Research in Mathematical Education (한국수학교육학회지시리즈D:수학교육연구)

Korean Society of Mathematical Education (한국수학교육학회)
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A Case Study on Students' Concept Images of the Uniform Convergence of Sequences of Continuous Functions

  • Jeong, Moonja (Department of Mathematics, The University of Suwon) ;
  • Kim, Seong-A (Department of Mathematics Education, Dongguk University)
  • Received : 2013.06.07
  • Accepted : 2013.06.29
  • Published : 2013.06.30
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Abstract

In this research, we investigated students' understanding of the definitions of sequence of continuous functions and its uniform convergence. We selected three female and three male students out of the senior class of a university and conducted questionnaire surveys 4 times. We examined students' concept images of sequence of continuous functions and its uniform convergence and also how they approach to the right concept definitions for those through several progressive questions. Furthermore, we presented some suggestions for effective teaching-learning for the sequences of continuous functions.

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References

  1. Brown, J. R. (1999). Philosophy of Mathematics-An Introduction to the World of Proofs and Pic-tures. London: Routledge. ME 2000d.02450
  2. Cho, C.-S. (2011). Exploring a teaching Method of Limits of Functions with Embodied Visualiza-tion of CAS Graphing Calculators. Communications of Mathematical Education 25(1), 63-78
  3. Dieudonne, J. (1969). Foundations of Modern Analysis. New York: Academic Press.
  4. Hwang, H. J.; Na, G. S.; Choi, S. H.; Park, K.; Yim, J. & Seo, D. Y. (2011). New Theory of Math-ematical Education. Seoul: Moonumsa.
  5. Hwang, S. & Shim, S. K. (2010). A Study on Students' Responses to Non-routine Problems Using Numerals or Figures (in Korean). J. Korea Soc. Math. Ed. Ser. A, Math. Educ. 49(1), 39-51. ME 2011b.00215
  6. Kim, E. H. (2011). Study on Point-wise and Uniform Convergence of Function Sequences and Se-ries. Dissertation of Master Degree. Kimhae: Inje University.
  7. Kim, E. T.; Park, H. S. & Woo, J. H. (2007). An Introduction to Mathematical Education. Seoul: Seoul National University Press.
  8. Lee, D.-H. & Park, B.-H. (2001). A Study on Intuition and Its Fallacy in Mathematics Education (in Korean). J. Korea Soc. Math. Ed. Ser. A, Math. Educ. 40(1), pp. 15-25. ME 2001d.03015
  9. Munkres, J. R. (1975). Topology: a Fist Course. New Delhi: Prentice Hall.
  10. Park, S. H. (1993). A study on cognitive conflicting factors occurring in concept instructions. Journal of Educational Research in Mathematics 3(1), 185-194.
  11. Seo, Y. O. (2001). Point-wise convergence and uniform convergence of a sequence of functions. Dissertation of Master Degree. Seoul: Yonsei University.
  12. Stoll, M. (2001). Introduction to Real Analysis (2nd Ed). Boston: Addison-Wesley Longman, Inc.
  13. Vinner, S. (1983). Concept Definition, Concept Image and the Notion of Function. Int. J. Math. Educ. Sci. Technol. 14(3), 293-305. ME 1984a.10119 https://doi.org/10.1080/0020739830140305
  14. Woo, J. H. (2005). Educational Basis on School Mathematics. Seoul: Seoul National University Press.