Abstract
Mathematical signs and symbols have a decisive role for coding, constructing and communicating mathematical knowledge. Nevertheless these mathematical signs do not already contain mathematical meaning and conceptual ideas themselves. The contribution will present basic elements of an epistemology of mathematical knowledge and then apply these theoretical ideas for analyzing case studies of two teaching episodes from elementary mathematics teaching. In this way different roles of mathematical signs as means of communication (oral function), of indicating (deictic function) and of writing (symbolic function) will be elaborated.
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References
Borel, E.: 1965, Elements of the Theory of Probability, Englewood Cliffs, New Jersey, Prentice-Hall.
Davis, P. J. and Hersh, R.: 1981, The Mathematical Experience, Birkhäuser, Boston.
Duval, R.: 2000, ‘Basic issues for research in mathematics education’, in T. Nakahara and M. Koyama (eds.), Proceedings of the 24th International Conference for the Psychology of Mathematics Education, Japan, Nishiki Print Co., Ltd. I, pp. 55–69.
Hacking, I.: 1975, The Emergence of Probability, Cambridge University Press, Cambridge.
Loève, M.: 1978, ‘Calcul des probabilités′, in J. Dieudonné (ed.), Abgrégé d'histoire des mathématiques 1700–1900, vol. II, Hermann, Paris, pp. 277–313.
Maistrov, L. E.: 1974, Probability Theory: A Historical Sketch, New York, Academic Press.
Menninger, K.: 1979, Zahlwort und Ziffer. Eine Kulturgeschichte der Zahl, (3. edition), Vandenhoek & Ruprecht, Göttingen.
Nöth, W.: 2000, Handbuch der Semiotik, Verlag J.B. Metzler, Stuttgart & Weimar.
Otte, M.: 1984, Was ist Mathematik?, Occasional Paper Nr. 43 des IDM Bielefeld, Universität Bielefeld, Bielefeld.
Otte, M.: 2001, ‘Mathematical epistemology from a semiotic point of view’, Paper presented to the Discussion Group on Semiotics in Mathematics Education at the 25th PME International Conference, July 12–17 2001, University of Utrecht, Utrecht, The Netherlands.
Peirce, C. S.: 1991, Schriften zum Pragmatismus und Pragmatizismus, Suhrkamp, Frankfurt am Main.
Pimm, D.: 1992, ‘Metaphor and metonymy in the mathematics classroom’, Paper presented to the WG7 Language and Communication in the Classroom ICME-7, Québec, Univerity of Quebec, Quebec.
Radford, L.: 1998, ‘On signs and representation’, Scientia Paedagogica Experimentalis XXXV(1), 277–302.
Radford, L.: 2000, ‘Signs and meanings in the students' emergent algebraic thinking: A semiotic analysis',educational Studies in Mathematics 42(3), 237–268.
Radford, L.: 2001, ‘On the relevance of semiotics in mathematics education’, Paper Presented to the Discussion Group on Semiotics in Mathematics Education at the 25th PME International Conference, July 12–17 2001, University of Utrecht, Utrecht, The Netherlands.
Radford, L.: 2003a, ‘On culture and mind' A post-Vygotskian semiotic perspective, with an example from greek mathematical thought’, in M. Anderson, A. Sáenz–Ludlow, S. Zellweger and V. Cifarelli (eds.), Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing, Legas Publishing, Ottawa, pp. 49–79.
Radford, L.: 2003b, ‘Gestures, speech and the sprouting of signs: A semiotic-cultural approach to students' types of generalization’, Mathematical Thinking and Learning 5(1), 37–70.
Resnik, M. D.: 2000, ‘Some remarks on mathematical progress from a structural perspective’, in E. Grossholz and H. Berger (eds.), The Growth of Mathematical Knowledge, Kluwer Academic Publishers, Dordrecht, pp. 353–362.
Rotman, B.: 1987, Signifying Nothing-The Semiotics of Zero, Stanford University Press, Stanford, California.
Sáenz–Ludlow, A.: 2001, ‘Classroom mathematics discourse as an interpreting game’, Paper Presented to the Discussion Group on Semiotics in Mathematics Education at the 25th PME International Conference, July 12–17 2001, University of Utrecht, Utrecht, The Netherlands.
Steinbring, H.: 1980, Zur Entwicklung des Wahrscheinlichkeitsbegriffs-Das Anwendungsproblem der Wahrscheinlichkeitstheorie aus didaktischer Sicht, Materialien und Studien Bd. 18 des IDM Bielefeld, Universität Bielefeld, Bielefeld.
Steinbring, H.: 1988, The Theoretical Nature of Probability and How to Cope with it in the Classroom, Occasional Paper Nr. 99 des IDM Bielefeld, Universität Bielefeld, Bielefeld.
Steinbring, H.: 1989, ‘Routine and meaning in the mathematics classroom’, For the Learning of Mathematics 9(1), 24–33.
Steinbring, H.: 1991, ‘The concept of chance in everyday teaching: Aspects of a social epistemology of mathematical knowledge’, Educational Studies in Mathematics 22, 503–522.
Steinbring, H.: 1997, ‘Epistemological investigation of classroom interaction in elementary mathematics teaching’, Educational Studies in Mathematics 32(1), 49–92.
Steinbring, H.: 1998, ‘Elements of epistemological knowledge for mathematics teachers’, Journal of Mathematics Teacher Education 1(2), 157–189.
Vygotsky, L. S.: 1987, ‘Thinking and speech’, in R. W. Riebe and A. S. Carton (eds.), The Collected Works of L.S. Vygotsky. vol. 1. Problems of General Psychology, Plenum Press, New York, pp. 37–285.
Wagner, R.: 1981, The Invention of Culture, University of Chicago Press, Chicago.
Wagner, R.: 1986, Symbols that Stand for Themselves, University of Chicago Press, Chicago.
Winter, H.: 1982, ‘Das Gleichheitszeichen im Mathematikunterricht der Primarstufe’, Mathematica Didactica 5, 185–211.
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Steinbring, H. What Makes a Sign a Mathematical Sign? – An Epistemological Perspective on Mathematical Interaction. Educ Stud Math 61, 133–162 (2006). https://doi.org/10.1007/s10649-006-5892-z
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DOI: https://doi.org/10.1007/s10649-006-5892-z