The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

An Analysis of the Whole Numbers and Their Operations in Mathematics Textbooks: Focused on Algebra as Generalized Arithmetic

범자연수와 연산에 관한 수학 교과서 분석 - 일반화된 산술로서의 대수 관점을 중심으로 -

  • Pang, Jeong-Suk (Dept. of Elementary Education (Mathematics Education), Korea National University of Education) ;
  • Choi, Ji-Young (Seoul DaeDong Elementary School)
  • Received : 2010.10.25
  • Accepted : 2011.02.10
  • Published : 2011.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

Given the importance of algebra in the early grades, this paper analyzed the contents of whole numbers and their operations from the perspectives of generalized arithmetic. In particular, the focus of analysis was given to the properties of 0 and 1, those of operations such as commutativity, associativity, and distributivity, and the relations between operations. As such, this paper analyzed in detail how such properties and relations were introduced and expanded across different grades. It is expected that many issues in this paper will serve basic information to develop instructional materials in a way to fostering students' algebraic thinking in the elementary grades.

Keywords

References

  1. 교육과학기술부 (2008). 초등학교 교육과정 해설(IV): 수학, 과학, 실과. 광주: 한솔사.
  2. 교육과학기술부 (2009a). 수학 1-1. 서울: 두산동아(주).
  3. 교육과학기술부 (2009b). 수학 1-2. 서울: 두산동아(주).
  4. 교육과학기술부 (2009c). 수학 2-1. 서울: 두산동아(주).
  5. 교육과학기술부 (2009d). 수학 2-2. 서울: 두산동아(주).
  6. 교육과학기술부 (2009e). 수학 1-1 교사용 지도서. 서울: 두산동아(주).
  7. 교육과학기술부 (2010a). 수학 3-1. 서울: 두산동아(주).
  8. 교육과학기술부 (2010b). 수학 3-2. 서울: 두산동아(주).
  9. 교육과학기술부 (2010c). 수학 4-1. 서울: 두산동아(주).
  10. 교육과학기술부 (2010d). 수학 3-1 교사용 지도서. 서울: 두산동아(주).
  11. 교육과학기술부 (2010e). 수학 3-2 교사용 지도서. 서울: 두산동아(주).
  12. 교육과학기술부 (2010f). 수학 4-1 교사용 지도서. 서울: 두산동아(주).
  13. 교육부 (1997). 수학과 교육과정. 교육부 고시 제1997-15호 [별책 2]. 서울: 대한교과서.
  14. 교육부 (1998). 초등학교 교육과정 해설(IV): 수학, 과학, 실과. 서울: 대한교과서.
  15. 교육인적자원부(2007a). 초.중등학교 교육과정. 교육인적자원부 고시 제2007-79호 [별책 1]. 서울: 대한교과서.
  16. 교육인적자원부 (2007b). 수학 1-가. 서울: (주)천재교육.
  17. 교육인적자원부 (2007c). 수학 1-나. 서울: (주)천재교육.
  18. 교육인적자원부 (2007d). 수학 2-나. 서울: (주)천재교육.
  19. 교육인적자원부 (2007e). 수학 3-가. 서울: (주)천재교육.
  20. 교육인적자원부 (2007f). 수학 1-나 교사용 지도서. 서울: (주)천재교육.
  21. 교육인적자원부 (2007g). 수학 3-가 교사용 지도서. 서울: (주)천재교육.
  22. 김성준 (2004). 대수의 사고 요소 분석 및 학습-지도 방향 탐색, 서울대학교 박사학위 논문.
  23. 백석윤 (2009). 창의중심 미래형 수학과 교육과정의 성격, 목표 및 초등학교 내용 개요(안). 수학교육논집, 27, 61-72, 대한수학회(2009년도 제27회 수학교육 심포지엄: 창의 중심의 미래형 수학과 교육과정 모형 연구).
  24. Bastable, V., & Schifter, D. (2008). Classroom stories: Examples of elementary students engaged in early elgebra. In J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp.165-184). Hillsdale, NJ: Erlbaum & The National Council of Teachers of Mathematics.
  25. Bodanskii, F. (1991). The formation of an algebra method of problem solving in primary school. In V. V. Davydov (Ed.) Psychological abilities of primary school children in learning mathemaics (Vol. 6, pp. 275-338). Reston, VA: National Council of Teachers of Mathematics.
  26. Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
  27. Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669-705). Reston, VA: The National Council of Teachers of Mathematics.
  28. Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithematic and algebra. Educational Studies in Mathematics, 27, 59-78. https://doi.org/10.1007/BF01284528
  29. Kaput, J. (1995). Transforming algebra from an engine of inequity to an engine of mathematical power by "algebrafying" the K-12 curriculum. Paper presented at the Annual Meeting of the National Council of Teachers of Mathematics, Boston, MA.
  30. Kaput, J. (2008). What is algebra? what is algebraic reasoning? In J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp.5-17). Hillsdale, NJ: Erlbaum & The National Council of Teachers of Mathematics.
  31. Kaput, J., Blanton, M., & Moreno, L. (2008). Algebra from a symbolization point of view. In J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp.19-55). Hillsdale, NJ: Erlbaum & The National Council of Teachers of Mathematics.
  32. Kieran, C., Boileau, A., & Carancon, A. (1996). Introducing algebra by means of a technology- supported, functional approaches. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 257-293). Dordrecht, the Netherlands: Kluwer.
  33. Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Dordrecht, the Netherlands: Kluwer.
  34. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  35. Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2009). Helping children learn mathematics (9th Ed.). Hoboken, NJ: John Wiley & Sons.
  36. Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 133-160). Hillsdale, NJ: Erlbaum & The National Council of Teachers of Mathematics.

Cited by

  1. A Study on the cognition for generality of solution in Algebra - Focusing on Quadratic equation - vol.28, pp.1, 2014, https://doi.org/10.7468/jksmee.2014.28.1.155