- Volume 24 Issue 3
DOI QR Code
A Case Study on the Effects of Primary Concept of Division upon the Concept Composition Process as to Division of Fraction for 3-rd grade Child Prodigies of Elementary Schools
나눗셈의 1차적 개념이 초등학교 3학년 영재아의 분수의 나눗셈에 대한 개념구성과정에 미치는 영향에 대한 사례연구
- Kim, Hwa Soo (Sehan University)
- 김화수 (세한대학교 수학교육과)
- Received : 2014.05.05
- Accepted : 2014.06.20
- Published : 2014.06.30
On the subjects of elementary 3-rd grade three child prodigies who learned primary concept of division, this study explored how they could compose schema and transformed schema through recognition of precise concepts and linking with the contents of division of fraction. That is to say, this study examined in depth what schema and transformed schema as primary concept of division they composed to get relational understanding of division of fraction, and how they used the schema and transformed schema composed by themselves to approach problem solving as well as how they transformed the schema in their concept composition and problem solving competence. As a result, it was found that learning of primary concept of division played a key role of composing schema and transformed schema needed for coping with division of fraction, and that at this time, composition of the transformed schema and transformed schema derived from the recognition of primary concept of division could play the inevitable role of problem solving for division of fraction.
- 고정일외 백과사전 편찬부(2003). 파스칼 세계대백과사전. 서울: 동서문화사.
- 김응태, 박한식, 우정호(1993). 수학교육학개론. 서울대학교 출판부.
- 김화수(2014). 수학의 1차적 개념이 초등학교 3학년 영재아의 수학적 개념구성과정에 미치는 영향에 대한 사례연구: 분수의 덧셈과 곱셈을 중심으로. 영재교육연구, 24(1), 17-43. https://doi.org/10.9722/JGTE.2014.24.1.17
- 라병소(1999). 수학 학습에서의 관계적 이해를 위한 스키마 구성에 관한 연구. 단국대학교 박사학위 논문.
- 송상헌(1998). 수학 영재성 측정과 판별에 관한 연구. 서울대학교 박사학위 논문.
- Heymann, H. W. (2003). Why teach mathematics? : A focus on general education. Dordrecht : Kluwer Academic Publishers.
- Markovits, Z. & Sowder, J. T. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), pp.4-29. https://doi.org/10.2307/749290
- Mclntosh, A., Reys. B. J. & Reys, R. E. (1995). A Proposed framework for examining basic number sense. In P. Murphy, M. Selinger, J. Bourbe, & M. Briggs (Eds.), Subject learning in the primary curriculum : A Proposed framework for examining basic number sense. (pp.218-231). New York: The Open University.
- NCTM(1989). Curriculum standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
- NCTM(2000). Principles and standards for school mathematics. Reston, VA : The Author.
- Resnick, L. B. (1989). Defining, assessing, and teaching number sense. In J. Soeder, & B. Schappelle (Eds.), Establishing foundations for research on number sense and related topics:Report of a conference (pp.35-39). San Diego, CA: San Diego State University.
- Reys, R. (1988). Computation versus number sense. Mathematics Teaching in the Middle School, 4(2), pp.110-112.
- Reys, R., Reys, B., Mclntosh, A., Emanuelsson, G., Johansson, B. & Yang, D. C.(1999). Assessing number sense a students in Australia, Sweden, Taiwan, and The United States. School Science and Mathematics, 99(2), pp.61-70. https://doi.org/10.1111/j.1949-8594.1999.tb17449.x
- Skemp, R. R.(1987). The Psychology of Learning Mathematics. Lawrence Erlbaum Associates, Inc. New Jersey. 황우형 역(1998). 수학학습심리학. 서울: 민음사.
- Sowder, J. T. (1988). Mental computation and number comparison: Their roles in the development of number sense and computational estimation. In J. Hiebert & M. Behr (Eds.), Research agenda for mathematics education: Number concepts and operations in the middle grades (pp.182-197). Hillsdale.
- Sowder, J. T. (1992). Making sense of numbers in school mathematics. In G. Leinhardt, R. Putnam & R. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 1-p 51). Hillsdale, NJ: Erlbaum.
- Van de Walle, J. A. (2004). Elementary and middleschool mathmatics: Teaching developmentally(5th Ed.). Boston: Pearson Education, Inc.
- Wagner, H. A.(1975). An analysis of the fraction concept. UMI Dissertation Services.
- Yang, D., Hsu, C. & Huang, M. (2004). A study of teaching and learning number sense for sixth Yagrade students in Taiwan. International Journal of Science and Mathematics Education, 2, pp.407-430. https://doi.org/10.1007/s10763-004-6486-9