Education of Primary School Mathematics (한국수학교육학회지시리즈C:초등수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Analysis of Problem-Solving Protocol of Mathematical Gifted Children from Cognitive Linguistic and Meta-affect Viewpoint

인지언어 및 메타정의의 관점에서 수학 영재아의 문제해결 프로토콜 분석

  • Do, Joowon (Seoul Banghyun Elementary School) ;
  • Paik, Suckyoon (Department of Mathematics Education, Seoul National University of Education)
  • Received : 2019.07.12
  • Accepted : 2019.09.03
  • Published : 2019.10.31
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Abstract

There is a close interaction between the linguistic-syntactic representation system and the affective representation system that appear in the mathematical process. On the other hand, since the mathematical conceptual system is fundamentally metaphoric, the analysis of the mathematical concept structure through linguistic representation can help to identify the source of cognitive and affective obstacles that interfere with mathematics learning. In this study, we analyzed the problem-solving protocols of mathematical gifted children from the perspective of cognitive language and meta-affect to identify the relationship between the functional characteristics of the text and metaphor they use and the functional characteristics of meta-affect. As a result, the behavior of the cognitive and affective characteristics of mathematically gifted children differed according to the success of problem solving. In the case of unsuccessful problem-solving, the use of metaphor as an internal representation system was relatively more frequent than in the successful case. In addition, while the cognitive linguistic aspects of metaphors play an important role in problem-solving, meta-affective attributes are closely related to the external representation of metaphors.

수학적 과정에서 나타나는 언어 구문론적 표현 체계와 정의적 표현 체계 사이에는 긴밀한 상호 작용이 이루어진다. 한편, 수학적 개념 체계도 본질적으로 은유적이므로 언어적 표현을 통해 나타나는 수학적 개념 구조에 대한 분석은 수학 학습에 작용하는 인지 정의적 장애 요인의 근원을 밝히는데 도움이 될 수 있다. 이에 본 연구에서는 수학 영재아의 문제해결 프로토콜을 인지언어와 메타정의의 관점에서 분석하여 텍스트 및 은유의 기능적 특성과 메타정의의 기능적 특성 사이의 관계성을 파악하였다. 그 결과 문제해결의 성공 여부에 따라 수학 영재아의 인지적, 정의적 특성이 반영된 행위의 양상이 서로 다르게 나타났다. 성공적이지 못한 문제해결의 경우에는 성공적인 경우에 비해 내부 표현 체계로서의 은유를 활용하는 행위가 상대적으로 빈번하게 나타났다. 또한 은유의 인지언어학적 측면이 문제해결에 중요하게 작용하면서 동시에 은유라는 외적 표현에는 메타정의적 속성이 긴밀하게 관련되어 나타났다.

