Mathematically and practically-based explanations: Individual preferences and sociomathematical norms

International Journal of Science and Mathematics Education

Volumn 4, Issue 2, 2006, Pages 319-344

  Levenson, Esther ^a   Tirosh, Dina ^b   Tsamir, Pessia ^b  

^a Tel Aviv University ^*  (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Elementary school; Explanations; Mathematically based and practically based explanations; Preferences; Sociomathematical norms

Indexed keywords

EID: 33749382907     PISSN: 15710068     EISSN: 15731774     Source Type: Journal    
DOI: 10.1007/s10763-005-9011-x     Document Type: Article

References (44)

1. Achinstein, P. (1983). The nature of explanation, New York: Oxford Univesity Press.
2. Ball, D. & Bass, H. (2000). Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In D. Phillips (Ed.), Yearbook of the National Society for the Study of Education, Constructivism in Education. Chicago, IL: University of Chicago Press.
3. Ben-Yehuda, M., Lavy, I., Linchevski, L. & Sfard, A. (2005). Doing wrong with words: What bars students' access to arithmetical discourses. Journal for Research in Mathematics Education, 36(3), 176-247.
4. Borasi, R. (1992). Learning mathematics through inquiry. Portsmouth, NH: Heinemann.
5. Bowers, J. & Doerr, H. (2001). An analysis of prospective teachers' dual roles in understanding the mathematics of change: Eliciting growth with technology. Journal of Mathematics Teacher Education, 4, 115-137.
6. Cobb, P., Wood, T. & Yackel, E. (1991). A constructivist approach to second grade mathematics. In E. von Glaserfeld (Ed.), Radical constructivism in mathematics (pp. 157-176). Dordrecht, The Netherlands: Kluwer Academic.
7. Cobb, P., McLain, K. & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 22(1), 1-78.
8. Cramer, K., Post, T. & del Mas, R. (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, 111-144.
9. Dreyfus, T. (1999). Why Johnny can't prove? Educational Studies in Mathematics, 38, 85-109.
10. Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, The Netherlands: Reidel.
11. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: Reidel.
12. Fuchs, L., Fuchs, D., Hamlett, C., Phillips, N., Karns, K. & Dutka, S. (1997). Enhancing students' helping behavior during peer-mediated instruction with conceptual mathematical explanations. Elementary School Journal, 97(3), 223-249.
13. Ginsburg, H. & Seo, K. (1999). Mathematics in children's thinking. Mathematical Thinking and Learning, 1(2), 113-129.
14. Hershkowitz, R. & Schwarz, B. (1999). The emergent perspective in rich learning environments: Some roles of tools and activities in the construction of sociomathematical norms. Educational Studies in Mathematics, 39, 149-166.
15. Hiebert, J. & Carpenter, T. (1992). Learning and teaching with understanding. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmilian.
16. Kazemi, E. & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. Elementary School Journal, 102(1), 59-80.
17. Knifong, J. & Burton, G. (1980). Intuitive definitions for division with zero. Arithmetic Teacher, 73, 179-186.
18. Koirala, H. (1999). Teaching mathematics using everyday contexts: What if academic mathematics is lost? In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, III (pp. 161-168). Haifa, Israel.
19. Lampert, M. (1990). When the problem is not the question and the solution is not the answer. American Educational Research Journal, 27(1), 29-63.
20. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
21. Mack, K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441.
22. McClain, K. & Cobb, P. (2001). An approach for supporting teachers' learning in social context. In F. Lin & T. Cooney (Eds.), Making sense of mathematics teacher education (pp. 207-232). Dordrecht, The Netherlands: Kluwer.
23. McNeal, B. & Simon, M (2000). Mathematics culture clash: Negotiating new classroom norms with prospective teachers. Journal of Mathematical Behavior, 18(4), 475-509.
24. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
25. Nyabanyaba, T. (1999). Whither relevance? Mathematics teachers' discussion of the use of 'real-life' contexts in school mathematics. For the Learning of Mathematics, 19(3), 10-14.
26. Perry, M. (2000). Explanations of mathematical concepts in Japanese, Chinese, and U.S. first- and fifth-grade classrooms. Cognition and Instruction, 18(2), 181-207.
27. Piaget, J. & Inhelder, B. (1969). The psychology of the child. New York: Basic Books.
28. Raman, M. (2002). Coordinating informal and formal aspects of mathematics: Student behavior and textbook messages. Journal of Mathematical Behavior, 21, 135-150.
29. Schoenfeld, A. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13, 55-80.
30. Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4-13.
31. Sfard, A. (2000). On reform movement and the limits of mathematical discourse. Mathematical Thinking and Learning, 2(3), 157-189.
32. Sfard, A. (2001). Learning mathematics as developing a discourse. In R. Speiser, C. Maher & C. Walter (Eds.), Proceedings of 21st Conference of PME-NA (pp. 23-44). Columbus, Ohio: Clearing House for Science, Mathematics, and Environmental Education.
33. Sfard, A. & Lavie, I. (2005). Why cannot children see as the same what grownups cannot see as different? - early numerical thinking revisited. Cognition and Instruction, 23(2), 237-309.
34. Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Dordrecht, the Netherlands: Kluwer Academic Publishers.
35. Szendrei, J. (1996). Concrete materials in the classroom. In A.J. Bishop (Ed.), International Handbook of Mathematics Education (pp. 411-434). Dordrecht the Netherlands: Kluwer Academic Publishers.
36. Thompson, A., Philipp, R., Thompson, P. & Boyd, B. (1994). Calculational and conceptual orientation in teaching mathematics. In A. Coxford (Ed.), 1994 Yearbook of the National Council of Teachers of Mathematics (pp. 79-92). Reston, VA: The National Council of Teachers of Mathematics.
37. Tsamir, P. & Sheffer, R. (2000). Concrete and formal arguments: The case of division by zero. Mathematics Education Research Journal, 12(2), 92-106.
38. Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9-35.
39. Van Fraassen, B. (1980). The scientific image. Oxford: Clarendon, UK.
40. Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.) Advanced mathematical thinking (pp. 65-81). Dordrecht, The Netherlands: Kluwer Academic Publishers.
41. Wu, H. (1999). Basic skills versus conceptual understanding: A bogus dichotomy. American Educator, 23(3), 14-19, 50-52.
42. Yackel, E. (2001). Explanation, justification and argumentation in mathematics classrooms. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th conference of the International Group for the Psychology of Mathematics Education, Vol. 1 (pp. 9-24). Utrecht, The Netherlands: Freudenthal institute.
43. Yackel, E. & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 22, 390-408.
44. Yackel, E., Rasmussen, C. & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. Journal of Mathematical Behavior, 19, 275-287.