Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
권호 표지

Phenomenology of the concept of functions

함수 개념의 현상학

  • Yoo, Yoon-Jae (Department of Mathematics Education, Kyungpook National University)
  • 유윤재 (경북대학교 사범대학 수학교육과)
  • Received : 2010.05.12
  • Accepted : 2010.06.03
  • Published : 2010.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper function concept is classified in the phenomenological aspect. According to the study, function concept is classified as causality, designation, operation, change, figure, morhism, variables, functional, and operator. This classifications are categorized as pre-level function, basic level function, and upper level function.

함수 개념을 실제로 사용되고 있는 측면에서 분석하면 인과, 명명, 연산, 변화, 도형, 형태, 변수, 범함수, 작용소 등 적어도 9가지의 양상이 존재한다. 이러한 분석을 통하여 함수 개념은 현재 3단계로 성장해 왔다는 것이 밝혀졌다.

Keywords

References

  1. Anderson, J. R., The Architecture of cognition, Cambridge, MA: Harvard University Press, 1983.
  2. Anderson, J. R., Cognitive Psychology and Its Implications, New York : W. H. Freeman & Company, 1995.
  3. Davis, P. J. & Hersh, R., The Mathematical Experience, Boston, NJ: Birkhauser, 1981.
  4. Davis, R. B., Complex mathematical Cognition. In H. Ginsburg (Ed.) The Development of Mathematical Thinking, New York: Academic Press, 254-290, 1983.
  5. Dienes, Z. P.,Building up mathematics, London: Hutchinson Educational, 1960.
  6. Dubinsky, E., Reflective Abstraction and Computer Experiences: A new approach to teaching theoretical mathematics, In Lappan, Glenda, Even, & Ruhama, (Eds), Proceedings of the Eighth Annual Meeting of PME-NA, E. Lansing, MI: Michigan State University, 1986.
  7. Freudenthal, H., Mathematics as an Educational Task, Dordrecht, Netherlands: Reidel, 1973.
  8. Gray E. M. & Tall, D., "Duality, ambiguity and flexibility: A proceptual view of simple arithmetic," The Journal for Research in Mathematics Education, 26(1994), No.2, 115–141.
  9. Greeno, J, Conceptual Entity. In D. Genter & A. L. Stevens(Eds.) Mental Models, 227–252,1983.
  10. Johnson-Laird, P. N, Mental models, Cambridge, MA: Harvard University Press, 1983.
  11. Lakoff, G. & Johnson, M., Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought, New York: Basic Books, 1999.
  12. Lakoff, G. & Johnson, M., Metaphors We Live By, Chicago, IL: The University of Chicago Press, 2003.
  13. Lakoff, G. & Nunez, R., Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, New York: Basic Books, 2000.
  14. MacLane, S., Categories for the working mathematician, New York: Springer Verlag, 1971.
  15. Piaget, J., The Principles of Genetic Epistemology, London: Routledge & Kegan Paul, 1972.
  16. Rosch, E., On the internal structure of perceptual and semantic categories. In T. E. Moore(Ed.), Cognitive development and the acquisition of language, New York: Academic Press, 1973.
  17. Rosch, E., Cognitive representation of semantic categories, Journal of Experimental Psychology 104(1975), 192-233. https://doi.org/10.1037/0096-3445.104.3.192
  18. Rosch, E.,& Mervis, C. B. "Family resemblance: Studies in the internal structure of categories," Cognitive Psychology 7(1975), 573-605. https://doi.org/10.1016/0010-0285(75)90024-9
  19. Rosch, E. & Mervis, C. B, "Categorization of natural objects," Annual Review of Psychology, 32(1981), 89-115. https://doi.org/10.1146/annurev.ps.32.020181.000513
  20. Sfard, A, Two conceptions of mathematical notions: operational and structural, Proceedings of PME XII Montreal, Canada(1988), 162–169.