Student reasoning constrained by the didactical contract
DOI:
https://doi.org/10.7146/nomad.v10i3-4.147173Abstract
This paper presents an analysis of an observation of student teachers’ small-group work on a generalization problem in algebra. I begin my analysis by looking at the student teachers’ attention to the teacher educator’s thinking, at the cost of their own interpretation of the problem. Further analysis deals with the difficulties in changing representation from natural language to mathematical symbols. The analysis is based on Brousseau’s theory of didactical situations in mathematics, and a semiotic approach to the problem of algebraic reference, informed by Radford.
References
Almeida, D. (2001). Pupils' proof potential. International Journal of Mathematics Education in Science and Technology, 32 (1), 53-60. https://doi.org/10.1080/00207390119535
Balacheff, N. (1991). The benefits and limits of social interaction: the case of mathematical proof. In A. Bishop, S. Mellin-Olsen & J. van Dormolen (Eds.), Mathematical knowledge: its growth through teaching (pp. 175-192). Dordrecht: Kluwer. https://doi.org/10.1007/978-94-017-2195-0_9
Bauersfeld, H. (1988). Interaction, construction and knowledge: alternative perspectives for mathematics education. In D. A. Grouwes, T. J. Cooney & D. Jones (Eds.), Effective mathematics teaching (27-46). Reston, Virginia: NCTM & Lawrence Erlbaum.
Brousseau, G. (1980). L'échec et le contrat. Recherches, 41, 177-182.
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.
Chazan, D. (1993). High school geometry students' justifications for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24 (4), 359-387. https://doi.org/10.1007/BF01273371
Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28 (3), 258-277. https://doi.org/10.2307/749781
Duval, R. (2002). The cognitive analysis of problems of comprehension in the learning of mathematics. Mediterranean Journal for Research in Mathematics Education, 1 (2), 1-16.
Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel. https://doi.org/10.1007/978-94-010-2903-2_2
Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. London: Addison Wesley.
Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: perspectives for research and teaching (pp. 65-86). Dordrecht: Kluwer. https://doi.org/10.1007/978-94-009-1732-3_5
Radford (2000). Signs and meanings in students' emergent algebraic thinking: a semiotic analysis. Educational Studies in Mathematics, 42 (3), 237-268. https://doi.org/10.1023/A:1017530828058
Radford, L. (2002a). The seen, the spoken and the written: a semiotic approach to the objectification of mathematical knowledge. For the Learning of Mathematics, 22 (2), 14-23.
Radford, L. (2002b). On heroes and the collapse of the narratives: a contribution to the study of symbolic thinking. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (pp. 81-88). Norwich: University of East Anglia.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
Voigt, J. (1994). Negotiation of mathematical meaning and learning mathematics. Educational Studies in Mathematics, 26, 275-298. https://doi.org/10.1007/BF01273665
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.