Education of Primary School Mathematics (한국수학교육학회지시리즈C:초등수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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A Study on mathematical imaginations shown in children's mathematical narratives

초등학생의 수학 이야기에 나타난 수학적 상상 연구

  • Kim, Sangmee (Department of Mathematics Education, Chuncheon National University of Education)
  • Received : 2016.10.19
  • Accepted : 2016.10.30
  • Published : 2016.10.31
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Abstract

This study aims to reflect on mathematical imaginations in learning mathematics and elementary students' mathematical imaginations. This was approaching a study of imagination not as psychological problems but as objects and methods of mathematics learning. First, children's mathematical narratives were analysed in terms of Egan(2008)'s basic cognitive tools using imagination, that is, metaphor, binary opposites, rhyme rhythm pattern, jokes humor, mental imagery, gossip, play, mystery. Second, how children's imaginations change under different grades was addressed.

이 연구는 상상이란 수학학습 전 영역에서 모든 학생들에게 필수적이고 주요한 것이라고 가정하고, 학교수학에서 초등학생이 보여주는 수학적 상상에 주목하였다. 첫째로, 상상에 대한 연구를 중심으로 상상의 개념과 발달을 살펴보고 수학교육에 주는 함의점을 논의하였다. 둘째로, Egan(2008)이 말하는 상상력을 활용하는 기초적인 인지도구 즉, 은유, 상반된 쌍, 운율 리듬 패턴, 농담 유머, 심상, 잡담, 놀이, 신비 등을 중심으로 초등학생들의 수학 이야기에 나타나는 상상의 사례를 찾았다. 셋째로, 학생의 학년 변화에 따라 상상은 어떻게 변화하는지 분석하였다. 상상은 단지 심리학적인 현상으로서가 아니라 수학교육의 대상과 방법으로서 후속적인 연구가 필요하다.

