Journal of the Korean School Mathematics Society (한국학교수학회논문집)

The Korean School Mathematics Society (한국학교수학회)
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A study on psychology in mathematics education and constructivism

수학학습심리학과 구성주의에 대한 고찰

  • Received : 2022.07.15
  • Accepted : 2022.08.10
  • Published : 2022.09.30
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Abstract

This article examines the educational background of the knowledge system in mathematics education from three perspectives-behaviorism, cognitivism, and constructivism-centered on psychology in mathematics education. First, the relationship between mathematical education and learning psychology is reviewed according to the flow of time. Second, we examine the viewpoints of objectivism and constructivism for school mathematics. Third, we look at the psychology in mathematics education and constructivism from the perspective of learning theory. Lastly, we discuss the implications of mathematics education.

본 글은 수학교육 지식체계의 교육적 배경이 되는 행동주의, 인지주의 중심의 수학학습심리학과 구성주의에 대한 세 가지 관점의 문헌 연구이다. 첫 번째는 수학교육과 학습심리학의 관계를 시대적 흐름으로 따라가 보는 것이고, 두 번째는 학교수학에 대한 객관주의와 구성주의의 입장을 들여다보았으며, 세 번째는 학습이론의 시각에서 바라보는 수학학습심리학과 구성주의이다. 그리고 이를 토대로 수학교육적 시사점을 논의해 보고자 하였다.

