Abstract
Although Imre Lakatos described the work published in his book Proofs and Refutations as a study of mathematical methodology, work which has been responded to and criticized by philosophers and historians of mathematics more on its own terms, a significant body of writing in the 30 years since its appearance has used it as a pertinent cognate text appropriable for school mathematics education. In this paper, we contrast the responses these two fields have generated, with an emphasis on that of mathematics education. Doing so offers a potentially salutary case study of how challenging and fraught it can be at times to undertake work at the nexus of history and philosophy on the one hand, while at the same time seeking to explore its possible relevance and significance for education. As our title suggests, we are concerned about the proliferating Lakatos personas that seem to exist, including a growing range of self-styled reform or progressive educational practices which get attributed to him.
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References
Agassi J. (1980) On mathematics education: The Lakatosian revolution. For the Learning of Mathematics 1(1): 27–31
Brodie K. (2000) Teacher intervention in small-group work. For the Learning of Mathematics 20(1): 9–16
Brown S. et al (1996) Towards humanistic mathematics education. In: Bishop A. (eds) International handbook of mathematics education.. Kluwer Academic Publishers, Dordrecht, NL, pp 1289–1311
Corfield D. (2002) Argumentation and the mathematical process. In: Kampis G., Kvasz L., Stöltzner M. (eds) Appraising Lakatos: Mathematics, methodology and the man.. Kluwer Academic Publishers, Dordrecht, NL, pp 115–138
Corfield D. (2003) Towards a philosophy of real mathematics. Cambridge University Press, New York, NY
Ernest P. (1991) The philosophy of mathematics education. Falmer Press, Bristol, PA
Hacking, I. (2000). Mitteleuropa am Aldwych. London Review of Books, 22(2), 28-29. (A review of Motterlini, 1999.)
Hanna G., Jahnke N. (1996) Proof and proving. In: Bishop A. et al (eds) International handbook of mathematics education. Kluwer Academic Publishers, Dordrecht, NL, pp 877–908
Herbst P., Chazan D. (2003) Exploring the practical rationality of mathematics teaching through conversations about videotaped episodes: The case of engaging students in proving. For the Learning of Mathematics 23(1): 2–14
Lakatos I. (1976) Proofs and refutations: The logic of mathematical discovery. Cambridge University Press, Cambridge, UK
Lampert M. (1990) When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal 27(1): 29–63
Motterlini, M. (eds) (1999) For and against method. University of Chicago Press, Chicago, IL
Nunokawa K. (1996) Applying Lakatos’ theory to the theory of mathematical problem solving. Educational Studies in Mathematics 31(3): 269–293
Phillips A. (1993) On kissing, tickling and being bored. Harvard University Press, Cambridge, MA
Reichel H.-C. (2002) Lakatos and aspects of mathematics education. In: Kampis G., Kvasz L., Stöltzner M. (eds) Appraising Lakatos: Mathematics, methodology and the man. Kluwer Academic Publishers, Dordrecht, NL, pp 255–260
Sierpinska A., Lerman S. (1996) Epistemologies of mathematics and of mathematics education. In: Bishop A. et al (eds) International handbook of mathematics education. Kluwer Academic Publishers, Dordrecht, NL, pp 827–876
Sriraman B. (2006) An ode to Imre Lakatos: Quasi-thought experiments to bridge the ideal and actual mathematics classroom. Interchange 37(1-2): 151–178
Webber S. (1991) Return to Freud: Jacques Lacan’s dislocation of psycholanalysis. Cambridge University Press, Cambridge, UK
Yackel, E. & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, W. Martin & D. Schifter (Eds), A research companion to principles and standards for school mathematics (pp. 227-236). Reston, VA: The National Council of Teachers of Mathematics.
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Pimm, D., Beisiegel, M. & Meglis, I. Would the Real Lakatos Please Stand Up. Interchange 39, 469–481 (2008). https://doi.org/10.1007/s10780-008-9076-x
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DOI: https://doi.org/10.1007/s10780-008-9076-x