Semiotics as an analytic tool for the didactics of mathematics
DOI:
https://doi.org/10.7146/nomad.v9i2.147121Abstract
This paper is a theoretical analysis of (what the author perceives to be) one of the most exciting and promising directions in research on the didactics of mathematics: studying the learning of mathematics as the initiation to, and internalisation of, certain semiotic systems. Three principal ways in which this point of view can contribute crucially to didactical research are presented and exemplified; they concern the cognitive, social and cultural aspects of mathematics education. Finally, as a topic transcending the three aspects, we consider the use of digital semiotic appliances in mathematics teaching; some results from research in this new area are outlined.
References
Andersen, P. B. (2002). Dynamic semiotics. Semiotica, 139 (1/4), 161-210. https://doi.org/10.1515/semi.2002.018
Balacheff, N. (2002). Cadre, registre et conception. Note sur les relations entre trois concepts clés de la didactique. Cahiers du lab. Leibniz-IMAG, 58.
Barthes, R. (1970). L'Empire des Signes. Genève: Editions d'Art Albert Skira.
De Saussure, F. (1966, 1916). Course in general linguistics. New York: McGraw Hill.
Duval, R. (1995). Semiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Bern: Peter Lang.
Duval, R. (1998). Signe et objet (I): Trois grandes étapes dans la problématique des rapports entre représentation et objet. Annales de Didactique et de sciences cognitives, 6, 139-163.
Duval, R. (2000). Basic issues for research in mathematics education. In T. Nakahara et al. (Eds.), Proceedings of the 24th conference of the international group for the Psychology of Mathematics Education, vol. 1 (pp. 55-69). Hiroshima University.
Emori, H. & Winsløw, C. (2002). Elements of a semiotic analysis of the secondary level classroom in Japan. In Pre-conference proceedings of ICMI comparative study conference (pp. 87-96). University of Hong Kong. (An elaborated version will appear in the 13 th ICMI study)
Ernest, P. (1998). Social constructivism as a philosophy of mathematics. New York: SUNY Press.
Guiraud, P. (1971). La sémiologie (Collection 'Que sais je' no. 1421). Paris: PUF. [English translation, 'Semiology', published by Routledge, 1975, several reprints]
Hirabayashi, I. (2002). A traditional aspect of mathematics education in Japan: mathematics as gei (art), its jutsu (technique) and do (way). In Pre- conference proceedings of ICMI comparative study conference. University of Hong Kong.
Misfeldt, M. (2003). Mathematicians' writing. In Pateman et. al. (Eds.), Proceedings of the 2003 joint meeting of PME and PMENA, vol. 3 (pp. 301-308). University of Hawaii.
Morgan, C. (2001, June). What does social semiotics have to offer mathematics education research? Paper presented at PME-26 in the discussion group on 'semiotics in mathematics education', Norwich.
Presmeg, N. (1997, October). A semiotic framework for linking cultural practice and classroom mathematics. Paper presented at the annual meeting of the North American chapter of the international group for the Psychology of Mathematics Education, Bloomington/Normal, IL.
Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: a semiotic analysis. Educational Studies in Mathematics, 42, 237-268. https://doi.org/10.1023/A:1017530828058
Radford, L. (2001). Sur les modes du savoir. In P. Radelet-de Grave (Ed.), Histoire et épistémologie dans l'éducation mathématique de la maternelle à l'université. Université Catholique de Louvain.
Resnik, M. (1997). Mathematics as a science of patterns. Oxford: Clarendon Press.
Rotman, B. (1988). Toward a semiotics of mathematics. Semiotica, 72, 1-35. https://doi.org/10.1515/semi.1988.72.1-2.1
Sfard, A.(1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36. https://doi.org/10.1007/BF00302715
Sfard, A. (1994). Reification as the birth of metaphor. For the learning of mathematics, 14(1), 44-55.
Sfard, A. (2000). Symbolizing mathematical reality into being: How mathematical discourse and mathematical objects create each other. In P. Cobb et al. (Eds.), Symbolizing and communicating in mathematics classrooms: perspectives on mathematical discourse, tools, and instructional design. Mahwah: Lawrence Erlbaum.
Steinbring, H. (2002, June). What makes a sign a mathematical sign? An epistemological perspective on mathematical interaction. Paper presented at PME-26 in the discussion group on 'semiotics in mathematics education', Norwich.
Winsløw, C. (2000a). Transformations in mathematical discourse. In B. Barton (ed.), Communication and language in mathematics education, the pre-conference publication of WGA 9 at the 9th International Congress for Mathematical Education (pp. 93-102). University of Auckland.
Winsløw, C. (2000b). Linguistic aspects of computer algebra systems in higher mathematics education. In T. Nakahara et al. (Eds.), Proceedings of the 24th conference of the international group for the Psychology of Mathematics Education, vol. 4 (pp. 281-288). Hiroshima University.
Winsløw, C. (2003a). Semiotic and discursive variables in CAS-based didactical engineering. Educational Studies in Mathematics, 52, 271-288. https://doi.org/10.1023/A:1024201714126
Winsløw, C. (2003b, September). L'usage des logiciels dans l'enseignement supérieur des mathématiques : un panorama des question du point de vue sémiotique. Paper presented at an invited symposium of Réseau Éducation Formation, Genève. [a book collecting the papers from this symposium is under edition]
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