Keywords

Acknowledgement

이 논문은 2021년도 전북대학교 연구교수 연구비 지원에 의하여 연구되었음

References

  1. 강완, 김상미, 박만구, 백석윤, 오영열, 장혜원 (2014). 초등수학교육론. 서울: 경문사.
  2. 권낙원, 김민환, 한승록, 추광재 (2011). 교사를 위한 교육과정론. 서울: 공동체.
  3. 김경희 (2000). 게슈탈트 심리학. 서울: 학지사.
  4. Adhikari, K. (2020). Ausubel's learning theory: Implications on Mathematics Teaching. Retrieved from https://www.researchgate.net/profile/Khagendra-Adhikari
  5. Ausubel, D. P. (1968). Educational psychology: A cognitive view. New York: Holt, Rinehart and Winston.
  6. Beth, E. W., & Piaget, J. (1966). Mathematical epistemology and psychology. Netherlands: D. Reidel Publishing Company.
  7. Birdwell, J. K., & Clason, R. G. (1970). Comment In J. K. Birdwell & R. G. Clason (Eds.), Reading in the History of Mathematics Education (pp. 361-362). Washington, D. C.: National Council of Teachers of Mathematics.
  8. Brownell, W. A. (1935). Psychological considerations in the learning and the teaching of arithmetic. In W. D. Reeve (Ed.), The teaching of arithmetic, tenth yearbook (pp. 1-31). Reston, VA: National Council of Teachers of mathematics.
  9. Brownell, W. A. (1945). When is arithmetic meaningful? Journal of Educational Research, 38, 481-498. https://doi.org/10.1080/00220671.1945.10881369
  10. Bruner, J. S. (1960). The Process of Education. Cambridge, MA: Harvard University Press.
  11. Bruner, J. S., & Kenney, H. J. (1965). Representation and mathematics learning. Society for Research in Child Development, 30(1), 50-59. https://doi.org/10.2307/1165708
  12. Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.
  13. Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. Educational Psychologist, 23(2), 87-103. https://doi.org/10.1207/s15326985ep2302_2
  14. Copley, J. (1992). The integration of teacher education and technology: a constructivist model. In D. Carey, R. Carey, D. Willis, and J. Willis (Eds.), Technology and Teacher Education, 681. Charlottesville, VA: AACE.
  15. Dienes, Z. P. (1960). Building up mathematics. London: Hutchinson.
  16. Duffy, T. M. and Jonassen, D. H. (1991). New implications for instructional technology?. Educational Technology, 31(3), 7-12.
  17. Duffy, T. M. and Jonassen, D. H. (1992). Constructivism and the technology of instruction: A conversation. Hillsdale, NJ: Erlbaum.
  18. Eisner, E. W. (1979). The educational imagination. New York, NY: Macmillan Publishing Co., Inc.
  19. English, L. D., & Halford, G. S. (1995). Mathematics education: Models and processes. Mahawah, NJ: Lawrence Erlbaum Associates.
  20. Ernest, P. (1991). The philosophy of mathematics education. London: The Falmer Press.
  21. Ernest, P. (1998). Social constructivism as a philosophy of mathematics. New York, NY: State University of New York Press.
  22. Ernest, P. (2018). 수학학습심리학 (박성선 역). 서울: 경문사. (원저 2011년 출판).
  23. Ernest, P. (2021). What is the philosophy of mathematics education?. Retrieved from https://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome18/PhoM_%for_ICME_04.htm.
  24. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel Publishing Company.
  25. Freudenthal, H. (1991) Revisiting mathematics education. Dordrecht: Kluwer Academic Publishers.
  26. Gagne, R. M. (1970). The conditions of learning (2nd Ed.). New York: Holt, Rinehart and Winston, Inc.
  27. Gagne, R. M. (1985). The conditions of learning and theory of instruction (4rd ed.). New York: Holt, Rinehart and Winston, Inc.
  28. Ginsberg, H., & Opper, S. (2006). 피아제의 인지발달이론 (김정민 역). 서울: 학지사. (원저 1969년 출판).
  29. Glasersfeld, E. von (1984). Radical constructivism. In P. Watzlawick (Ed.), The invented reality, 17-40. Cambridge, MA: Harvard University Press.
  30. Glasersfeld E. von (1989). Constructivism in education. In T. Husen & N. Postlethwaite (Eds.), International Encyclopedia of Education (pp. 162-163). Oxford: Pergamon.
  31. Glasersfeld, E. von (1995). Radical constructivism: A way of Knowing and Learning. London: The Falmer Press.
  32. Glasersfeld, E. von (1996). Aspects of radical constructivism and its educational recommendations. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin & B. Greer (Eds.), Theories of mathematical learning (pp. 307-314). New Jersey: Lawrence Erlbaum.
  33. Graven, M., & Hedy-Metzuyanim, E. (2019). Mathematics identity research: the state of the art and future directions. ZDM: The International Journal on Mathematics Education 51(3), 361-377. https://doi.org/10.1007/s11858-019-01050-y
  34. Jonassen, D. H. (1991). Objectivism versus constructivism: do we need a new philosophical paradigm?. Journal of Educational Research, 39(3), 5-14.
  35. Kilpatrick, J. (2020). History of research in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 267-272). New York, NY: Springer.
  36. Kline, M. (1973). Why J ohnny can't add: The failure of the New Math. New York, NY: St. Martin's Press.
  37. Kneller, G. F. (1971). Introduction to the philosophy of education(2nd ed.). New York: John Wiley & Sons.
  38. Konold, C. & Johnson, D. K. (1991). Philosophical and psychological aspects of constructivism. In L. P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 1-13). New York, NY: Springer-Verlag.
  39. Lambdin, D. V., & Walcott, C. (2007). Changes through the years. In W. G. Martin, & M. E. Strutchens, & P. C. Elliott (Eds.), The learning of mathematics, sixty-ninth yearbook (pp. 3-26). Reston, VA: National Council of Teachers of mathematics.
  40. National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
  41. National Council of Teachers of Mathematics (2000). Principle and standards for school mathematics. Reston, VA: Author
  42. Novak, J. D. (2011). A theory of education: meaningful learning underlies the constructive integration of thinking, feeling, and acting leading to empowerment for commitment and responsibility. Aprendizagem Significativa em Revista/Meaningful Learning Review 1(2), 1-14.
  43. Omstein, A. C., & Hunkins, F. P. (2004). Curriculum: Foundations, principle, and issues(4th ed.). Boston: Allyn and Bacon.
  44. Richey, R. C. (1986). The theoretical and conceptual bases of instructional design. London: Kogan Page, Ltd.
  45. Richey, R. C. (1993). Instructional design theory and a changing field. Educational Technology, 33(2), 16-21.
  46. Richey, R. C., Klein, J. D. & Tracey, M. W. (2011). The instructional design knowledge base. New York, NY: Routledge.
  47. Rogoff, B. (1990). Apprenticeship in thinking: cognitive development in social context. New York: Oxford University Press.
  48. Runes, D. D. (1962). Dictionary of philosophy (15th ed.), Paterson, NJ: Littlefield, Adams & Co.
  49. Saettler, P. (1998). Antecedents, Origins, and theoretical evolution of AECT. Techtrends, 43(1), 51-57. https://doi.org/10.1007/BF02818140
  50. Schoenfeld, A. H. (2004). The math wars. Educational Policy, 18(1), 253-286. https://doi.org/10.1177/0895904803260042
  51. Tam, M. (2000). Constructivism, instructional design, and technology: Implications for transforming distance learning. Educational Technology & Society, 3(2), 50-60.
  52. Thorndike, E. L. (1922). The psychology of arithmetic. New York, NY: MacMillan.
  53. Treffers, A. (1987) Three dimensions. A model of goal and theory description in mathematics instruction-The Wiskobas project. D. Dordrecht: Reidel Publishing Company. (Original work published in 1978).
  54. Van den Heuvel-Panhuizen, M., Drijvers, P. (2014). Encyclopedia of mathematics education. In S. Lerman (Ed.), Realistic mathematics education (pp. 521-525). Dordrecht: Springer.
  55. Van Engen, H. (1949). Analysis of meaning in arithmetic, The Elementary School Journal. 49(7), 395-400. https://doi.org/10.1086/459064
  56. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
  57. Vygotsky, L. S. (1986). Thought and Language. Massachusetts: MIT Press. (Original work published in 1934).
  58. Wertheimer, M. (1922). Untersuchungen zur Lehre von der Gestalt, I: Prinzipielle Bemerkungen. Psycologische Forschung 1, 47-58. https://doi.org/10.1007/BF00410385
  59. Wertheimer, M. (1945). Productive thinking. New York: Harper.
  60. Wheeler, R. H. (1935). The new psychology of learning. In W. D. Reeve (Ed.), The teaching of arithmetic, tenth yearbook (pp. 233-250). Reston, VA: National Council of Teachers of mathematics.