School Mathematics (대한수학교육학회지:학교수학)

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

A Study on the Word 'is' in a Sentence "A Parallelogram is Trapezoid."

"평행사변형은 사다리꼴이다."에서 '이다'에 대한 고찰

  • Received : 2016.08.09
  • Accepted : 2016.09.05
  • Published : 2016.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

A word 'is' in "A parallelogram is trapezoid." is ambiguous and very rich when it comes to its meaning. In this paper, 'is' as in everyday language will be identified as semantic primes that can be interpreted in different ways depending on context and situation, and meanings of 'is' in mathematics will be discussed separately. Focusing on 'identity', 'is' will be reinterpreted in the view of equivalence relation and van Hieles' work. 'Is', as a mathematical sign, is thought to have a significant importance in producing mathematical ideas meaningfully.

"평행사변형은 사다리꼴이다."에서 '이다'는 애매하고 그 의미가 매우 풍부한 기호이다. 이 연구는 일상적 언어 '이다'가 문맥과 상황에 따라 다양하게 해석되는 의미원소임을 밝히고 수학에서 사용되는 '이다'의 의미를 구분하여 논의한다. 그리고 '동일성'의 관념에 주목하여, 수학적으로 '같음'을 나타내기 위해 사용되기도 하는 '이다'를 동치관계의 개념과 Van Hieles의 기하 사고 수준 이론으로 재해석하여 살펴본다. 수학적 기호로서 '이다'에 대한 분석 결과 '이다'는 수학적 아이디어를 의미 있게 생성하는 데 중요한 의의가 있다고 판단된다.

Keywords

References

  1. 강성훈. (2013). 아리스토텔레스는 계사와 존재사를 구별했는가?. 인간.환경.미래, (11), 31-68.
  2. 나귀수. (1998). 중학교 기하의 증명 지도에 관한 소고-van Hieles 과 Freudenthal 의 이론을 중심으로. 대한수학교육학회논문집, 8(1).
  3. 도종훈, 최영기. (2003). 수학적 개념으로서의 등호 분석. A-수학교육, 42(5), 697-706.
  4. 박경미, 임재훈. (1998). 학교 수학 기하 용어의 의미론적 탐색. 수학교육학연구, 8(2), 565-586.
  5. 우정호. (1998). 학교 수학의 교육적 기초. 서울: 서울대학교 출판부.
  6. 철학사전편찬위원회. (2009). 철학사전. 서울: 중원문화.
  7. 한국 서양 고전 철학회(박희영 외). (1995). 서양고대 철학의 세계. 서울: 서광사.
  8. Battista, M. T. (2007). The development of geometric and spatial thinking. Second handbook of research on mathematics teaching and learning, 2, 843-908.
  9. Baroody, A. J., & Ginsburg, H. P. (1983). The effects of instruction on children's understanding of the "equals" sign. The Elementary School Journal, 84(2), 199-212. https://doi.org/10.1086/461356
  10. Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics, 420-464. New York, NY, England: Macmillan Publishing.
  11. De Villiers, M. D. (1987). Research evidence on hierarchical thinking, teaching strategies and the van Hieles theory: some critical comments. Research Unit for Mathematics Education, University of Stellenbosch.
  12. De Villiers, M. D. (1994). The role and function of a hierarchical classification of quadrilaterals. For the learning of mathematics, 14(1), 11-18.
  13. De Villiers, M. D. (2010, June). Some reflections on the van Hiele theory. In Invited plenary from 4th Congress of teachers of mathematics.
  14. Fujita, T., & Jones, K. (2007). Learners' Understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20. https://doi.org/10.1080/14794800008520167
  15. Goddard, C., & Wierzbicka, A. (Eds.). (2002). Meaning and universal grammar: Theory and empirical findings (Vol. 1). John Benjamins Publishing.
  16. Goddard, C., & Wierzbicka, A. (2014). Semantic fieldwork and lexical universals. Studies in Language, 38(1), 80-127. https://doi.org/10.1075/sl.38.1.03god
  17. Hersh, R. (1991). Mathematics has a front and a back, Synthese, 88(2), 127-133. https://doi.org/10.1007/BF00567741
  18. Kieran, C. (1981). Concepts associated with the equality symbol. Educational studies in Mathematics, 12(3), 317-326. https://doi.org/10.1007/BF00311062
  19. Muis, K. R. (2004). Personal epistemology and mathematics: A critical review and synthesis of research, Review of educational research, 74(3), 317-377. https://doi.org/10.3102/00346543074003317
  20. Russell, B. (1903). The principles of mathematics. University Press.
  21. Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of 'well-taught' mathematics courses, Educational psychologist, 23(2), 145-166. https://doi.org/10.1207/s15326985ep2302_5
  22. Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior, Journal for research in mathematics education, 338-355.
  23. Usiskin, Z., Griffin, J., Witonsky, D., & Willmore, E. (2008). The classification of quadrilaterals: A study of definition. IAP.
  24. van Hiele, P. M. (2009). 구조와 통찰. (우정호 외 역), 서울: 겅문사. (원저 1986년 출판).
  25. Vygotsky, L. S. (2013). 사고와 언어. (이병훈 외 역), 서울: 한길사. (원저 1962 출판).
  26. Whitehead, A. N. (1967). Aims of education. Simon and Schuster.
  27. Wierzbicka, A. (1992). Semantics, culture, and cognition: Universal human concepts in culture-specific configurations. oxford university Press.
  28. http://stdweb2.korean.go.kr/main.jsp.(국립국어원 표준국어대사전)
  29. https://en.wikipedia.org/wiki/Semantic_primes.
  30. https://www.griffith.edu.au/_data/assets/pdf_file/0005/636890/NSM_Chart_ENGLISH_v16_05_2015_Greyscale.pdf.