Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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Reconceptualization of Histo-Genetic Principle

역사발생적 원리의 재개념화

  • Received : 2013.09.10
  • Accepted : 2013.11.01
  • Published : 2013.11.30
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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.

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References

  1. YOO Yoon Jae, An invitation to mathematics education, Kyung Moon Sa, Seoul, 2013. (유윤재, 수학교육으로 초대, 서울 : 경문사, 2013.)
  2. J. R. Anderson, Cognitive Psychology and Its Applications (4th ed.), New York: Freeman & Company, 1995.
  3. J. B. Biggs, "Student learning in the context of school", in J. B. Biggs (Ed.), Teaching for Learning: The View from Cognitive Psychology (7-29). Hawthorn, Australia: Australian Council for Educational Research, 1991.
  4. C. B. Boyer & U. C. Merzbach, A History of Mathematics, New York: John Wiley & Sons, 1991.
  5. J. S. Bruner, "The course of cognitive growth", American Psychologist 19 (1964), 1-15. https://doi.org/10.1037/h0044160
  6. F. Cajori, A History of Mathematics, New York: Chelsea, 1985.
  7. A. Collins, J. S. Brown & S. E. Newman, "Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics", in L. B. Resnick (Ed.), Knowing, Learning, and Instruction: Essays in Honor of Robert Glaser (453-494). Hillsdale, NJ: Erlbaum.
  8. G. Cooper & J. Sweller, "The effects of schema acquisition and rule automation on mathematical problem-solving transfer", Journal of Educational Psychology 79 (1987), 347-362. https://doi.org/10.1037/0022-0663.79.4.347
  9. P. J. Davis & R. Hersh, The Mathematical Experience, New York: Houghton Mifflin, 1981.
  10. E. Dubinsky, "Reflective Abstraction in Advanced Mathematical Thinking", in D. Tall (Ed.), Advanced Mathematical Thinking, Dordrecht, Netherlands: Kluwer Academic Publisher, 1991.
  11. J. Enkenberg, "Instructional design and emerging models in higher education", Computers in Human Behavior 17 (2001), 495-506. https://doi.org/10.1016/S0747-5632(01)00021-8
  12. H. W. Eves, Introduction to the History of Mathematics (6th. ed.), Philadelphia, PA: Saunders College, 1990.
  13. E. Fischbein, Intuition in Science and Mathematics, An Educational Approach, Dordrecht, Netherlands: Reidel Publishing Company, 1987.
  14. H. Freudenthal, "Should a mathematics teacher know something about the history of mathematics?", For the Learning of Mathematics 2(1) (1981), 30-33.
  15. H. Freudenthal, Didactical Phenomenology of Mathematical Structures, Dordrecht, Netherlands: Reidel, 1983.
  16. R. Gagne, The Conditions of Learning, New York: Holt, Rinehart & Winston, 1985.
  17. A. Gehlen, Man. His Nature and Place in the World, New York: Columbia University Press, 1988.
  18. E. M. Gray & D. O. Tall, "Duality, ambiguity and flexibility: A proceptual view of simple arithmetic", The Journal of Research in Mathematics Education 26(2) (1994), 115-141
  19. G. Harel & D. Tall, "The general, the abstract and the generic in advanced mathematics", For the Learning of Mathematics 11 (1991), 38-42.
  20. I. Lakatos, Proofs and Refutation: The Logic of Mathematical Discovery, New York: Cambridge University Press, 1976.
  21. G. Lakoff & M. Johnson, Metaphor We Live By, Chicago: The University of Chicago Press, 1980.
  22. G. Lakoff & M. Johnson, Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought, New York: Basic Books, 1999.
  23. G. Lakoff & R. Nunez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, New York: Basic Books, 2000.
  24. R. Lesh, "Book review of mathematical solving by A. Schoenfeld", Teaching, Thinking, and Problem Solving 8 (1987), 4-11.
  25. NCTM, Curriculum and Evaluation Standards for School Mathematics Reston, VA: NCTM, 1989.
  26. NCTM, Principles and Standards for School Mathematics, Reston, VA: NCTM, 2000.
  27. J. Piaget, The Psychology of Intelligence, Totowa, NJ: Littlefield, Adams, 1972.
  28. C. S. Pierce, Philosophical writings of Peirce, Selected and edited with an introduction by Justus Buchler. New York: Dover, 1955.
  29. G. Polya, How to Solve It, Garden City, NY: Double day, 1957.
  30. K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, London, UK: Routledge & Kegan Paul, 1963.
  31. L. Radford, "Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings", Educational Studies in Mathematics 70(3) (2009), 111-126. https://doi.org/10.1007/s10649-008-9127-3
  32. M. A. Ringenberg & K. VanLehn, "Scaffolding problem solving with annotated, worked-out examples to promote deep learning", in M. Ikeda, K. D. Ashley & T. Chan (Eds.), Proceedings of the 8th international conference on Intelligent Tutoring Systems (625-634). Berlin: Springer, 2006.
  33. M. K. Richardson, "Haeckel's embryos, continued", Science 281 (1998), 1289.
  34. M. K. Richardson & G. K. Keuck, "A question of intent: when is a 'schematic' illustration a fraud?", Nature 410 (2001), 144.
  35. B. Rosenshine & C. Meister, "The use of scaffolds for teaching higher-level cognitive strategies", Educational Leadership 49(7) (1992), 26-32.
  36. S. Schworm & A. Renkl, "Learning by solved example problems: Instructional explanations reduce self-explanation activity", in W. D. Gray & C. D. Schunn (Eds.), Proceeding of the 24th Annual Conference of the Cognitive Science Society (816-821). Mahwah, NJ: Erlbaum, 2002.
  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 (1991), 1-36.
  38. R. J. Sternberg & W. M. Williams, Educational Psychology (2nd ed.), New York: Allyn & Bacon, 2010.
  39. H. Struve, "Probleme der Begriffsbildung in der Schulgeometrie", Journal für Mathematik-Didaktik 8 (1987), 257-276. https://doi.org/10.1007/BF03339277
  40. P. M. Van Hiele, Structure and Insight: A Theory of Mathematics Education, New York: Academic Press, 1986.