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A Case Study about Influence of Primary Mathematic Concepts on the Composition of Mathematic Concepts in 3rd Grade Prodigies of Elementary Schools -Focusing on Addition of Decimals-

수학의 1차적 개념이 초등학교 3학년 영재아의 수학적 개념구성 과정에 미치는 영향에 대한 사례연구 -소수의 덧셈을 중심으로-

  • 김화수 (세한대학교 수학교육과)
  • Received : 2017.06.07
  • Accepted : 2017.07.12
  • Published : 2017.09.28

Abstract

This study was conducted as a qualitative case study for examining what transformed primary concepts and transformed schemas were formed for the addition of decimals and how they were formed, and how the relational understanding of the addition of decimals was in three 3rd grade elementary school children who had studied the primary concepts of division, fraction and decimal. That is, this study investigated how the subjects approached problems of decimal addition using transformed primary concepts and transformed schemas formed by themselves, and how the subjects formed concepts and transformed schemas in problem solving. According to the results of this study, transformed primary concepts and transformed schemas formed through the learning of the primary concepts of division, fraction, and decimal functioned as important factors for the relational understanding of decimal addition.

Keywords

Primary Concepts;Transformed Primary Concepts;Schema;Transformed Schema

Acknowledgement

Supported by : 세한대학교

References

  1. 김화수, "나눗셈의 1차적 개념이 초등학교 3학년 영재아의 분수의 나눗셈에 대한 개념구성과정에 미치는 영향에 대한 사례연구," 영재교육연구, 제24권, 제3호, pp.339-358, 2014.
  2. 김화수, "수학의 1차적 개념이 초등학교 3학년 영재아의 수학적 개념구성과정에 미치는 영향에 대한 사례연구: 분수의 덧셈과 곱셈을 중심으로," 영재교육연구, 제24권, 제1호, pp.17-43, 2014.
  3. A. J. Baroody and R. T. Coslick, Fostering children's mathematical power: an investigative approach, Lawrence erlbaum associates, 1998.
  4. V. A. Krutetskii, The psychology of mathematical abilities in school children, The University of Chicago Press, 1976.
  5. D. T. Johnson and B. T. Sher, Resource Guide to Mathematics Curriculum Materials for High-ability Learners in Grades K-8, William and Mary, 1997.
  6. D. T. Johnson, "Mathematical Curriculum for the Gifted," In J. VanTassel-Baeka (Ed.), "Comprehensive Curriculum for Gifted Learners," Needham Heights, MA: Allyn and Bacon, pp.231-261, 1993.
  7. L. J. Sheffield, Developing Mathematically Promising Students, Reston, VA: National Council of Teachers of Mathematics, 1999.
  8. 고정일외 백과사전 편찬부, 파스칼 세계대백과사전, 서울: 동서문화사, 2004.
  9. R. R. Skemp, The Psychology of Learning Mathematics, Lawrence Erlbaum Associates, Inc. New Jersey, 1987. 황우형 역, 수학학습심리학, 서울: 민음사, 1998.
  10. E. Fennema and T. Romberg, Mathematics Classrooms that Understanding, 2007, 이광호, 이현숙, 이경미, 윤혜영, 정미혜, 하수현 역, 이해를 촉진하는 수학교실, 서울: 경문사, 2011.
  11. R. Hersh, What is mathematics, really?, New York: Oxford University Press, 1997.
  12. W. P. Thurston, Letters from the editors, Quantum, pp.6-7, 1990.
  13. J. Hiebert, "Mathematical, cognitive, and instructional analyses of decimal fractions," pp.283-322, In G. Leinhardt et. al. (ed), Analysis of arithmetic for mathematics teaching, Hillsdale, New Jersey: Lawrence Erlbaum Associates, Publishers, 1992.
  14. L. B. Resnick, P. Nesher, F. Leonard, M. Magone, S. Omanson, and I. Peled, "Conceptual bases of arithmetic errors: The case of decimal fractions," Educational Studies in Mathematics, Vol.20, pp.8-27, 1989.
  15. R. E. Drexel, Connecting common and decimal fraction concepts: a common fraction perspective. Doctoral Dissertation, University of Wisconsin-Madision, 1997.
  16. K. Gravemeijer and F. van. Galen, "Fact and algorithms as products of students' own mathematical activity," In J. Kilpatrick, W. G. Martin, & D. Schifter(Eds.), "A research companion to principlesand standards for school mathematics," pp.114-122, Reston, VA: NCTM, 2003.
  17. NCTM, Principles and standards for school mathematics, Reston, VA: The Author, 2000.
  18. 송상헌, 수학 영재성 측정과 판별에 관한 연구, 서울대학교, 박사학위논문, 1998.
  19. 라병소, 수학 학습에서의 관계적 이해를 위한 스키마 구성에 관한 연구, 단국대학교, 박사학위논문, 1999.
  20. 김화수, "나눗셈과 분수의 1차적 개념이 소수의 관계적 이해에 미치는 영향에 대한 사례연구," 한국학교수학회 논문집, 제18권, 제4호, pp.353-370, 2015.
  21. D. Huinker, "Examining dimensions of fraction operation sense," In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions(pp.72-78), Reston, VA: NCTM, 2002.
  22. 박만구, 박경선, "Skemp 이론에 따른 곱셈 놀이활동이 수학학업성취도 및 수학적 태도에 미치는 효과," 한국학교수학학회논문집, 제12권, 제3호, pp.211-230, 2009.
  23. NCTM, Curriculum standards for school mathematics, Reston, VA: National Council of Teachers of Mathematics, 1989.