Fifthgrade students’ use and preferences for mathematically and practically based explanations
 Esther Levenson
 … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Abstract
This paper focuses on fifthgrade students’ use and preference for mathematically (MB) and practically based (PB) explanations within two mathematical contexts: parity and equivalent fractions. Preference was evaluated based on three parameters: the explanation (1) was convincing, (2) would be used by the student in class, and (3) was one that the student wanted the teacher to use. Results showed that students generated more MB explanations than PB explanations for both contexts. However, when given a choice between various explanations, PB explanations were preferred in the context of parity, and no preference was shown for either type of explanation in the context of equivalent fractions. Possible bases for students’ preferences are discussed.
Inside
Within this Article
 Introduction
 Background
 Methodology
 Results
 Summary and discussion
 References
 References
Other actions
 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.
 Bartolini Bussi, M. G. (1996). Mathematical discussion and perspective drawing in primary school. Educational Studies in Mathematics, 31, 11–41. CrossRef
 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. CrossRef
 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.
 Bingolbali, E., & Monaghan, J. (2008). Concept image revisited. Educational Studies in Mathematics, 68, 19–35. CrossRef
 Bonotto, C. (2005). How informal outofschool mathematics can help students make sense of formal inschool mathematics: The case of multiplying by decimal numbers. Mathematical Thinking and Learning, 7(4), 313–344. CrossRef
 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.
 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. CrossRef
 Bruner, J. (1966). Towards a theory of instruction. New York: Norton.
 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. CrossRef
 Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62, 211–230. CrossRef
 Cobb, P., McLain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21(1), 1–78. CrossRef
 Connell, M., & Peck, D. (1993). Report of a conceptual intervention in elementary mathematics. Journal of Mathematical Behavior, 12, 329–350.
 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.
 Davydov, V., & Tsvetkovich, Z. (1991). On the objective origin of the concept of fractions. Focus on Learning Problems in Mathematics, 13(1), 13–64.
 Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38, 85–109. CrossRef
 Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht: Reidel.
 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.
 Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel.
 Fuchs, L., Fuchs, D., Hamlett, C., Phillips, N., Karns, K., & Dutka, S. (1997). Enhancing students’ helping behavior during peermediated instruction with conceptual mathematical explanations. The Elementary School Journal, 97(3), 223–249. CrossRef
 Ginsburg, H., & Seo, K. (1999). Mathematics in children’s thinking. Mathematical Thinking and Learning, 1(2), 113–129. CrossRef
 Healey, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31, 396–428. CrossRef
 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.
 Hoyles, C., Noss, R., & Pozzi, S. (2001). Proportional reasoning in nursing practice. Journal for Research in Mathematics Education, 32(1), 4–28. CrossRef
 Israel national mathematics curriculum (2006). Retrieved December 10, 2008, from http://cms.education.gov.il.
 Koren, M. (2004). Acquiring the concept of signed numbers: Incorporating practicallybased and mathematicallybased explanations. Aleh (in Hebrew), 32, 18–24.
 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.
 Levenson, E., Tirosh, D., & Tsamir, P. (2004). Elementary school students’ use of mathematicallybased and practicallybased 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.
 Levenson, E., Tirosh, D., & Tsamir, P. (2006). Mathematically and practicallybased explanations: Individual preferences and sociomathematical norms. International Journal of Science and Mathematics Education, 4, 319–344. CrossRef
 Levenson, E., Tsamir, P., & Tirosh, D. (2007a). First and second graders’ use of mathematicallybased and practicallybased explanations for multiplication with zero. Focus on Learning Problems in Mathematics, 29(2), 21–40.
 Levenson, E., Tsamir, P., & Tirosh, D. (2007b). Elementary school teachers’ preferences for mathematicallybased and practicallybased explanations. In J. Novotna & H. Morava (Eds.), Approaches to teaching mathematics at the elementary level (pp. 166–173). Prague: SEMT 07.
 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. CrossRef
 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. CrossRef
 Mack, N. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21(1), 16–32. CrossRef
 Mack, N. (1995). Confounding wholenumber and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422–441. CrossRef
 National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston: NCTM.
 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.
 Nunes, T., Schliemann, A., & Carraher, W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.
 Nyabanyaba, T. (1999). Whither relevance? Mathematics teachers’ discussion of the use of ‘reallife’ contexts in school mathematics. For the Learning of Mathematics, 19(3), 10–14.
 Parameswaran, R. (2007). On understanding the notion of limits and infinitesimal quantities. International Journal of Science and Mathematics Education, 5(2), 193–216. CrossRef
 Perry, M. (2000). Explanations of mathematical concepts in Japanese, Chinese, and U.S. first and fifthgrade classrooms. Cognition and Instruction, 18(2), 181–207. CrossRef
 Piaget, J. (1952). The child’s conception of number. New York: Humanities.
 Raman, M. (2002). Coordinating informal and formal aspects of mathematics: Student behavior and textbook messages. Journal of Mathematical Behavior, 21, 135–150. CrossRef
 Ried, D. (2002). Elements in accepting an explanation. Journal of Mathematical Behavior, 20, 527–547. CrossRef
 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 (PMEXI) vol I (pp. 405–410). Montreal.
 Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Dordrecht: Kluwer Academic.
 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.
 Tsamir, P., & Sheffer, R. (2000). Concrete and formal arguments: The case of division by zero. Mathematics Education Research Journal, 12(2), 92–106.
 Van den HeuvelPanhuizen, 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. CrossRef
 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. CrossRef
 Wu, H. (1999). Basic skills versus conceptual understanding: A bogus dichotomy. American Educator, 23(3), 14–19. 5052.
 Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 22, 390–408. CrossRef
 Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. Journal of Mathematical Behavior, 19, 275–287. CrossRef
 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. CrossRef
 Title
 Fifthgrade students’ use and preferences for mathematically and practically based explanations
 Journal

Educational Studies in Mathematics
Volume 73, Issue 2 , pp 121142
 Cover Date
 20100301
 DOI
 10.1007/s106490099208y
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Elementary school students
 Mathematically based explanations
 Practically based explanations
 Parity
 Equivalent fractions
 Industry Sectors
 Authors

 Esther Levenson ^{(1)}
 Author Affiliations

 1. Tel Aviv University, Tel Aviv, Israel, 69978