Proportional Reasoning Strategy of Pre-service Elementary Teachers

초등예비교사의 비례추론 과제에 대한 전략 분석

  • Received : 2016.10.15
  • Accepted : 2016.11.25
  • Published : 2016.11.30

Abstract

In this study, I hoped to reveal the understanding of pre-service elementary teachers about proportional reasoning and the traits of proportional reasoning strategy used by pre-service elementary teachers. The results of this study are as follows. Pre-service elementary teachers should deal with various proportional reasoning tasks and make a conscious effort to analyze proportional reasoning task and investigate various proportional reasoning strategies through teacher education program. It is necessary that pre-service elementary teachers supplement the lacking tasks such as qualitative reasoning and distinction between proportional situation and non-proportional situation. Finally, It is suggested to preform the future research on teachers' errors and mis-conceptions of proportional reasoning.

본 연구는 비례추론 과제에 대한 초등예비교사들의 반응을 분석함으로써 예비교사들의 비례추론 과제에 대한 이해 정도를 살펴보고, 비례추론 전략에 따른 비례추론 과제의 적합도와 비례추론 과제에 따른 전략의 특징을 살펴보고자 하였다. 이를 위해 총 8개로 구성된 검사도구를 개발하여 초등예비교사 72명에게 적용하였으며, 연구결과를 종합하여 예비교사교육에서의 비례추론 지도에 대한 시사점을 다음과 같이 도출하였다. 예비교사들이 실제적이고 다양한 비례추론 과제들을 다루는 경험, 양적 관계에 대한 의식적인 분석을 행하는 경험, 예비교사들이 미흡한 이해를 보이는 특정 과제 유형에 대한 보완, 다양한 비례추론 전략들을 분류하고 탐구하는 경험, 비례추론 전략에 적합한 과제 유형을 파악하고, 비례추론 과제에 보다 유용하고 사용가능한 비례추론 전략을 파악하도록 하는 학습경험이 필요하다고 보았다.

Keywords

References

  1. 권미숙, 김남균 (2009). 초등학교 6학년 학생들의 교과서 비례 문제 해결과 비례 추론에 관한 연구. 한국초등수학교육학회지, 13(2), 211-229.
  2. 고은성, 이경화 (2007). 초등학교 6학년 학생의 비례 추론 능력 분석. 수학교육학연구, 17(4), 359-380.
  3. 박지연, 김성준 (2016). 초등학교 6학년 학생들의 비례 추론 능력 분석 -'비교' 상황을 중심으로. 한국초등수학교육학회지, 20(1), 105-129.
  4. 안숙현, 방정숙 (2008). 5, 6, 7학년 학생들의 비례추론 능력 실태 조사. 수학교육학연구, 18(1), 103-121.
  5. 정영옥 (2015). 초등학교에서 비례 추론 지도에 관한 논의. 수학교육학연구, 25(1), 21-58.
  6. 정유경, 정영옥 (2015). 초등학생들의 비례추론 전략 분석 -6학년을 중심으로. 한국초등수학교육학회지, 19(4), 457-484.
  7. 정은실 (2013). 초등학교 수학교과서에서의 비례추론에 대한 연구. 수학교육학연구, 23(4), 505-516.
  8. Ben-Chaim, D., Keret, Y., Ilany, B. (2007). Designing and implementing authentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers' content and pedagogical knowledge and attitudes. Journal of Mathematics Teacher Education, 10, 333-340. https://doi.org/10.1007/s10857-007-9052-x
  9. Cramer, K., & Post, T. (1993). Proportional reasoning. The Mathematics Teacher, 86(5), 404-407.
  10. Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 159-178). NY: Macmillan.
  11. Ekawati, R., Lin, F. & Yang, K. (2015). Primary teachers' knowledge for teaching ratio and proportion in Mathematics: The case of Indonesia. Eurasia Journal of Mathematics, Science & Technology Education, 11(3), 513-533. https://doi.org/10.12973/eurasia.2015.1354a
  12. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: D. Reidel Publishing Company.
  13. Hull, L.S.H. (2000). Teachers' mathematical understanding of proportionality: Links to curriculum, professional development, and support. Unpublished doctoral dissertation, The University of Texas at Austin, Austin, TX.
  14. Lamon, S. J. (1993). Ratio and proportion: Children's cognitive and metacognitive processes. In T. P. Carpenter, E. Fennema, & T. A. Romberg(Eds.), Rational Numbers An Integration of Research (pp. 131-156). New Jersey, Hillsdale: Lawrence Erlbaum Associates, Publishers.
  15. Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). Charlotte, NC: Information Age Publishing.
  16. Langrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School, 6(4), 254-261.
  17. Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). Reston, VA: National Council of Teachers of Mathematics, INC.
  18. Lobato, J., & Ellis, A. B. (2010). Essential understandings: Ratios, proportions, and proportional reasoning. In R. M. Zbiek (Series Ed.), Essential understandings. Reston, VA: National Council of Teachers of Mathematics (NCTM).
  19. Lobato, J., Orrill, C., Druken, B., & Jacobson, E. (2011). Middle school teachers' knowledge of proportional reasoning for teaching. In Annual Meeting of the American Educational Research Association (AERA), ew Orleans, LA. Abstract retrieved from http://www.kaputcenter.umassd.edu/downloadsproducts/workshops/AERA2011/Lobato_Orrill_Druken_Erikson_AERA_2011.pdf.
  20. Nabors, W. K. (2003). From fractions to proportional reasoning: a cognitive schemes of operation approach. Journal of Mathematical Behavior, 22, 133-179. https://doi.org/10.1016/S0732-3123(03)00018-X
  21. NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM
  22. Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of pre-algebra understandings. In A. Coxford & A. Shulte (Eds.), The Idea of Algebra K-12 (1988 Yearbook, pp. 78-90). Reston, VA: National Council of Teachers of Mathematics.
  23. Simon, M. A., & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25(5), 472-494. https://doi.org/10.2307/749486
  24. Van de Walle, J. A. (2008). 수학을 어떻게 가르칠 것인가. (남승인 외 역). 서울: 경문사. (영어 원작은 2004년 출판).