Journal for History of Mathematics (한국수학사학회지)

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

DOI QR Code

A Study on the Mathematics Education via Intuition

직관을 통한 수학교육에 관한 고찰

  • LEE, Daehyun (Dept. of Math. Edu., Gwangju National Univ. of Edu.)
  • Received : 2015.08.10
  • Accepted : 2015.10.23
  • Published : 2015.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

As intuition is more unreliable than logic or reason, its studies in mathematics and mathematics education have not been done that much. But it has played an important role in the invention and development of mathematics with logic. So, it is necessary to recognize and explore the value of intuition in mathematics education. In this paper, I investigate the function and role of intuition in terms of mathematical learning and problem solving. Especially, I discuss the positive and negative aspects of intuition with its characters. The intuitive acceptance is decided by self-evidence and confidence. In relation to the intuitive acceptance, it is discussed about the pedagogical problems and the role of intuitive thinking in terms of creative problem solving perspectives. Intuition is recognized as an innate ability that all people have. So, we have to concentrate on the mathematics education via intuition and the complementary between intuition and logic. For further research, I suggest the studies for the mathematics education via intuition for students' mathematical development.

Keywords

References

  1. American Psychological Association, APA Dictionary of Psychology, American Psychological Association, 2015.
  2. E. W. Beth, J. Piaget, Mathematical Epistemology and Psychology, D. Reidel Publishing Company, 1966.
  3. J. S. Bruner, Lee, H. W. (Tran.), The Process of Education, Educational New Book 5, 1973. 이홍우 (역), 교육의 과정, 교육신서 5, 1973.
  4. L. Burton, Why is Intuition so important to mathematicians but missing from mathematics education?, For the Learning of Mathematics 19(3) (1999), 27-32.
  5. P. J. Davis, R. Hersh, Mathematical Experience, Boston: Houghton Mifflin Company, 1981.
  6. G. Ervynck, Mathematical creativity, In D. Tall(Ed.), Advanced Mathematical Thinking(42-53), Dordrecht: Kluwer Academic Publishers, 1991.
  7. E. Fischbein, Intuition and proof, For the Learning of Mathematics 3(2) (1982), 9-18.
  8. E. Fischbein, Intuition in Science and Mathematics, D. Reidel publishing company, 1987.
  9. E. Fischbein, D. Tirosh, P. Hess, The Intuition of infinity, Educational Studies in Mathematics 10 (1979), 3-40. https://doi.org/10.1007/BF00311173
  10. E. Fischbein, D. Tirosh, U. Melamed, Is it possible to measure the intuitive acceptance of a mathematical statement?, Educational Studies in Mathematics 12 (1981), 491-512. https://doi.org/10.1007/BF00308145
  11. J. I. Friedman, Intuition, Improving college and University Teaching 26(1) (1978), 31-38. https://doi.org/10.1080/00193089.1978.9927515
  12. J. Hadamard, An Essay on the Psychology of Invention in the Mathematical Field, Priceton university press, Princeton, 1945.
  13. R. Hersh, What is Mathematics, Really? Heo, M. (Tran.), What is Mathematics, Really?, Seoul: Kyungmoonsa, 1997. 허민 (역)(2003), 도대체 수학이란 무엇인가?, 서울 : 경문사, 1997.
  14. Kim, U. T., Park, H. S., Woo, J. H., Introduction to the Theory of Mathematics Education, Seoul: Seoul National University Press, 1995. 김응태, 박한식, 우정호, 증보 수학교육학개론, 서울 : 서울대학교 출판부, 1995.
  15. M. Klein, Mathematics: The Loss of Certainty, Park, S. H. (Tran.), 1988. The Certainty of Mathematics, Seoul: Minumsa, 1980. 박세희 (역) (1988), 수학의 확실성, 서울 : 민음사, 1980.