Keywords

References

  1. 김상미 (2005). 수학수업을 보는 관점으로서의 은유, 대한수학교육학회지 <학교수학>, 7(4), 447-469.(Kim, S. M. (2005b). Metaphors on mathematics teaching, School Mathematics, 7(4), 447-469.)
  2. 김상미.신인선 (2007). 초등 4학년 도형 영역의 수학수업에 나타난 은유 사례 연구, 한국수학교육학회지 시리즈 C <초등수학교육>, 10(1), 1-9.(Kim, S. M. & Shin, I .S. (2007). On the mathematical metaphors in the mathematics classroom, Journal of the Korean Society of Mathematical Education Series C, Education of Primary School Mathematics, 10(1), 1-9.)
  3. 김용선 (1991). 상상력을 위한 교육학 - 바슐라르를 중심으로. 서울: 인간사랑.(Kim, Y. S. (1991). Philosophy of education for imagination. Seoul: Ingansalang)
  4. 김진호.김상미 (2014). 예비초등교사의 수학교과서에 대한 은유 분석, 한국수학교육학회지 시리즈 A <수학교육>, 53(1), 147-162.(Kim, J. H. & Kim, S. M. (2007). Elementary school teachers' metaphors on mathematics textbooks, Journal of the Korean Society of Mathematical Education Series A, The Mathematical Education, 53(1), 147-162.)
  5. 박소화 (2012). 스토리텔링 기반 교수 설계 원리 및 모형 탐색. 서울대학교 박사학위논문,(Park, S. H. (2012). Exploration of instructional design principles and a model based on storytelling, Unpublished doctoral dissertation, Seoul National University.)
  6. 서보억 (2013). 수학교육에서 스토리텔링에 대한 문헌 분석 연구. 한국수학교육학회지 시리즈 A <수학교육>, 52(1), 65-82.(Suh, B. E. (2013). A literature research on storytelling in mathematics education. Journal of the Korean Society of Mathematical Education Series A, The Mathematical Education, 52(1), 65-82.)
  7. 이상오 (2009). Gaston Bachelard의 '상상력 철학'의 교육학적 의미. 교육철학, 46, 163-188.(Lee, S. O. (2009). Gaston Bachelard's philosophy of imagination and its meaning for education. The Korean Journal of Philosophy of Education, 46, 163-188.)
  8. 이주하 (2008). 바슐라르와 뒤랑의 상상력 재발견과 그 교육적 함의. 교육철학, 34, 351-390.(Lee, J. H. (2008). Rediscovery of Bachelard and Durand's imagination and its educational implications. The Korean Journal of Philosophy of Education, 34, 351-390.)
  9. 전명남 (2002). 상상과 창의성의 관계 분석. 교육심리연구, 16(1), 163-181.(Jun, M, N. (2002). An empirical analyses of relationships between imagination and creativity. The Korean Journal of Educational Psychology, 16(1), 163-181.)
  10. 채은숙(2013), 스토리텔링 수학 수업에서 나타나는 의미 생성. 서울교육대학교 교육대학원 석사학위논문.(Chae, E. S. (2013). The generation of meaning in mathematics teaching with storytelling. Master's Thesis in Seoul National University of Education)
  11. 허영주 (2011). 교사의 상상력의 교육과정적 함의. 교육과정연구, 29(1), 137-163.(Hur, Y. J. (2011). Importance of teacher's imagination in curriculum reconstruction and implementation. The Journal of Curriculum Studies, 29(1), 137-163.)
  12. 홍명희 (2006). 교육에 있어서의 상상력의 의미와 역할. 프랑스문화예술연구, 16, 1-18.(Hong, M. H. (2006). Le sens et le role de l'imagination dans l'education. Etude de la Culture Franccaise et des Arts en France, 16, 1-18.)
  13. 홍명희 (2008). 바슐라르의 상상력의 현상학. 프랑스문화예술연구, 24, 357-375.(Hong, M. H. (2008). La phenomenologie de l'imagination chez Bachelard, Etude de la Culture Franccaise et des Arts en France, 24, 357-375.)
  14. 황석하 (2006). 칸트 상상력 개념의 교육적 안목. 교육학논총, 27(2), 77-96.(Hwang, S. H. (2006). Educational appreciative eyes of a concepts of Kant's imagination. The Journal of Educational Research, 27(2), 77-96.)
  15. Bachelard, G. 공기와 꿈: 운동에 관한 상상력 (정영란 역). 서울: 민음사. (원작 1943년 출판)
  16. Chapman, O. (2008). Imagination as a tool in mathematics teacher education. Journal of Mathematics Teacher Eduction. 11: 83-88. https://doi.org/10.1007/s10857-008-9074-z
  17. Chapman, O. (1997). Metaphor in the teaching of mathematical problem solving. Educational Studies in Mathematics, 32(3), 201-228. https://doi.org/10.1023/A:1002991718392
  18. Chui, M. M. (1994). Metaphorical reasoning in mathematics: Experts and novices solving negative number problems. Paper Presented at the Annual Meeting of the American Education Association, April, 4-8. LA: New Orleans (ERIC Document Reproduction Service No. ED 374-988).
  19. Chui, M. M. (1996). Building mathematical understanding during collaboration: Students' learning functions and graphs in an urban, public high school. Doctoral dissertation, Berkeley: University of California.
