Journal of Elementary Mathematics Education in Korea (한국초등수학교육학회지)

Korea Society of Elementary Mathematics Education (한국초등수학교육학회)
권호 표지

An Analysis of Mathematical Modeling Process and Mathematical Reasoning Ability by Group Organization Method

모둠 구성에 따른 수학적 모델링 과정 수행 및 수학적 추론 능력 분석

  • Received : 2018.10.19
  • Accepted : 2018.11.23
  • Published : 2018.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this study is to compare the process of mathematical modeling in mathematical modeling class according to group organization, and to investigate whether it shows improvement in mathematical reasoning ability. A total of 24 classes with 3 mathematical modeling activities were designed to investigate the research problem. The result of this study showed that the heterogeneous groups performed better than the homogeneous groups in terms of both the performance ability of mathematical modeling and mathematical reasoning ability. This study implies that, with respect to group design for applying mathematical modeling in teaching mathematics, heterogeneous group design would be more efficient than homogeneous group design.

본 연구는 초등학교 5학년 학생들의 수학적 모델링 수업에서 모둠 구성 방법에 따라 수학적 모델링 과정 수행 능력과 수학적 추론 능력에 차이가 있는지 분석하였다. 이를 위하여 3가지 문제 상황으로 각각 8차시에 걸쳐 총 24차시의 수학적 모델링 수업을 설계 및 실시하였다. 그 결과 동질 모둠 보다는 이질 모둠에서 더 낳은 수학적 모델링 과정 수행 능력과 수학적 추론 능력을 보여 주었다. 본 연구 결과는 수학 수업에서 수학적 모델링을 적용할 때 모둠 구성의 관점에서 이질 모둠이 보다 효과적임을 시사한다.

Keywords

References

  1. 고창수, 오영열 (2015). 수학적 모델링 활동이 수학적 문제해결력 및 수학적 성향에 미치는 영향. 한국초등수학교육학회지, 19(3), 347-370.
  2. 교육부 (2015). 수학과 교육과정 [별책 8]. 교육부 고시 제2015-74호.
  3. 김민경, 홍지연, 김은경 (2009). 수학적 모델링 사례 분석을 통한 초등 수학에서의 지도 방안 연구. 한국수학교육학회지 시리즈 A <수학교육>, 48(4), 365-385.
  4. 남승인 (2011). 귀납 추론을 통한 수학적 원리.법칙 지도안에 관한 고찰. 한국초등수학교육학회지, 15(3), 641-654.
  5. 정은실 (2015). 초등학교 수학과 문제해결 교육 재고. 한국초등수학교육학회지, 19(2), 123-141.
  6. 최인숙 (2013). 문제해결과정에서 수학적 추론이 일어나는 언어적 상호작용 분석. 이화여자대학교 대학원 박사학위논문.
  7. Blum, W., & Leiss, D. (2005). Filling up-the problem of independence-preserving teacher interventions in lessons with demanding modeling tasks. Proceedings of the fourth congress of the European society for research in mathematics education (pp. 1623-1633). Sant Feliu De Guíxols, Spain.
  8. Burkhardt, A. (2007). Functional mathematics and teaching mathematics. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 177-186). Chichester, UK: Horwood.
  9. Caron, F. & Belair, J. (2007). Exploring university students' competencies in modeling. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 120-129). Chichester, UK: Horwood.
  10. Common Core State Standards for Mathematics (2014). Common core state standards initiatives.
  11. Dewey, J. (1896). The reflex arc concept in psychology. Psychological Review 3, 357-370. https://doi.org/10.1037/h0070405
  12. English, L. D. (2010) Modeling with complex data in the primary school. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competencies: ICTMA 13 (pp. 287-299). New York, NY: Springer.
  13. English, L. D., & Watters, J. J. (2004). Mathematical modeling with young children. The 28th conference of the international group for the psychology of mathematics education, Vol 2. pp. 335-342.
  14. Galbraith, P. L., Stillman, G., & Brown, J. (2010). Turning ideas into modeling problems. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competencies: ICTMA 13 (pp. 133-144). New York, NY: Springer.
  15. Haines, C. R., & Crouch, R. (2010). Remarks on a modeling cycle and interpreting behaviours. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competencies: ICTMA 13 (pp. 145-154). New York, NY: Springer.
  16. Hestenes, D. (2010). Modeling theory for math and science education. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competencies: ICTMA 13 (pp. 13-41). New York, NY: Springer.
  17. Hogan, K., Nastasi, B., & Pressley, M. (1999). Discourse patterns and collaborative scientific reasoning in peer and teacher-guided discussions. Cognition and Instruction, 17(4), 379-432. https://doi.org/10.1207/S1532690XCI1704_2
  18. Julie, C. (2002). Making relevance relevant in mathematics teacher education. Proceedings of the 2nd international conference on the teaching of mathematics [CD]. Hoboken, NJ: Wiley.
  19. Kaiser, G. (2010). Introduction: ICTMA and the teaching of modeling and applications. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competencies: ICTMA 13 (pp. 1-2). New York, NY: Springer.
  20. Kaiser, G., Schwarz, B., & Tiedemann, S. (2010). Future teachers' professional knowledge on modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competencies: ICTMA 13 (pp. 433-443). New York, NY: Springer.
  21. Larson, C. (2010). Modeling and quantitative teasoning: The summer jobs problem. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competencies: ICTMA 13 (pp. 111-118). New York, NY: Springer.
  22. Lesh, R., Young, R., & Fennewald, T. (2010). Modeling in K-16 mathematics classrooms and beyond. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competencies: ICTMA 13 (pp. 275-283). New York, NY: Springer.
  23. Mousoulides, N., Sriraman, B., & Christou, C. (2008). A modeling perspective in mathematical problem solving. Mathematical Thinking and Learning, 10(3), 293-304. https://doi.org/10.1080/10986060802218132
  24. NCTM (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.
  25. NCTM (2000). Principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.
  26. Noss, R. & Hoyles, C. (2010). Modeling to address techno-mathematical literacies in work. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling competences (pp. 75-86). New York: Springer.
  27. Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modelling activities at Year 9. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modelling competencies: ICTMA 13 (pp. 385-398). New York: Springer.
  28. Zawojewski, J. (2010). Problem solving versus modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students' mathematical modelling competencies: ICTMA 13 (pp. 237-243). New York: Springer.
  29. Zbiek, R. & Connor, A. (2006). Beyond motivation: Exploring mathematical modeling as a context for deepening students' understandings of curricular mathematics. Educational Studies in Mathematics, 63(1), 89-112. https://doi.org/10.1007/s10649-005-9002-4