Philosophies and Pedagogies of Mathematics

Abstract

The paper discusses major philosophical stances on the nature of mathematics as held by foundationalists and quasi-empiricalism supporters. It is argued that the contrasting philosophical views between the two groups parallels in many respects the pedagogical debate between behaviourism and socioconstructivism. It is also argued that behaviourism has been influenced by foundationalist conceptions of mathematics while socio-constructivism has been influenced by quasi-empirical philosophies.

Keywords

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Matematik Pedagojisi ve Felsefesi

Öz

Bu makale mutlakçılık ve yarı-deneyselcilik taraftarlarının sahip olduğu, matematiğin doğasıyla ilgili felsefi yaklaşımları tartışmaktadır. Bu iki felsefi görüşüyle ​​zıtlıkların olduğu yönden davranışçılık ve sosyal- pedagojik tartışmalara paralel olmuştur. Ayrıca, davranışcılığın mutlakçı matematik düşünceinden ve sosyal-hazırlıkmacılığın yarı-deneyselci felsefyalı etki etkilenen düşünülmektedir.

Anahtar Kelimeler

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Kaynakça

1. Ascher, M. (1991). Ethnomathematics: a multicultural view of mathematical idea. California: Brooks/Cole Publishing Company.
2. Australian Education Council (1991). A national statement on mathematics for Australian schools. Melbourne: Curriculum Corporation.
3. Baldor, J.A. (1984). Geometria Plana y del Espacio. Madrid: Codice.
4. Biggs, J., & Moore, P. (1993). The process of learning. Sydney: Prentice Hall.
5. Board of Studies NSW. (1996). Stage 5 support document for Advanced, Intermediate and Standard Courses. Sydney: BOS.
6. Candy, P. C. (1991). Understanding the individual nature of learning. In Self-direction for lifelong learning: A comprehensive guide to theory and practice. (pp. 249-278). San Francisco: Jossey-Bass.
7. Cockcroft, W.H. (Chair) (1982). Mathematics Counts. HMSO: London.
8. Elliot, S.N., Kratochwill, J., & Travers, J.F. (1996). Educational psychology: Effective teaching, effective learning. Dubuque: Brown and Benchmark Publishers.