  20. Collingwood, R. G. (1996). 상상과 표현 (김혜련 역). 서울: 고려원. (원작 1937년 출판)
  21. Devlin, K. J. (1996). 수학 : 양식의 과학 (허민.오혜영 공역). 서울: 경문사. (원작 1994년 출판)
  22. Durand, G. (2007). 상상계의 인류학적 구조들 (진형준 역). 파주: 문학동네. (원작 1992년 출판)
  23. Egan, K. (1986). Teaching as story telling: An alternative approach to teaching and curriculum in the elementary school. Chicago: The University of Chicago Press.
  24. Egan, K. (1992). Imagination in teaching and learning. London: Routledge.
  25. Egan, K. (1997). The educated mind: How cognitive tools shape our understanding. Chicago: The University of Chicago Press.
  26. Egan, K. (2008). 상상력을 활용하는 교수법 (송영민 역). 서울: 도서출판 울력. (원작 2005년 출판)
  27. Egan, K., & Nadaner, D. (Eds.) (1988). Imagination and education. New York: Teachers College Press.
  28. Gajdamaschko, N. (2005) Vygotsky on Imagination: Why an understanding of the imagination is an important issue for school teachers. Teaching Education. 16(1), 13-22. https://doi.org/10.1080/1047621052000341581
  29. Gajdamaschko, N. (2006). Theoretical Concerns: Vygotsky on Imagination Development. Educational Perspectives, 39(2), 34-40.
  30. Greene, M. (1995). Releasing the imagination: Essays on education, the arts, and social change. CA: John Wiley & Sons, Inc.
  31. Hadamard, J. (1989) 수학분야에서 발명의 심리학 (정계섭 역). 서울: 범양사출판부. (원서 1975년 출판).
  32. Hagen, P. (2003). For the beauty of ideas: mathematics and imaginative education. 18th IERG Conference Proceedings.
  33. Hagen, P., & Percival, I. (2007). Fostering engagement in elementary mathematics through imaginative education. IERG 2nd Annual Reseach Symposium on Imaginative Education.
  34. Lim, C. S. (1999a). Using metaphor analysis to explore adults' images of mathematics. Philosophy of Mathematics Education Journal, 12, November.
  35. Michael D. H., & Elaine, M. K. (1988). Imagination and education for intercultural understanding. In Egan, K., & Nadaner, D. (Eds.) (1988). Imagination and education. New York: Teachers College Press.
  36. Mazur, B. (2008). 허수: 시인의 마음으로 들여다본 수학적 상상의 세계 (박병철 역). 서울: 승산. (원작 2003년 출판).
  37. Mathematical Science Education Board, National Research council (1989). Everybody Counts: A Report to the Nation on the Future of Mathematics Education. Washington D.C.: National Academey Press.
  38. Mathematical Science Education Board, National Research council (1990). Perspectives on school: Reshaping School Mathematics, A Philosophy and framework for Curriculum. Washington D.C.: National Academy Press.
  39. National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
  40. National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author.
  41. National Council of Teachers of Mathematics (1995). Assessment standards for school mathematics Reston, VA: Author.
  42. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
  43. Nunez, R. E. (2000a). Conceptual metaphor and the embodied mind: What makes mathematics possible? In F. Hallyn (Ed.), Metaphor and analogy in the science (125-145). Netherlands, Kluwer Academic Publishers.
  44. Nunez, R. E. (2000b). Mathematical idea analysis: What embodied cognitive science can say about the human nature of mathematics. Proceedings of the Conference of the International Group for the Psychology of Mathematics Education(PME 24th), Vol. 1. Hiroshima, Japan. (ERIC Document Reproduction Service No. ED 466-734).
  45. Johnson, M. (1981). Introduction: Metaphor in the philosophical tradition. In M. Johnson (Ed), Philosophical perspectives on metaphor (3-47). Minneapolis: The University of Minnesota Press.
  46. Johnson, M. (1992). 마음 속의 몸 (이기우 역), 서울: 한국문화사. (원저 1987년 출판)
  47. Johnson, M. (2000) 마음 속의 몸: 의미, 상상력, 이성의 신체적 근거 (노양진 역). 서울: 철학과 현실사. (원저 1990년 출판)
  48. Jonker, L. (2004). Mathematics and beauty: Kieran Egan's kinds of understanding as a filter for identifying manifestations of beauty in the study of mathematics. 19th IERG Conference Proceedings.
