Journal of Educational Research in Mathematics (대한수학교육학회지:수학교육학연구)

The Korea Society of Educational Studies in Mathematics (대한수학교육학회)
권호 표지

A Semiotical Analysis of Expressions Which is Involved with The Process of A Conceptual Formation

개념 형성 과정에 관여하는 표현의 기호학적 분석

  • Received : 2017.10.09
  • Accepted : 2017.11.08
  • Published : 2017.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

Semiotic studies in mathematical education have been based on Saussure, Peirce, and Frege and many prior researches have explored the concepts in a perspective of semiotics. However, the relationship among semiotical elements and the formation and the evolution of a conception are still ambiguous and veiled in many aspects. This thesis is intended to show how a conception was formed and evolved by expression, which is an element of semiotics. In this process, I sought to partially illuminate the relationship among expressions, concepts, and objects.

수학교육학 연구 중에서 기호학적 연구는 Saussure, Peirce, Frege의 기호학에 근거하고 있음을 알게 된다. 이들 선행연구는 기호학의 관점에서 개념을 다루어 왔지만 기호학의 요소들의 관계와 개념의 형성과 발전 과정은 여전히 많은 부분이 모호하고 베일에 싸여 있다. 본 논문은 기호학의 관점에서 기호학의 한 요소인 표현에 의해서 개념이 어떻게 형성되고 발전하는지를 보이고자 하였으며 이 과정에서 기호학의 세 요소인 표현, 개념, 대상의 관계를 부분적으로 조명하고자 하였다.

Keywords

References

  1. 김선희, 이종희(2002). 수학기호와 그 의미에 대한 고찰 및 도입 방법. 학교수학, 4(4), pp. 539-554.
  2. 김선희, 이종희(2003). 기호학 관점에서의 문자와 식 분석. 학교수학, 5(1), pp. 59-76.
  3. 송상헌, 신은주(2007). 수학 영재의 추상화 학습에서 기호의 의미 작용 과정 사례 분석. 학교수학, 9(1), pp. 161-180.
  4. 최병철(2016). 질량중심 개념의 구조적 개념 형성에 관한 연구. 수학교육학연구, 26(1). pp. 23-45.
  5. Azarello, F., Bazzini, L., & Chiappini, G.(2001). A Model For Analysing Algebraic Processes of Thinking. In Sutherland et al.(eds), Perspectives on School Algebra. Kluwer Academic Publishers: Dordrecht. pp. 13-36.
  6. Bakker, A.(2004). Design research in statistics education On symbolizing and computer tools. Dissertation Utrecht University.
  7. Bakker, A., & Hoffmann, M. H. G.(2005). Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students' learning about statistical distribution. Educational Studies in Mathematics 60, pp. 333-358. https://doi.org/10.1007/s10649-005-5536-8
  8. Bakker, A.(2007). Diagrammatic reasoning and hypostatic abstraction in statistics and education. Semiotica 164. pp. 9-29.
  9. Cobb, P. (2002). Modeling, symbolizing, and tool use in statistical data analysis. In K. P. E. Gravemeijer, R. Lehrer, B. van Oers & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education. Dordrecht, the Netherlands: Kluwer Academic Publishers. pp. 171-196.
  10. Davis, R. B. & Maher, C. A.(1997). How students think: The role of representation. In English, L. D.(Eds.), Mathematical reasoning: Analogies, metaphors, and images. pp. 93-115.
  11. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learnin of mathematics. Educational Studies in Mathematics 61, pp. 103-131. https://doi.org/10.1007/s10649-006-0400-z
  12. Gravemeijer, K. & Stephan, M.(2002). Emergent models as an instructional design heuristic. In K. P. E. Gravemeijer, R. Lehrer, B. van Oers & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education. Dordrecht, the Netherlands: Kluwer Academic Publishers. pp. 145-169.
  13. Otte, M.(2006). Mathematical epistemology from a Peircean semiotic point of view. Educational Studies in Mathematics 61, pp. 11-38. https://doi.org/10.1007/s10649-006-0082-6
  14. Presmeg, N.(2006) Semiotic and the "connections" standards: Signification of semiotics for teachers of mathematics. Educational Studies in Mathematics 61, pp. 163-182. https://doi.org/10.1007/s10649-006-3365-z
  15. Saussure, F, de (1986). Course in General Linguistics. Eds. Charles Bally, Albert Sechehaye, and Albert Riedlinger. Trans. Roy Harris. LaSalle, Ill: Open Court.
  16. Sfard, A.(1991). on the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics 22. pp. 1-36.
  17. Thomas, G. B., Weir, M.D. & Hass, J. R(2010). Thomas' Calculus: Early Transcendentals. Twelfth Edition. PEARSON: International Edition.
  18. Vygotsky, L. S.(1987). Thinking and speech. In Rieber, R. W. & Caton, A. S.(Eds.), The collection works of L.S. Vygotsky: Volume 1, Problems of general Psychology. New York and London: Plenum Press. pp. 39-285.
  19. Whitson, J. A. (1997). Cognition as a semiotic process: From situated mediation to critical reflective transcendence. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition theory: Social, semiotic, and neurological perspectives. Hillsdale, NJ: Erlbaum. pp. 97-150.