Keywords

References

  1. Ministry of Education (2015). Mathematics curriculum, Ministry of Education Notice No. 2015-74 [Separate Book 8].
  2. Kim, S. M. (2005). Metaphors on Mathematics Teaching. School Mathematics, 7(4), 445-467.
  3. Kim, S. M., & Shin, I. S. (2007). On the Mathematical Metaphors in the mathematics classroom, J. Korea Soc. Math. Ed. Ser. C: Education of Primary School Mathematics, 10(1), 29-39.
  4. Kim, J. D. (2003). Metaphorical world in cognitive linguistic perspective. Seoul: Korean Cultural History.
  5. Kim, J. Y. (2011). A Study of Teaching Methods Using Metaphor in Mathematics. School Mathematics, 13(4), 563-580.
  6. Do. J. (2018). Aspects of Meta-affect in Collaborative Mathematical Problem-Solvong Processes. Dissertation, Seoul National University of Education.
  7. Do, J., & Paik, S. (2019). Aspects of Meta-affect in Problem-Solving Process of Mathematically Gifted Children, Mathematics Education in Korea, 23(1), 59-74.
  8. Lee, S. Y., & Woo, J. H. (2002). Analogies and metaphors in school mathematics. The Journal of Educational Research in Mathematics, 12(4), 523-542.
  9. Ju, M. K., & Kwon, O. N. (2003). Students' Conceptual Metaphor of Differential Equations: A Sociocultural Perspective on the Duality of the Students' Conceptual Model. School Mathematics, 5(1), 135-149.
  10. Bal, A. P. (2015). Skill of using and transform multiple representations of the prospective teachers. Journal of Mathematical Behavior, 197(25), 682-588.
  11. Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A. (1983). Rational number concepts. In R. Lesh., & M. Landau (Eds.), Acquisition of Mathematics Concepts and Process (pp. 91-126). New York: Academic Press, Inc.
  12. Brinker, K. (1992). Linguistische Textanalyse. Eine Einfuhrung in Grundbegriffe und Methoden. 3. Aufl. (Grundlagen der Germanistik 29). Berlin. 이성만(역) (1994). 텍스트언어학의 이해 - 언어학적 베스트분석의 기본 개념과 방법. 서울: 한국문화사.
  13. Clark, B. (1988). Growing up gifted(3th ed.). Columbus, OH: Merrill.
  14. DeBellis, V. A. (1996). Interactions between Affect and Cognition during Mathematical Problem Solving: A Two-year Case Study of Four Elementary School Children. Ann Arbor, MI: University Microfilms No. 96-30716.
  15. DeBellis, V. A. & Goldin, G. A. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63(2), 131-147. https://doi.org/10.1007/s10649-006-9026-4
  16. Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17(2), 137-165. https://doi.org/10.1016/S0364-0213(99)80056-1
  17. Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving, Mathematical Thinking and Learning, 2(3), 209-219. https://doi.org/10.1207/S15327833MTL0203_3
  18. Goldin, G. A. (2006). Commentary on "The articulation of symbol and mediation in mathematics education" by Moreno-Armella and Sriraman. ZDM: The International Journal on Mathematics Education, 38, 70-72. https://doi.org/10.1007/BF02655908
  19. Goldin, G. A. (2009). The affective domain and students' mathematical inventiveness. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in Mathematics and the Education of Gifted Students (pp. 181-194). Rotterdam: Sense Publishers.
  20. Goldin, G. A. & Kaput, J. (1996). A joint perspective on the idea of representation in learningand doing mathematics. In L. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of Mathematical Learning, Erlbaum (pp. 397-430). NJ: Hillsdale.
  21. Goldin, G. A. & Steingold, N. (2001). System of mathematical representations and development of mathematical concepts. In F. R. Curcio (Ed.), The Roles of Representation in School Mathematics: 2001 Yearbook (pp. 1-23). Reston: National Council of teachers of Mathematics.
  22. Knowles, M. & Moon, R. (2006). Introducing Metaphor. Routledge. 김주식.김동환(역) (2008). 은유 소개. 서울: 한국문화사.
  23. Kosslyn, S. M. (1980). Image and Mind. Cambridge. MA: Harvard University Press.
  24. Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren. Chicago: The University of Chicago Press.
  25. Lakoff, G. & Johnson, M. (1980, 2003). Metaphors We Live by, Chicago & London: University of Chicago Press. 노양진.나익주(역) (2006). 삶으로서의 은유. 서울: 박이정.
  26. Lakoff, G. & Nunez, R. E. (2000). Where Mathematics Comes from? NY: Basic Books.
  27. Malmivuori, M. L. (2001). The dynamics of affect, cognition, and social environment in the regulation of personal learning processes: The case of mathematics. Research Report 172. Helsinki: Helsinki University Press.
  28. Moscucci, M. (2010). Why is there not enough fuss about affect and meta-affect among mathematics teacher? In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds), Proceedings of the CERME-6 (pp. 1811-1820). INRP, Lyon.
  29. McLeod, D. B. & Adams, V. M. (1989). Affect and Mathematical Problem Solving: A New Perspective (pp. 245-258). New York: Springer-Verlag.
  30. NCTM (2000). Principles and Standards for School Mathematics. 류희찬 외(역) (2007). 학교수학을 위한 원리와 규준. 서울: 경문사.
  31. Nunez, R. E. (2000). Mathematical idea analysis: What embodied cognitive science can say about the human nature of mathematics. PME 1, 3-22.
  32. Renzulli, J. S. & Reis, S. M. (1997). The schoolwide enrichment model: A how-to guide foe educational excellence (2nd ed.). Mansfield Center, CT: Creative Learning Press.
  33. Schoenfeld, A. H. (1985). Mathematical Problem Solving. NY: Academic Press.
  34. Yin, R. K. (2014). Case Study Research: Design and Methods(5th ed.). Thousand Oaks, CA: Sage.