본문 바로가기
KERD
논문KCI 등재

역사발생적 원리의 재개념화

Reconceptualization of histo-genetic principle

유윤재
한국수학사학회 (The Korean Society For History Of Mathematics)|2013.11|한국수학사학회지 (Journal for History of Mathematics)|제26권 제6호|pp. 389-400

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

역사발생적 원리
주제분류수학

초록

본 연구는 역사발생적 원리를 실제 역사적 관점에서 재구성하려는 데 있다. 19세기에 나타났던 고전적역사발생적 원리의 정초는 생물학자 헤켈의 재현의 법칙에 바탕을 두고 있으나 현재 그 법칙은 더이상 유효하지 않음이 밝혀졌다. 이에 대한 대안으로서 여러 역사적 현상을 은유 관점에서 재구성하는전략을 택한다. 이에 따르면 역사발생적 원리는 문제해결, 개념적 지식과 절차적 지식의 변환과정,일반화 과정, 추상화 과정, 현상과 본질의 교대 과정, 대수화 과정, 인식론적 전환과정, 알고리듬의조직 과정, 추측, 증명, 논박의 변증법적 교대과정, 이론과 응용의 순환 과정 등으로 나타난다. 이러한역사적 특징을 통하여 학교수학의 교육과정과 지도 방법을 개발하고 실천하는 것이 바람직하다.

Abstract

The article makes a discussion to conceptualize a histo-genetic principle in the real historical view point. The classical histo-genetic principle appeared in 19th century was founded by the recapitulation law suggested by biologist Haeckel, but recently it was shown that the theory on it is no longer true. To establish the alternative rationale, several metaphoric characterizations from the history of mathematics are suggested: among them, problem solving, transition of conceptual knowledge to procedural knowledge, generalization, abstraction, circulation from phenomenon to substance, encapsulation to algebraic representation, change of epistemological view, formation of algorithm, conjecture-proof-refutation, swing between theory and application, and so on.

참고문헌 (40)

