The Mathematical Event: Mapping the Axiomatic and the Problematic in School Mathematics

Studies in Philosophy and Education

Volumn 32, Issue 6, 2013, Pages 581-599

  de Freitas, Elizabeth ^a  

^a ADELPHI UNIVERSITY   (United States)

Author keywords

Concept; Deleuze; Event; Indeterminacy; Mathematics; Multiplicity; Undecidability

Indexed keywords

EID: 84886085840     PISSN: 00393746     EISSN: 1573191X     Source Type: Journal    
DOI: 10.1007/s11217-012-9340-5     Document Type: Article

References (38)

1. Alunni, C. (2006). Continental genealogies: Mathematical confrontations in Albert Lautman and Gaston Bachelard. In S. Duffy (Ed.), Virtual mathematics: The logic of difference (pp. 65-99). Machester, UK: Clinamen Press.
2. Badiou, A. (2006). Mathematics and philosophy. In S. Duffy (Ed.), Virtual mathematics: The logic of difference (pp. 12-30). Machester, UK: Clinamen Press.
3. Badiou, A. (2009). Logics of worlds. (Trans. Alberto Toscano). New York: Continuum.
4. Badiou, A. (2011). Second manifesto for philosophy. (Trans. Louise Burchill). Malden, MA: Polity Press.
5. Baker, A. (2009). Mathematical accidents and the end of explanation. In O. Bueno & O. Linnebo (Eds.), New waves in philosophy of mathematics. New York: Palgrave Macmillan.
6. Bowden, S. (2011). The priority of events: Deleuze's logic of sense. Edinburgh: Edinburgh University Press.
7. Brown, S. I. (1994). The problem of the problem and curriculum fallacies. In P. Ernest (Ed.), Constructing mathematical knowledge: Epistemology and mathematics education (pp. 175-189). New York: Routledgefalmer.
8. Brown, S. I., & Walter, M. I. (2005). The art of problem posing. New York: Lawrence Erlbaum.
9. Casati, R., & Varzi, A. (2010). Events. In Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Spring 2010 Edition). URL .
10. Châtelet, G. (2000). Figuring space: Philosophy, mathematics and physics. Shore, R. & Zagha, M. (Trans.). London, UK: Kluwer Academic Publishers.
11. Corfield, D. (2005). Mathematical kinds, or being kind to mathematics. Philosophica, 74, 30-54.
12. Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers practices. Educational Studies in Mathematics, 52, 243-270.
13. Cutler, A., & MacKenzie, I. (2011). Bodies of learning. In L. Guillaume & J. Hughes (Eds.), Deleuze and the body. Edinburgh: Edinburgh University Press.
14. de Freitas, E. (2012a). The diagram as story: Unfolding the event-structure of the mathematical diagram. For the Learning of Mathematics, 32(2), 27-33.
15. de Freitas, E. (2012b). What were you thinking? A Deleuzian/Guattarian analysis of communication in the mathematics classroom. Educational Philosophy and Theory. Available for early view: doi: 10. 1111/j. 1469-5812. 2012. 00860. x.
16. de Freitas, E., & Sinclair, N. (2012). Diagram, gesture, agency: Theorizing embodiment in the mathematics classroom. Educational Studies in Mathematics, 80(1-2), 133-152.
17. Deleuze, G. (1990). Logic of sense. Lester, M. (Trans.). New York: Columbia University Press.
18. Deleuze, G. (1993). The fold: Leibniz and the baroque. Conley, T. (Trans.). Minneapolis, MN: Regents of University of Minnesota Press.
19. Deleuze, G. (1994). Difference and repetition. Patton, P. (Trans.). New York: Columbia University Press.
20. Deleuze, G., & Guattari, F. (1987). A thousand plateaus: Capitalism and schizophrenia. Massumi, B. (Trans.). Minneapolis, MN: University of Minnesota Press.
21. Durie, R. (2006). Problems in the relation between maths and philosophy. In S. Duffy (Ed.), Virtual mathematics: The logic of difference (pp. 169-186). Machester, UK: Clinamen Press.
22. Feltham, O. (2008). Alain Badiou: Live theory. New York: Continuum.
23. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12-18.
24. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., et al. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. Educational Researcher, 26(2), 24-26.
25. Lecoutre, B., & Fischbein, E. (1998). Evolution avec l'âge de 'misconceptions' dans les intuitions probabilistes en France et en Israël. Recherches en Didactique des Mathématiques, 18, 311-332.
26. Merleau-Ponty, M. (1968). The visible and the invisible. Evanston: Northwestern University Press.
27. Nancy, J.-L. (1997). The sense of the world. Librett, J. S. (Trans.). Minnesota: University of Minnesota Press.
28. New York State Common Core P-12 Learning standards for mathematics (pp. 1-83). Available at http://www. p12. nysed. gov/ciai/common_core_standards/. Accessed 2 Dec 2012.
29. Plotnitsky, A. (2012). Adventures of the diagonal: Non-Euclidean mathematics and narrative. In A. Doxiadis & B. Mazur (Eds.), Circles disturbed: The interplay of mathematics and narrative (pp. 407-446). Princeton, NJ: Princeton University Press.
30. Popkewitz, T. (2004). The alchemy of the mathematics curriculum: Inscriptions and the fabrication of the child. American Educational Research Journal, 41(1), 3-34.
31. Roth, W.-M. (2012). First-person methods: Toward an empirical phenomenology of experience. Boston: Sense Publishing.
32. Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American Educator, Summer, 4.
33. Smith, D. W. (2005). Deleuze on Leibniz: Difference, continuity, and the calculus. In S. H. Daniel (Ed.), Current continental theory and modern philosophy (pp. 127-147). Evanston, IL: Northwestern University Press.
34. Smith, D. W. (2006). Axiomatics and problematics as two modes of formalization: Deleuze's epistemology of mathematics. In S. Duffy (Ed.), Virtual mathematics: The logic of difference (pp. 145-168). Machester, UK: Clinamen Press.
35. Smith, D. W. (2007). The conditions of the new. Deleuze Studies, 1(1), 1-21.
36. Walkerdine, V. (1988). The mastery of reason: Cognitive development and the production of rationality. New York, NY: Routledge.
37. Whitehead, A. N. (1911). An introduction to mathematics. Classic reprint series. Cambridge University Press, Cambridge, MA.
38. Williams, J. (2009). If not here, then where? On the location and individuation of events in Badiou and Deleuze. Deleuze Studies, 3(1), 97-123.