Fifth-grade students' use and preferences for mathematically and practically based explanations

Educational Studies in Mathematics

Volumn 73, Issue 2, 2010, Pages 121-142

  Levenson, Esther ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Elementary school students; Equivalent fractions; Mathematically based explanations; Parity; Practically based explanations

Indexed keywords

EID: 77951879421     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-009-9208-y     Document Type: Article

References (54)

1. 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: University of Chicago Press.
2. Bartolini Bussi, M. G. (1996). Mathematical discussion and perspective drawing in primary school. Educational Studies in Mathematics, 31, 11-41.
3. Bartolini Bussi, M. G., Boni, M., Ferri, F., & Garuti, R. (1999). Early approach to theoretical thinking: Gears in primary school. Educational Studies in Mathematics, 39, 67-87.
4. Bezuk, N., & Bieck, M. (1993). Current research on rational numbers and common fractions: Summary and implications for teachers. In D. T. Owens (Ed.), Research ideas for the classroom-middle grades mathematics (pp. 118-136). New York: MacMillan.
5. Bingolbali, E., & Monaghan, J. (2008). Concept image revisited. Educational Studies in Mathematics, 68, 19-35.
6. Bonotto, C. (2005). How informal out-of-school mathematics can help students make sense of formal in-school mathematics: The case of multiplying by decimal numbers. Mathematical Thinking and Learning, 7(4), 313-344.
7. Bonotto, C. (2006). Extending students' understanding of decimal numbers via realistic mathematical modeling and problem posing. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics (vol. 2, pp. 193-200). Prague: Charles University Faculty of Education.
8. 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.
9. Bruner, J. (1966). Towards a theory of instruction. New York: Norton.
10. Busse, A. (2005). Individual ways of dealing with the context of realistic tasks-first steps towards a typology. ZDM: The International Journal on Mathematics Education, 37(5), 354-360.
11. Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62, 211-230.
12. Cobb, P., McLain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21(1), 1-78.
13. Connell, M., & Peck, D. (1993). Report of a conceptual intervention in elementary mathematics. Journal of Mathematical Behavior, 12, 329-350.
14. Cramer, K., & Henry, A. (2002). Using manipulative models to build number sense for addition and fractions. In B. Litwiller (Ed.), Making sense of fractions, ratios, and proportions (pp. 41-48). Reston: The National Council of Teachers of Mathematics.
15. Davydov, V., & Tsvetkovich, Z. (1991). On the objective origin of the concept of fractions. Focus on Learning Problems in Mathematics, 13(1), 13-64.
16. Dreyfus, T. (1999). Why Johnny can't prove. Educational Studies in Mathematics, 38, 85-109.
17. Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht: Reidel.
18. Fischbein, E. (1993). The interaction between the formal, the algorithmic and the intuitive components in a mathematical activity. In R. Biehler, R. Scholz, R. Straber, B. Winkelmann (Eds.), Didactics of Mathematics as a Scientific Discipline (pp. 231-245). Dordrecht, the Netherlands: Kluwer.
19. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel.
20. 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. The Elementary School Journal, 97(3), 223-249.
21. Ginsburg, H., & Seo, K. (1999). Mathematics in children's thinking. Mathematical Thinking and Learning, 1(2), 113-129.
22. Healey, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31, 396-428.
23. 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: Macmillan.
24. Hoyles, C., Noss, R., & Pozzi, S. (2001). Proportional reasoning in nursing practice. Journal for Research in Mathematics Education, 32(1), 4-28.
25. Israel national mathematics curriculum (2006). Retrieved December 10, 2008, from http://cms. education. gov. il.
26. Koren, M. (2004). Acquiring the concept of signed numbers: Incorporating practically-based and mathematically-based explanations. Aleh (in Hebrew), 32, 18-24.
27. 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.
28. Levenson, E., Tirosh, D., & Tsamir, P. (2004). Elementary school students' use of mathematically-based and practically-based explanations: The case of multiplication. In M. Hoines, & A. Fuglestad (Eds.) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, vol. 3 (pp. 241-248). Bergen, Norway.
29. Levenson, E., Tirosh, D., & Tsamir, P. (2006). Mathematically and practically-based explanations: Individual preferences and sociomathematical norms. International Journal of Science and Mathematics Education, 4, 319-344.
30. Levenson, E., Tsamir, P., & Tirosh, D. (2007a). First and second graders' use of mathematically-based and practically-based explanations for multiplication with zero. Focus on Learning Problems in Mathematics, 29(2), 21-40.
31. Levenson, E., Tsamir, P., & Tirosh, D. (2007b). Elementary school teachers' preferences for mathematically-based and practically-based explanations. In J. Novotna & H. Morava (Eds.), Approaches to teaching mathematics at the elementary level (pp. 166-173). Prague: SEMT 07.
32. Levenson, E., Tsamir, P., & Tirosh, D. (2007c). Neither even nor odd: Sixth grade students' dilemmas regarding the parity of zero. Journal of Mathematical Behavior, 26, 83-95.
33. Linchevsky, L., & Williams, J. (1999). Using intuition from everyday life in 'filling' the gap in children's extension of their number concept to include the negative numbers. Educational Studies in Mathematics, 39, 131-147.
34. Mack, N. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21(1), 16-32.
35. Mack, N. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441.
36. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston: NCTM.
37. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.
38. Nunes, T., Schliemann, A., & Carraher, W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.
39. 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.
40. Parameswaran, R. (2007). On understanding the notion of limits and infinitesimal quantities. International Journal of Science and Mathematics Education, 5(2), 193-216.
41. 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.
42. Piaget, J. (1952). The child's conception of number. New York: Humanities.
43. Raman, M. (2002). Coordinating informal and formal aspects of mathematics: Student behavior and textbook messages. Journal of Mathematical Behavior, 21, 135-150.
44. Ried, D. (2002). Elements in accepting an explanation. Journal of Mathematical Behavior, 20, 527-547.
45. Streefland, L. (1987). Free production of fraction monographs. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the eleventh international conference Psychology of Mathematics Education (PME-XI) vol I (pp. 405-410). Montreal.
46. Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Dordrecht: Kluwer Academic.
47. 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: The National Council of Teachers of Mathematics.
48. Tsamir, P., & Sheffer, R. (2000). Concrete and formal arguments: The case of division by zero. Mathematics Education Research Journal, 12(2), 92-106.
49. 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.
50. Verschaffel, L., De corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4(4), 273-294.
51. Wu, H. (1999). Basic skills versus conceptual understanding: A bogus dichotomy. American Educator, 23(3), 14-19. 50-52.
52. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 22, 390-408.
53. Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. Journal of Mathematical Behavior, 19, 275-287.
54. Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties. Learning and Instruction, 7(4), 329-338.