  16. V. A. Krutetskii, The Psychology of Mathematical Abilities in School Children, The University of Chicago Press, 1976.
  17. Kwon, O. N. et al, Cultivating Mathematical Creativity through Open-ended Approaches:Development of a Program and Effectiveness Analysis, The Mathematical Education 44(2) (2005), 307-323. 권오남 외, 개방형 문제 중심의 프로그램이 수학적 창의력에 미치는 효과, 수학교육 44(2) (2005), 307-323.
  18. Lee, K. S., Hwang, D. J., Correlation between Gifted and Regular Students in Mathematical Problem Posing and Mathematical Creativity Ability, The Mathematical Education 46(4) (2007), 503-519. 이강섭, 황동주, 영재학생과 일반학생의 수학 창의성과 문제설정과의 상관 연구, 수학교육 46(4) (2007), 503-519.
  19. Lee, D. H., An Analysis of Intuitive Thinking of High School Students in Mathematical Problem Solving Process, Korea National University of Education Doctoral Dissertation, 2001. 이대현, 수학문제해결과정에서 고등학생들의 직관적 사고의 분석, 한국교원대학교 박사학위논문, 2001.
  20. Lee, D. H., The Intuition in History of Mathematical Philosophy and Mathematics, The Korean Journal for History of Mathematics 18(2) (2005), 23-30. 이대현, 수리철학과 수학의 역사에서 직관, 한국수학사학회지 18(2) (2005), 23-30.
  21. Lee, D. H., A Study on the History of Intuition Research and its Mathematics Educational Implication, Journal of the Korean School Mathematics Society 11(3) (2008), 363-376. 이대현, 직관에 관한 연구 역사와 수학교육적 의미 고찰, 한국학교수학회논문집 11(3) (2008), 363-376.
  22. Lee, D. H., An Analysis on the Effect by the Characteristics of Intuition of Elementary Students in Mathematical Problem Solving Process, Journal of Elementary Mathematics Education in Korea 14(2) (2010), 197-215. 이대현, 초등학생들의 문제해결 과정에서 직관의 특징에 의한 영향 분석, 한국초등수학교육학회지 14(2) (2010), 197-215.
  23. Lee, D. H., A Study on the Factors of Mathematical Creativity and Teaching and Learning Models to Enhance Mathematical Creativity, Journal of Elementary Mathematics Education in Korea 16(1) (2012), 39-61. 이대현, 수학적 창의성의 요소와 창의성 개발을 위한 수업 모델 탐색, 한국초등수학교육학회지 16(1) (2012), 39-61.
  24. R. Leikin, Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, B. Koichu(Eds.), Creativity in Mathematics and the Education of Gifted Students(129-145), Sense Publishers, 2009.
  25. Ministry of Education, Science and Technology, Mathematics Curriculum, Ministry of Education, Science and Technology, 2011. 교육과학기술부, 수학과 교육과정, 교육과학기술부, 2011.
  26. R. B. Nelsen, Proofs without Words: Exercises in Visual Thinking, The Mathematical Association of America, 1993.
  27. N. Noddings, P. J. Shore, Awaking the Inner Eye, New York: Teachers College Press, 1984.
  28. On, K. C., Intuitive Thinking and Education, Seoul: Haksisa, 2001. 온기찬, 직관적 사고와 교육, 서울 : 학지사, 2001.
  29. Park, S. T. et al, Mathematics Education, Seoul: Dongmyeongsa, 1993. 박성택 외, 수학교육, 서울 : 동명사, 1993.
  30. H. Poincare, Kim, H. B. (Tran.), The Value of Science, Dandae Press, 1983. 김형보 (역), 과학의 가치, 단대 출판부, 1983.
  31. H. Poincare, Kim, H. B., Oh, B. S. (Trans.), The Methods of Science, Dandae Press, 1982. 김형보, 오병승 (역), 과학의 방법, 단대출판부, 1982.
  32. H. Poincare, Intuition and Logic in Mathematics, The Mathematics Teacher 62(3) (1969), 205-212.
  33. D. Tall, Intuition of infinity, Mathematics in School 10(3) (1981), 30-33.
  34. G. Wallas, The Art of Thought, Harcourt Brace, 1926.
  35. M. Wertheimer, Productive Thinking, New York: Harper Brothers published, 1945.
  36. R. L. Wilder, The Role of intuition, Science, New Series 156(3775) (1967) 605-610.
  37. E. Wittmann, The complementary roles of intuitive and reflective thinking in mathematics teaching, Educational Studies in Mathematics 12(3) (1981), 389-397. https://doi.org/10.1007/BF00311068