Exploring one student’s explanations at different ages: the case of Sharon
 Esther Levenson
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This study describes the types of explanations one student, Sharon, gives and prefers at different ages. Sharon is interviewed in the second grade regarding multiplication of onedigit numbers, in the fifth grade regarding even and odd numbers, and in the sixth grade regarding equivalent fractions. In the tenth grade, she revisits each of these concepts again. The study investigates the different forms Sharon’s explanations take at different ages as well as how she perceives the nature of mathematical explanations at different ages. Sharon’s explanations are also used to investigate her conceptualization of the number zero, a concept which runs across the curriculum at different ages. Finally, the study explores a method for investigating the longterm mathematical development of one student. Implications for future research are discussed.
 Achinstein, P. (1983). The nature of explanation. New York: Oxford University Press.
 Anthony, G., & Walshaw, M. (2004). Zero: A “none” number? Teaching Children Mathematics, 11(1), 38–41.
 Balacheff, N. (2010). Bridging knowing and proving in mathematics: A didactical perspective. In G. Hanna, H. N. Jahnke, & H. Pulte (Eds.), Explanation and proof in mathematics: Philosophical and educational perspectives (pp. 115–136). New York: Springer. CrossRef
 Ball, D. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144. CrossRef
 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 (pp. 193–224). Chicago, IL: University of Chicago Press.
 Board of Studies NSW (2006). Mathematics K6 syllabus. Retrieved February 5, 2010 from http://k6.boardofstudies.nsw.edu.au/files/maths/k6_maths_syl.pdf
 De Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17–24.
 Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38(1–3), 85–109. CrossRef
 Eynde, P., De Corte, E., & Verschaffel, L. (2006). Epistemic dimensions of students’ mathematicsrelated belief system. International Journal of Educational Research, 45(1–2), 57–70. CrossRef
 Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, the Netherlands: Reidel.
 Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht, the Netherlands: Kluwer Academic.
 Hanna, G. (1989). More than formal proof. For the Learning of Mathematics, 9(1), 20–25.
 Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44, 5–25. CrossRef
 Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428. CrossRef
 Israel National Mathematics Curriculum (2006). Retrieved December 10, 2009, from http://cms.education.gov.il
 Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229–269). Hillsdale, NJ: Lawrence Erlbaum Associates.
 Krummheuer, G. (2000). Mathematics learning in narrative classroom cultures: Studies of argumentation in primary mathematics education. For the Learning of Mathematics, 20(1), 22–32.
 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. CrossRef
 Levenson, E. (2010). Fifth grade students’ use and preferences for mathematically and practically based explanations. Educational Studies in Mathematics, 73(2), 121–142. CrossRef
 Levenson, E., Tirosh, D., & Tsamir, P. (2009). Students’ perceived sociomathematical norms: The missing paradigm. The Journal of Mathematical Behavior, 28, 83–95. CrossRef
 Levenson, E., Tsamir, P., & Tirosh, D. (2007). First and second graders’ use of mathematicallybased and practicallybased explanations for multiplication with zero. Focus on Learning Problems in Mathematics, 29(2), 21–40.
 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
 Maher, C., & Martino, A. (1996). The development of the idea of mathematical proof: A 5year case study. Journal for Research in Mathematics Education, 27(2), 194–214. CrossRef
 Mancosu, P. (2008). Explanation in mathematics. In E. Zalta (Ed.), The Stanford encyclopedia of philosophy. Retrieved July 2, 2010 from http://plato.stanford.edu/archives/fall2008/entries/mathematicsexplanation/
 Mueller, M. (2009). The coconstruction of arguments by middleschool students. The Journal of Mathematical Behavior, 28, 138–149. CrossRef
 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
 Nunokawa, K. (2010). Proof, mathematical problemsolving, and explanation in mathematics teaching. In G. Hanna, H. N. Jahnke, & H. Pulte (Eds.), Explanation and proof in mathematics: Philosophical and educational perspectives (pp. 223–236). New York: Springer. CrossRef
 Pogliani, L., Randic, M., & Trinajstic, N. (1998). Much ado about nothing—an introductive inquiry about zero. International Journal of Mathematics Education in Science and Technology, 29(5), 729–744. CrossRef
 Seife, C. (2000). Zero: The biography of a dangerous idea. New York: Viking Penguin.
 Tall, D. (2004). Thinking through three worlds of mathematics. In M. Hoines & A. Fuglestad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 281–288). Bergen, Norway: PME.
 Tsamir, P., Sheffer, R., & Tirosh, D. (2000). Intuitions and undefined operations: The case of division by zero. Focus on Learning Problems in Mathematics, 22(1), 1–16.
 Van Fraassen, B. (1980). The scientific image. Oxford: Clarendon. CrossRef
 Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking. Dordrecht, the Netherlands: Kluwer.
 Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah, NJ: Lawrence Erlbaum Associates.
 Wilson, P. (2001). Zero: A special case. Mathematics Teaching in the Middle School, 6(5), 300–303, 308–309.
 Yackel, E. (2001). Explanation, justification and argumentation in mathematics classrooms. In M. Van den HeuvelPanhuizen (Ed.), Proceedings of the 25th conference of the International Group for the Psychology of Mathematics Education PME25, (Vol. 1, pp. 1–9). Utrecht, the Netherlands: PME.
 Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 22, 390–408. CrossRef
 Yackel, E., Cobb, P., & Wood, T. (1998). The interactive constitution of mathematical meaning in one second grade classroom: An illustrative example. The Journal of Mathematical Behavior, 17, 469–488. CrossRef
 Zazkis, R., & Chernoff, E. J. (2008). What makes a counterexample exemplary? Educational Studies in Mathematics, 68(3), 195–208. CrossRef
 Title
 Exploring one student’s explanations at different ages: the case of Sharon
 Journal

Educational Studies in Mathematics
Volume 83, Issue 2 , pp 181203
 Cover Date
 20130601
 DOI
 10.1007/s1064901294471
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Mathematically based explanations
 Practically based explanations
 Zero
 Authors

 Esther Levenson ^{(1)}
 Author Affiliations

 1. Tel Aviv University, Tel Aviv, Israel