  1. 유윤재, "수학교육으로 초대" (2013), 경문사
  2. J. R. Anderson, "Cognitive Psychology and Its Applications" (1995), Freeman & Company
  3. J. B. Biggs, "Student learning in the context of school, In Teaching for Learning: The View from Cognitive Psychology", pp.7~29 (1991), Australian Council for Educational Research
  4. C. B. Boyer, "A History of Mathematics" (1991), John Wiley & Sons
  5. J. S. Bruner, "The course of cognitive growth", American Psychologist, 19, pp.1~15 (1964)
  6. F. Cajori, "A History of Mathematics" (1985), Chelsea
  7. A. Collins, "Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics, In Knowing, Learning, and Instruction: Essays in Honor of Robert Glaser", pp.453~494, Erlbaum
  8. G. Cooper, "The effects of schema acquisition and rule automation on mathematical problem-solving transfer", Journal of Educational Psychology, 79, pp.347~362 (1987)
  9. P. J. Davis, "The Mathematical Experience" (1981), Houghton Mifflin
  10. E. Dubinsky, "Reflective Abstraction in Advanced Mathematical Thinking, In Advanced Mathematical Thinking" (1991), Kluwer Academic Publisher
  11. J. Enkenberg, "Instructional design and emerging models in higher education", Computers in Human Behavior, 17, pp.495~506 (2001)
  12. H. W. Eves, "Introduction to the History of Mathematics" (1990), Saunders College
  13. E. Fischbein, "Intuition in Science and Mathematics, An Educational Approach" (1987), Reidel Publishing Company
  14. H. Freudenthal, "Should a mathematics teacher know something about the history of mathematics?", For the Learning of Mathematics, 2(1), pp.30~33 (1981)
  15. H. Freudenthal, "Didactical Phenomenology of Mathematical Structures" (1983), Reidel
  16. R. Gagné, "The Conditions of Learning" (1985), Holt, Rinehart & Winston
  17. A. Gehlen, "Man. His Nature and Place in the World" (1988), Columbia University Press
  18. E. M. Gray, "Duality, ambiguity and flexibility: A proceptual view of simple arithmetic", The Journal of Research in Mathematics Education, 26(2), pp.115~141 (1994)
  19. G. Harel, "The general, the abstract and the generic in advanced mathematics", For the Learning of Mathematics, 11, pp.38~42 (1991)
  20. I. Lakatos, "Proofs and Refutation: The Logic of Mathematical Discovery" (1976), Cambridge University Press
  21. G. Lakoff, "Metaphor We Live By" (1980), The University of Chicago Press
  22. G. Lakoff, "Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought" (1999), Basic Books
  23. G. Lakoff, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being" (2000), Basic Books
  24. R. Lesh, "Book review of mathematical solving by A. Schoenfeld", Teaching, Thinking, and Problem Solving, 8, pp.4~11 (1987)
  25. NCTM, "Curriculum and Evaluation Standards for School Mathematics Reston", NCTM, ~ (1989)
  26. NCTM, "Principles and Standards for School Mathematics", NCTM, ~ (2000)
  27. J. Piaget, "The Psychology of Intelligence" (1972), Littlefield, Adams
  28. C. S. Pierce, "Philosophical writings of Peirce, Selected and edited with an introduction by Justus Buchler" (1955), Dover
  29. G. Polya, "How to Solve It" (1957), Double day
  30. K. R. Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge" (1963), Routledge & Kegan Paul
  31. L. Radford, "Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings", Educational Studies in Mathematics, 70(3), pp.111~126 (2009)
  32. M. A. Ringenberg, "Scaffolding problem solving with annotated, worked-out examples to promote deep learning", Proceedings of the 8th international conference on Intelligent Tutoring Systems, pp.625~634 (2006), Springer
  33. M. K. Richardson, "Haeckel’s embryos, continued", Science, 281, pp.1289~ (1998)
  34. M. K. Richardson, "A question of intent: when is a ‘schematic’ illustration a fraud?", Nature, 410, pp.144~ (2001)
  35. B. Rosenshine, "The use of scaffolds for teaching higher-level cognitive strategies", Educational Leadership, 49(7), pp.26~32 (1992)
  36. S. Schworm, "Learning by solved example problems: Instructional explanations reduce self-explanation activity", Proceeding of the 24th Annual Conference of the Cognitive Science Society, pp.816~821 (2002), Erlbaum
  37. A. Sfard, "On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin", Educational Studies in Mathematics, 22, pp.1~36 (1991)
  38. R. J. Sternberg, "Educational Psychology" (2010), Allyn & Bacon
  39. H. Struve, "Probleme der Begriffsbildung in der Schulgeometrie", Journal für Mathematik-Didaktik, 8, pp.257~276 (1987)
  40. P. M. Van Hiele, "Structure and Insight: A Theory of Mathematics Education" (1986), Academic Press

관련 논문AI추천

역사-발생적 분석을 통한 대수 지도김성준한국수학사학회 · 한국수학사학회지2005 · 제18권 제3호예비수학교사를 위한 수학사 활용 방안정해남한국수학사학회 · 한국수학사학회지2012 · 제25권 제3호수학교육에서의 '기본개념'과 수학사의 접목-평균값의 예를 통해서 본 수업 모형-한경혜한국수학사학회 · 한국수학사학회지2004 · 제17권 제3호수학적 개념의 발생적 분해의 적용에 대하여김서령, 김완순, 박혜숙한국수학교육학회 · 수학교육2005 · 제44권 제4호수학교육에서 진보주의와 구성주의 적용에 대한 성찰박정선, 신재홍한국수학교육학회 · 수학교육2021 · 제60권 제3호수학에서의 지식의 변화와 수학혁명박창균한국수학사학회 · 한국수학사학회지2010 · 제23권 제4호

이 간행물의 다른 논문 (6건)

Division Algorithm in SuanXue QiMeng홍영희, 이승온, 홍성사pp. 323-328和算家的累约术曲安京pp. 329-343Looking at HPM through an old chestnut: Sum of the angles of a triangle肅文強pp. 345-353해리엇의 기호주의와 방정식론계영희, 신경희pp. 355-370아르키메데스가《The Method》에서원뿔의 무게중심을 구한 방식에 대한 하나의 가설박선용, 홍갑주pp. 371-388
원문 보기