  49. Jonker, L. (2007). Memory and Understanding in Mathematics Education. IERG 2nd Annual Reseach Symposium on Imaginative Education.
  50. Kaplan, R. & Kaplan, E. (2004). On mathematical imagination: From whole numbers to infinity - and beyond. Harvard Magazine, January2004.
  51. Kasner, E. & Newman, J. (1940). Mathematics and the Imagination. NY: Simon & Schuster.
  52. Lakoff, G. (1994). 인지의미론 (이기우 역), 서울: 한국문화사. (원저 1987년 출판)
  53. Lakoff, G. (1993). The contemporary theory of metaphor. In A. Ortony (Ed.), Metaphor and thought (2nd ed.) (202-251). NY: Cambridge University Press.
  54. Lakoff, G. & Johnson, M. (1995). 삶으로서의 은유 (노양진, 나익주 역), 서울: 서광사. (원저 1980년 출판)
  55. Lakoff, G. & Johnson, M. (2002). 몸의 철학: 신체화된 마음의 서구 사상에 대한 도전 (임지룡, 윤희수, 노양진, 나익주 역), 서울: 도서출판 박이정. (원저 1999년 출판)
  56. Lakoff, G. & Nunez, R. E. (1997). The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics. In L. D. English(Ed.), Mathematical reasoning: Analogies, metaphors, and images (21-89). Mahwah, NJ: Lawrence Erlbaum Associates.
  57. Lakoff, G. & Nunez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. NY: Basic Books.
  58. Luria, A. R. (2013). 비고츠키와 인지 발달의 비밀 (배희철 역), 서울: 살림터. (원저 1974년 출판)
  59. Presmeg, N. C. (1992). Prototypes, metaphor, metonymies, and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23(6), 595-610. https://doi.org/10.1007/BF00540062
  60. Presmeg, N. C. (1997). Reasoning with metaphors and metonymies in mathematics learning. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (267-279). Mahwah NJ: Lawrence Erlbaum Associates.
  61. Poincare, H.(1983). 과학의 가치 (김형보 역). 서울: 단국대학교출판부. (원저 1905년 출판)
  62. Sacks, S. (Ed.) (1978). On metaphor. Chicago: University of Chicago Press.
  63. Schon, D. (1993). Generative metaphor: A perspective on problem solving in social policy. In A. Ortony (Ed.), Metaphor and thought (2nd ed.) (137-163). NY: Cambridge University Press.
  64. Sfard, A. (1994). Reification as the birth of metaphor. For the Learning of Mathematics, 14(1), 44-54.
  65. Sfard, A. (1997) Commentary: On the metaphorical roots of conceptual growth. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (339-371). Mahwah, NJ: Lawrence Erlbaum Associates.
  66. Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4-13.
  67. Sfard, A. (2000). Steering (dis)course between metaphor and rigor: Using focal analysis to investigate and emergence of mathematical objects. Journal for Research in Mathematics Education, 31(3), 296-327. https://doi.org/10.2307/749809
  68. Singer, J. L. (1999). Imagination. In M. A. Runco & S. R. Pritzker(Eds.). Encyclopedia of creativity 2. San Diego: Academic Press.
  69. Skovsmos, O. (2011). Ctitique, generativity and imagination. For the Learning of Mathematics, 31(3), 19-23.
  70. Steen, L. A. (1988). The Science of patterns. Science 240, April, pp.611-616. https://doi.org/10.1126/science.240.4852.611
  71. Steen, L. A. (1990). On the shoulders of giants ; new approaches to numeracy. Washington D.C.:The National Academy of Sciences.
  72. Stewart, I. (1996). 자연의 수학적 본성 (김동광.과학세대 역). 서울: 두산동아 주식회사. (원저 1995년 출판).
  73. van Dormolen, J. (1991). Metaphors mediating the teaching and understanding of mathematics. In A. J. Bishop, S. Mellin-Olsen, & J. van Dormolen (Eds.), Mathematical knowledge: Its growth through teaching (pp.89-106). Netherlands: Kluwer Academic Publishers.
  74. Vygotsky, L. S. (1985). 사고와 언어 (신현정 역). 서울: 성원사. (원저 1962년 출판).
  75. Vygotsky, L. S. (1999). 아동의 상상력과 창조 (팽영일 역). 서울: 창지사. (원저 1930년 출판)
  76. Wheatley, W. J., Anthony, W. P., & Maddox, E. N. (1991). Selecting and training strategic planners with imagination and creativity. Journal of Creative Behavior, 25, 52-60. https://doi.org/10.1002/j.2162-6057.1991.tb01353.x
  77. Zittoun, T., & Cerchia, F. (2013). Imagination as expansion of experience. Integrative Psychological and Behavioral Science April 2013.