Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

PROBABILITY EDUCATION FOR PREPARATION OF MATHEMATICS TEACHERS USING PARADOXES

  • Lee, Sang-Gone (Department of Mathematics Education, Chonbuk National University)
  • Received : 2008.03.03
  • Accepted : 2008.05.14
  • Published : 2008.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

Mathematical paradoxes may arise when computations give unexpected results. We use three paradoxes to illustrate how they work in the basic probability theory. In the process of resolving the paradoxes, we expect that student-teachers can pedagogically gain valuable experience in regards to sharpening their mathematical knowledge and critical reasoning.

Keywords

References

  1. P. J. Bickel, E. A. Hammel, J. W. O'Connell, Sex Bias in Graduate Admissions: Data from Berkeley, Science, 187 (1975), pp. 398-404. https://doi.org/10.1126/science.187.4175.398
  2. G. L. Brager, Reader Reflections: Higher or Lower Average?, Mathematics Teacher, 77 (1984), pp. 254.
  3. R. B. Bronson, Linear Algebra: An Introduction, Academic Press, (1995).
  4. D. Moore and G. McCabe, Introduction to the Practice of Statistics, W.H. Freeman and Co, (1999).
  5. G. N. Cantor, Conflict, Learning and Piaget: Comments on Zimmerman and Blom's Toward an Empirical Test of the Role of Cognitive Conflict in Learning, Developmental Review, 3 (1983), pp. 39-53. https://doi.org/10.1016/0273-2297(83)90006-0
  6. G. P. Harmer and D. Abbott and P. G. Taylor and J. M. R. Parrondo, Parrondo's Paradoxical Games and the Discrete Brownian Ratchet, Proc. 2nd Int. Conf. Unsolved Problems of Noise and Fluctuations, 11-15 (2000), pp. 189-200.
  7. G. P. Harmer and D. Abbott, Parrondo's Paradox, Statistical Science, 14 (1999), pp. 206-213. https://doi.org/10.1214/ss/1009212247
  8. M. R. Cohen and E. Nagel, An Introduction to Logic and Scientic Method, Harcourt Brace Co, (1934).
  9. H. Eves, Great Moments in Mathematics, Dolciani Mathematical Expositions(Vol.5-before 1650, Vol.7-after 1650), Mathematical Association of America, (1983).
  10. S. H. Friedberg and A. J. Insel and L. E. Spence, Linear Algebra, Prince Hall, (1979).
  11. J. Mitchem, Paradoxes in Averages, Mathematics Teacher, 82 (1989), pp. 250-253.
  12. K. Middleton, The Role of Russell's Paradox in the Development of Twentieth Century Mathematics, Pi Mu Epsilon, 8 No. 4 (1986), pp. 234-241.
  13. R. S. Nickerson and D. N. Perkins and E. E. Smith, The Teaching of Thinking, Lawrence Erlbaum, (1985).
  14. O. Ore, Pascal and the Invention of Probability Theory, The American Math. Monthly, 67 (1960), pp. 409-419. https://doi.org/10.2307/2309286
  15. G. Polya, How to solve it, Princeton University Press, (1945).
  16. Z. Usiskin, Reade Reflections:Simpson's Paradox, Mathematics Teacher, 78 (1985), pp. 240.