Abstract
Evidence from two research projects, one with high school students and the other with graduate students in an Ethnomathematics course, is presented to suggest that the beliefs students hold about the nature of mathematics both enables and constrains their ability to construct conceptual bridges between familiar everyday practices and mathematical concepts taught in school or university. Using a semiotic theoretical framework, graduate students learned to construct chains of signifiers linking a cultural practice that was personally meaningful to them, with abstract and general mathematical ideas. In the process, a majority of students broadened their conceptions, both of the nature of mathematics and of its relationship with cultural practices.
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References
Civil, M. (1998, April). Bridging in-school mathematics and out-of-school mathematics. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, California.
Cooney, T. J. (1985). A beginning teacher’s view of problem solving. Journal for Research in Mathematics Education, 16, 324–336.
Cooney, T. J. (1999, November). Examining what we believe about beliefs. In E. Pehkonen & G. Törner (Eds.), Mathematical beliefs and their impact on teaching and learning of mathematics (pp. 18–23). Proceedings of the Workshop in Oberwolfach.
de Lange, J. (1993). Between end and beginning. Educational Studies in Mathematics, 25, 137–160.
Gerdes, P. (1998). On culture and mathematics teacher education. Journal of Mathematics Teacher Education, 1(1), 33–53.
Goldin, G. A. (1999, November). Affect, meta-affect, and mathematical belief structures. In E. Pehkonen & G. Törner (Eds.), Mathematical beliefs and their impact on teaching and learning of mathematics pp. 37–42. Proceedings of the Workshop in Oberwolfach.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
Peirce, C. S. (1998). The essential Peirce: Selected philosophical writing Vol. 2 (pp. 1893–1912). Bloomington, Indiana: Indiana University Press.
Pimm, D. (1995). Symbols and meanings in school mathematics. New York: Routledge.
Presmeg, N. C. (1980). Albert Einstein’s thought, creativity, and mathematics education. Unpublished M.Ed. dissertation, University of Natal, South Africa.
Presmeg, N. C. (1985). Visually mediated processes in high school mathematics: A classroom investigation. Unpublished Ph.D. dissertation, University of Cambridge, England.
Presmeg, N. C. (1986). Visualisation in high school mathematics. For the Learning of Mathematics, 6(3), 42–46.
Presmeg, N. C. (1988). School mathematics in culture-conflict situations. Educational Studies in Mathematics, 19(2), 163–177.
Presmeg, N. C. (1993, October). Changing visions in mathematics pre-service teacher education. In J. R. Becker & B. J. Pence (Eds.), Proceedings of the Fifteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Vol. 2 (pp. 210–216). Asilomar, California.
Presmeg, N. C. (1997). Generalization using imagery in mathematics. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors and images (pp. 299–312). Hillsdale, New Jersey: Lawrence Erlbaum Associates.
Presmeg, N. C. (1997). A semiotic framework for linking cultural practice and classroom mathematics. In J. A. Dossey, J. O. Swafford, M. Parmantie, & A. E. Dossey (Eds.), Proceedings of the Nineteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Vol. 1 (pp. 151–156). Columbus, Ohio: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
Presmeg, N. C. (1998a). Ethnomathematics in teacher education. Journal of Mathematics Teacher Education, 1(3), 317–339.
Presmeg, N. C. (1998b). A semiotic analysis of students’ own cultural mathematics. Research Forum Report, in A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education Vol. 1 (pp. 136–151).
Rokeach, M. (1960). The open and closed mind. New York: Basic Books.
Shaw, K. L., & Jakubowski, E. H. (1991). Teachers changing for changing times. Focus on Learning Problems in Mathematics, 13(4), 13–20.
Streefland, L. (1988). Reconstructive learning. In A. Borbás (Ed.), Proceedings of the 12th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 75–89).
Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 125–127.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
Treffers, A. (1993). Wiskobas and Freudenthal: Realistic mathematics education. Educational Studies in Mathematics, 25, 89–108.
Walkerdine, V. (1988). The mastery of reason: Cognitive development and the production of rationality. New York: Routledge.
Whitson, J. A. (1997). Cognition as a semiosic process: From situated mediation to critical reflective transcendence. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition: Social, semiotic, and psychological perspectives (pp. 97–149). Mahwah, New Jersey: Lawrence Erlbaum Associates.
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Presmeg, N. (2002). Beliefs About the Nature of Mathematics in the Bridging of Everyday and School Mathematical Practices. In: Leder, G.C., Pehkonen, E., Törner, G. (eds) Beliefs: A Hidden Variable in Mathematics Education?. Mathematics Education Library, vol 31. Springer, Dordrecht. https://doi.org/10.1007/0-306-47958-3_17
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DOI: https://doi.org/10.1007/0-306-47958-3_17
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