9. Goodman, N.D. (1986). Mathematics as an objective science. In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 79-94). Boston: Birkhauser.
10. Grabiner, J.V. (1986). Is mathematical truth time-dependent? In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 201-214). Boston: Birkhauser.
11. Hersh, R. (1979). Some proposals for reviving the philosophy of mathematics. Advances in Mathematics, 31, 31-50.
12. Jackson, P.W. (1986). The practice of teaching. New York: Teachers College Press.
13. Krathwohl, D.L., Bloom, B.S., & Masia, B.B. (1964). Taxonomy of educational objectives: Handbook II. Affective domain. New York: Longman.
14. Lakatos, I. (1976). Proofs and refutations: The logic of mathematics discovery. London: Cambridge University Press.
15. Lakatos, I. (1986). A Renaissance of Empiricism in the recent philosophy of mathematics? In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 29-49). Boston: Birkhauser.
16. Laurenson, D.J. (1995). Mathematics and the drift towards constructivism: Are teacher beliefs and teaching practice following the beat of the same drummer?. NCSSSMST Journal, 1(2), 3-7.
17. Leder, G.C. (1994). Research in mathematics education – constraints on construction? In G. Bell (Ed.), Challenges in mathematics education: Constraints on construction. Proceedings of the 17th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 31-48). Lismore: MERGA.
18. Lerman, S. (1983). Problem-solving or knowledge-centred; the influence of philosophy of mathematics teaching. International Journal of Mathematics Education for Science and Technology, 14(1), 59-66.
19. Marland, P.W. (1994). Teaching: Implicit theories. In T. Husen, & T.N. Postlewaite (Editors-in-chief), The international encyclopaedia of education (pp. 6178-6183). New York: Pergamon.
20. McGinnis, J.R., Shama, G., McDuffie, A., Huntley, M.A., King, K., & Watanabe, T. (1996). Researching the preparation of specialized mathematics and science upper elementary/middle-level teachers: The 2nd year report. Proceedings of the Annual Conference of the National Science Teachers Association, St. Louis, Missouri. (ERIC document ED 395 792.)
21. McLeod, D.B. (1992). Research on affect in mathematics education: a reconceptualization. In D. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-596). New York: Macmillan.
22. Moreira, C., & Noss, R. (1995). Understanding teachers’ attitudes to change in a Logomathematics environment. Educational Studies in Mathematics, 28(2), 155-176.
23. Mura, R. (1995). Images of mathematics held by university teachers of mathematics education. Educational Studies in Mathematics, 28(4), 385-399.
24. Murphy, E. (1997). Characteristics of constructivist learning and teaching. Universite Laval, Quebec. Available: http://www.stemnet.nf.ca/~elmurphy/emurphy/cle3.html.
25. National Council of Teachers of Mathematics (1989). Curriculum and evaluation Standards for school mathematics. Reston: NCTM.
26. National Council of Teachers of Mathematics (1991). Professional standards for the teaching of mathematics. Reston: NCTM.
27. National Council of Teachers of Mathematics (1995). Assessment standards for school mathematics. Reston: NCTM.
28. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: NCTM.
29. Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19(4), 317-328.
30. Nisbert, S., & Warren, E. (2000). Primary school teachers’ beliefs relating to mathematics teaching and assessing mathematics and factors that influence these beliefs. Mathematics Education Research Journal, 13(2), 34-47.
31. O’Laughlin, M., & Campbell, M.B. (1988). Teacher preparation, teacher empowerment, and reflective enquiry: A critical perspective. Teacher Education Quarterly, 15(4), 25-53.
32. Phillip, D.C. (1995). The good, the bad, and the ugly. The many faces of constructivism. Educational Researcher, 24(7), 512.
33. Perry, B., Howard, P., & Tracey, D. (1999). Head mathematics teachers’ beliefs about the learning and teaching of Mathematics. Mathematics Education Research. Journal, 11, 39-57.
34. Polya, G. (1986). Induction and analogy in mathematics. In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 99-102). Boston: Birkhauser.
35. Putnam, H. (1986). What is mathematical truth? In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 49-66). Boston: Birkhauser.
36. Raymond, A.M. (1997). Inconsistency between a teacher’s beliefs and practice. Journal for Research in Mathematics Education, 28(5), 550-576.
37. Robitaille, D., & Dirks, M. (1982). Models for the mathematics curriculum. For the Learning of Mathematics, 2(3), 3-21.
38. Rogerson, A. (1989). The human and social context for problem solving, modelling and applications. In W. Blum, M. Niss & I. Huntley (Eds.), Modelling, applications and applied problem solving: Teaching mathematics in a real context (pp. 4955). England: Ellis Horwood.
39. Rogerson, A. (1994). Symbols as cultural communication – A historical and didactical perspective. Paper presented at the 46th International Meeting of the CIEAEM, Toulouse, France.
40. Schmidt, W.H., & Kennedy, M.M. (1990). Teachers’ and teacher candidates’ beliefs about subject matter and about teaching responsibilities. (ERIC document ED 320 902.)
41. Shavelson, R.J., & Stern, P. (1981). Research on teachers’ pedagogical thoughts, judgements, decisions, and behavior. Review of Education Research, 51(4), 455-498.
42. Sosniak, L.A., & Ethington, C.A., & Varelas, M. (1991). Teaching mathematics without a coherent point of view: Findings from the IEA Second International Mathematics Study. Journal of Curriculum Studies, 23, 119-131.
43. Southwell, B. (1999). The lowdown on the philosophy of mathematics education. Reflections, 24(1), 44-47.
44. Taylor, T. (1990). Mathematical attitude development from a Vygotskian perspective. Mathematical Education Research Journal, (4)3, 8-23.
45. Thom, R. (1986). “Modern” mathematics: An educational and philosophic error? In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 67-78). Boston: Birkhauser.
46. Wilder, R. (1986). The cultural basis of mathematics. In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 185-200). Boston: Birkhauser.
47. Wood, T., Cobb, P., & Yackel, E. (1991). Change in teaching mathematics. American Educational Research Journal, 28(3), 587-616.