Abstract
Much reference has been made to Paul Ernest’s ‘philosophy of mathematics education’ to legitimise a strong fallibilist trend in mathematics education. This article presents the argument that: (1) This philosophy makes unwarranted assumptions that have been taken as ‘given’. For example, that ‘absolutist’ or ‘Platonist’ views of mathematics necessarily imply the transmission model of teaching mathematics. (2) The very basis of this philosophy contains a contradiction: that mathematics cannot be separated from its social origins, yet mathematics has a logical necessity that is independent of its origin. (3) This philosophy downplays mathematics as a formal, academic system of knowledge in the attempt to promote a child-centred pedagogy or the mathematics of social practices. (4) Ernest’s attempt to semiotically reduce proof to calculation is flawed. This article explores what is meant by fallibilism in relation to the views of many educationalists who appear not to like mathematics as a formal, academic body of knowledge and draws out the educational implications of these views.
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References
Anderson, S. E. (1997). Worldmath curriculum: Fighting Eurocentrism in mathematics. In A. B. Powell & M. Frankenstein (Eds.), Ethnomathematics: Challenging Eurocentrism in mathematics education. Albany: SUNY.
Barton, B. (1999). Ethnomathematics and philosophy. Zentralblatt für Didaktic der Mathematik, 31(2), 54–58.
Bloor, A. (2003). A multidisciplinary study of fiction writing. New York: Edwin Mellin Press.
Borba, M. C., & Skovsmose, O. (1997). The ideology of certainty in mathematics education. For the Learning of Mathematics, 17(3), 17–23.
Burton, L. (1995). Moving towards a feminist epistemology of mathematics. In P. Rogers & G. Kaiser (Ed.), Equity in mathematics education. London: Falmer. Also reproduced in Educational Studies in Mathematics 28, 275–291.
Carson, R., & Rowlands, S. (2001). A critical assessment of Dewey’s attack on dualism. The Journal of Educational Thought, 35(1), 27–60.
Carson, R., & Rowlands, S. (2007). Teaching the conceptual revolutions in geometry. Science & Education, 16, 921–954.
Chalmers, A. (1982). What is this thing called science? (2nd ed.). Milton Keynes: Open University Press.
Corry, L. (1989). Linearity and reflexivity in the growth of mathematical knowledge. Science in Context, 3(2), 409–440.
Crawford, K. (1996). Vygotskian approaches in human development in the information era. Educational Studies in Mathematics, 32, 43–62.
D’Ambrosio, U. (1997). Ethnomathematics and its place in the history and pedagogy of mathematics. In A. B. Powell & M. Frankenstein (Eds.), Ethnomathematics: Challenging Eurocentrism in mathematics education. Albany: SUNY.
Davis, P. J., & Hersh, R. (1981). The mathematical experience. Boston: Houghton Mifflin.
Descartes, R. (1968). Discourse on method and the meditations. Harmondsworth: Penguin.
Ernest, P. (1991). The philosophy of mathematics education. London: Falmer.
Ernest, P. (1998). Social constructivism as a philosophy of mathematics. New York: SUNY.
Ernest, P. (2007). The philosophy of mathematics, values, and keralese mathematics. Available online at: http://www.people.ex.ac.uk/PErnest/pome20/index.htm. Accessed Nov 2007.
Frege, G. (1977). On sense and reference. In P. Geach & M. Black (Eds.), Translations from the philosophical writings of Gottlob Frege. Oxford: Blackwell.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel.
Guardian. (2007). Who needs maths? Available online at: http://education.guardian.co.uk/schools/story/0,,2209769,00.html. Accessed Nov 2007.
Hanna, G. (1996). The ongoing value of proof. Proceedings of the international group for the psychology of mathematics education, Valencia, Spain, Vol I. Available online at: http://fcis.oise.utoronto.ca/~ghanna/pme96prf.html. Accessed June 2008.
Hersh, R. (1998). What is mathematics really. London: Vintage.
Inset Maths. (1990). Inset maths—secondary. Devon Educational Television and Resources Centre.
Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. London: Falmer.
Katz, V. (1993). A History of mathematics. New York: Harper Collins.
Kitcher, P. (1984). The nature of mathematical knowledge. New York: Oxford University Press.
Kline, M. (1982). Mathematics: The loss of certainty. New York: Oxford University Press.
Koetsier, T. (1991). Lakatos’s philosophy of mathematics: A historical approach. Amsterdam: North-Holland.
Lakatos, I. (1976). Proofs and refutations. Cambridge: Cambridge University Press.
Matthews, M. R. (1998). Introductory comments on philosophy and constructivism in science education. Science & Education, 6(1–2), 329–342.
Matthews, M. R. (date unknown). Constructivism in science and mathematics education. Available online at: http://wwwcsi.unian.it/educa/inglese/matthews.html. Accessed Nov 2007.
Oliveras, M. L. (1999). Ethnomathematics and mathematics education. Zentralblatt für Didaktic der Mathematik, 31(3), 85–91.
Phillips, D. C. (1997). Coming to grips with radical social constructivisms. Science & Education, 6, 85–103.
Piaget, J. (1977/1972). Comments on mathematics education. In H. E. Gruber & J. J. Vonèche (Eds.), The essential Piaget. New York: Basic Books.
Radford, L. (1997). On psychology, historical epistemology, and the teaching of mathematics: Towards a socio-cultural history of mathematics. For the Learning of Mathematics, 17(1), 26–33.
Rowlands, S. (2008). The crisis in science education and the need to enculturate all learners in science. In C. L. Petroselli (Ed.), Science education issues and developments. New York: Nova Science Publishers.
Rowlands, S., & Carson, R. (2004). Our response to Adam, Alangui and Barton’s “a comment on Rowlands & Carson ‘Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics? A critical review’”. Educational Studies in Mathematics, 56(2–3), 329–342.
Rowlands, S., Graham, E., & Berry, J. (2001). An objectivist critique of relativism in mathematics education. Science & Education, 10, 215–241.
Russell, B. (1972). Russell’s logical atomism. In D. F. Pears (Ed.) London: Fontana.
Shultz, R. (2009). Reforming science education: Part I. The search for a philosophy of science education. Science & Education, 18(3/4), 225–250.
Siegal, M., & Borasi, R. (1994). Demystifying mathematics education through inquiry. In P. Ernest (Ed.), Constructing mathematical knowledge. London: The Falmer Press.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Taylor, P. C. (1996). Mythmaking and mythbreaking in the mathematics classroom. Educational Studies in Mathematics, 31, 151–173.
Tzanakis, C., & Arcavi, A. (2000). Integrating history of mathematics in the classroom: An analytic survey. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI study. Dordrecht: Kluwer.
Walkerdine, V. (1994). Reasoning in a post-modern age. In P. Ernest (Ed.), Mathematics, education and philosophy: An international philosophy. London: Falmer.
Wertsch, J. (1996). The role of abstract rationality in Vygotsky’s image of mind. In A. Tryphon & J. Vonèche (Eds.), Piaget—Vygotsky, the social genesis of thought. East Sussex: Psychology Press.
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Rowlands, S., Graham, T. & Berry, J. Problems with Fallibilism as a Philosophy of Mathematics Education. Sci & Educ 20, 625–654 (2011). https://doi.org/10.1007/s11191-010-9234-2
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DOI: https://doi.org/10.1007/s11191-010-9234-2