlock, R. D. (1990). Error patterns in computation. New York: Macmillan.
2. Australian Education Council. (1991). A national statement on mathematics for Australian schools. Melbourne, Australia: Curriculum Corporation.
3. Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21, 132-144.
4. Barash, A., & Klein, R. (1996). Seventh grades students' algorithmic, intuitive and formal knowledge of multiplication and division of non negative rational numbers. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 35-42). Valencia, Spain: University of Valencia.
5. Borasi, R. (1994). Capitalizing on errors as "springboards for inquiry": A teaching experiment. Journal for Research in Mathematics Education, 25, 166-208.
6. Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23, 194-222.
7. Bruner, J. S. (1960). The process of education. Cambridge, MA: Harvard University Press.
8. Carpenter, T. C., Lindquist, M. M., Brown, C. A., Kouba, V. L., Silver, E. A., & Swafford, J. O. (1988). Results of the fourth NAEP assessment of mathematics: Trends and conclusions. Arithmetic Teacher, 36(4), 38-41.
9. Cobb, P., Wood, T., Yackel, E., & McNeal, E. (1993). Mathematics as procedural instructions and mathematics as meaningful activity: The reality of teaching for understanding. In R. B. Davis & C. A. Maher (Eds.), School, mathematics, and the world of reality (pp. 119-134). Boston: Allyn & Bacon.
10. Cooney, T. (1994). Teacher education as an exercise in adaptation. In A. F. Coxford (Series Ed.) & D. B. Aichele (Vol. Ed.), Professional development for teachers of mathematics. 1994 Yearbook of the National Council of Teachers of Mathematics (pp. 9-22). Reston, VA: National Council of Teachers of Mathematics.
11. Even, R., & Markovitz, Z. (1995). Some aspects of teachers' and students' views on student reasoning and knowledge construction. International Journal of Mathematics Education in Science Technology, 26, 531-544.
12. Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject matter. Educational Studies in Mathematics, 29, 1-20.
13. Fendel, D. M. (1987). Understanding the structure of elementary school mathematics. Newton, MA: Allyn & Bacon.
14. Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403-434.
15. Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht, The Netherlands: Reidel.
16. Fischbein, E., Deri, M., Nello, M., & Marino, M. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16, 3-17.
17. Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20, 95-102.
18. 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: Macmillan.
19. Hart, K. M. (Ed.). (1981). Children's understanding of mathematics: 11-16. London: John Murray.
20. Janvier, C. (Ed.). (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Erlbaum.
21. Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21, 16-32.
22. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
23. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
24. Noddings, N. (1992). Professionalization and mathematics teaching. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 197-208). New York: Macmillan.
25. Orton, A., & Frobisher, L. (1996). Insights into teaching mathematics. London: Cassell.
26. Payne, J. N. (1976). Review of research on fractions. In R. Lesh (Ed.), Number and measurement (pp. 145-188). Athens: University of Georgia.
27. Sherzer, L. (1973). McKay's theorem. Mathematics Teacher, 66, 229-230.
28. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
29. Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114-145.
30. Steffe, L. (1990). On the knowledge of mathematics teachers. In R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics. Journal for Research in Mathematics Education Monograph Series, Number 4 (pp. 167-184). Reston, VA: National Council of Teachers of Mathematics.
31. Tirosh, D. (1993). Como comprenden los profesores las expresiones matematicas indefinidas [Teachers' understanding of undefined mathematical expressions]. Substratum: Temas Fundamentales en Psicologia Education, 1, 61-86.
32. Tirosh, D., Fischbein, E., Graeber, A., & Wilson, J. (1993). Conceptual adjustments in progressing from whole to rational numbers. Final report of the United States-Israel Binational Science Grant, Tel Aviv, Israel: Tel-Aviv University.
33. Warrington, M. A. (1997). How children think about division with fractions. Mathematics Teaching in the Middle School, 2, 390-394.