Volume 2 | Issue 3 | Year 2011 | Article Id. IJMTT-V2I3P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V2I3P503

The survey of the literature shows that conceptions of mathematics fall along an externally-internally developed continuum, [4] comments, along with others [13], indicate that mathematicians behave like construction lists until challenged. Similar findings may hold for mathematics teachers. The retreat to the external model to discuss their conceptions shows a strong predilection for Platonic views of mathematics. Such conceptions are strongly flavored by dualistic or multiplistic beliefs about mathematics, allowing few teachers to reject an authoritarian teaching style. Even so, the leaders and professional organizations in mathematics education are promoting a conception of mathematics that reflects a decidedly relativistic view of mathematics [14]. Steps to address the gaps between the philosophical bases for current mathematics instruction are important ones that must be addressed in the development and study of mathematics education at all levels.

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[2] Fisher, c., & Berliner, D. (Eds.). (1985). Perspectives on instructional time. New York: Longman.

[3] Davis, 1', & Hersh, R. (1980). The mathematical experience. Boston:Birkhauser.

[4] Davis, 1', & Hersh, R. (1986). Descartes' dream: The world according to mathematics. San Diego: Harcourt Brace Jovanovich.

[5] Courant, R., & Robbins, H. (1941). What is mathematics? New York: Oxford University Press.

[7] Aristotle. (1952). Metaphysics. In R. M. Hutchins (Ed.), Great books of the western world: Vol. 8. Aristotle 1 (pp. 495-626). Chicago: Encyclopaedia Britannica, Ine

[8] Boyer, C. (1968). A history of mathematics. New York: Wiley

[9] Korner, S. (1960). The philosophy of mathematics: An introduction. New York: Harper & Row

[10] Hersh, R. (1986). Some proposals for reviving the philos'ophy of mathematics. In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 9-28). Boston: Birkhauser.

[11] Sowder,]. (Ed.). (1989). Setting a research agenda. Reston, VA:National Council of Teachers of Mathematics.

[12] Shavelson, R., Webb, N., Stasz, c., & McArthur, D. (1988). Teaching mathematical problem solving: Insights from teachers and tutors. In R. Charles & E. Silver (Eds.),The teaching and assessing ofmathematical problem solving (pp. 203-231). Reston, VA:National Council of Teachers of Mathematics.

[13] Tymoczko, T. (1986). New directions in the philosophy of mathematics. Boston: Birkhauser.

[14] Ernest, P. (1989). Philosophy, mathematics and education. International journal of Mathematics Education in Science and Technology, 20, 555-559.

[15] Baroody, A. J. & Coslick, R.T. (1998). Fostering Children’s Mathematical Power: An Investigative Approach to K-8 Mathematics Instruction. Lawrence Erlbaum Associates: Mahwah, NJ.

[16] Hardy, G. (1940). A mathematicians apology. Cambridge, England: Cambridge University Press.

[17] Hilton, P (1984). Current trends in mathematics and future trends in
mathematics education. For the Learning of Mathematics, 4, 2-8.

[18] Saaty, T., & Weyl, F. (1969). The spirit and the uses of the
mathematical sciences. New York: McGraw-Hill.

[19] Steen, L. (1978). Mathematics today: 7Welve informal essays. New
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[20] Stewart, 1. (1987). The problems of mathematics. New York: Oxford
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[21] Benacerraf, P.,& Putnam, H. (1964). Philosophy of mathematics.
Englewood Cliffs, NJ: Prentice Hall.

Mukesh Kumar, "Conceptions Of Mathematics To
Mathematics Education Research," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 2, no. 3, pp. 7-10, 2011. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V2I3P503