ACODESA(Collaborative Learning, Scientific Debate and Self Reflection) 방법을 적용한 문제해결 과정에서 나타난 표상의 분석

Kang, Young Ran;Cho, Cheong Soo

  • 투고 : 2015.12.04
  • 심사 : 2015.12.25
  • 발행 : 2015.12.31


본 연구는 초등학교 6학년 수학 영재 학생을 대상으로 ACODESA 방법을 적용한 문제해결 과정에서 나타나는 표상 사용의 유형을 분석하였다. 수업 설계는 다양한 표상의 조직화된 사용을 강화시키는 ACODESA 방법에 따라 이루어졌으며 40분 동안 4차시에 걸쳐 수업이 진행되었다. 자료 분석을 위해 동영상 촬영, 학생과의 인터뷰 등을 수집하여 녹취록을 작성하였고, Despina(2011)의 표상 사용유형에 따라 표상의 변화를 분석한 결과 추가형, 정교화, 그리고 제한형이 나타났다. 이러한 연구 결과를 통해 문제해결 과정에서는 개인적 표상이 소그룹별 토론과 확인의 과정을 거쳐 제도적 표상으로 생성될 수 있는 수업 설계가 필요함을 알 수 있었다.




  1. Gonzalez-Martin, A. S., Hitt, F., & Morasse, C.(2008). The introduction of the graphicrepresentation of functions through the conceptof covariation and spontaneous representations.In O. Figueras & A. Sepúlveda (Eds.),Proceedings of the 32nd conference of theInternational Group for the Psychology ofMathematics Education and the 30th PME-NA(pp. 89-97). Morelia Mexico: PME.
  2. 강영란․조정수 (2015). CBR을 활용한 초등 영재 학생의 그래프 활동에 관한 연구. 학교수학, 17(1), 65-78. Kang young ran, Cho cheong soo (2015). The study of the graph activity of gifted elementary students using CBR. School Mathematics, 17(1), 65-78.
  3. 김남균 (2002). 초등학교 수학 교수-학습에서의 수학적 상징화에 관한 연구. 한국교원대학교 대학원 박사학위논문. Kim nam gyun (2002). Study on the mathematical symbolizing in elementary school. Unpublished doctoral dissertation, Korea National University of Education, Chungju.
  4. 심은영 (2006). 다면적 표상 기반 전략훈련이 수학 문장제 해결에 미치는 영향. 국민대학교 대학원 박사학위논문. Sim eun young (2006). The effects of strategy training based on multiple representations on the mathematical word-problem solving. Unpublished doctoral dissertation, Kookmin University of Education, Chungju.
  5. Andrew, I. (2003). We want a statement that is always true: Criteria for good algebraic representations and the development of modeling knowledge. Journal for Research in Mathematics Education, 34(3), 164-187.
  6. Cobb, P. (2000). From representations to symbolizing: Comments on semiotics and mathematical learning. In P. Cobb, K. McClain, & E. Yackel (Eds.), Symbolizing and communicating in mathematics classrooms (pp. 17-36). Mahwah, NJ: Lawrence Erlbaum Associates.
  7. Despina, A. S. (2011). An examination of middel school students' representation practices in mathematical problem solving through the lens of expert work: Towards an organizing scheme. Educational Studies in Mathematics, 76, 265-280.
  8. Dufour-Janvier, B., Bednarz, N., & Belanger, N. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 109-122). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  9. Duval, R. (1993). Registers of semiotic representation and cognitive functioning of thought. Annales de Didactique et de Sciences Cognitives, 5, 37-65.
  10. Engestrom, Y. (2001). Expansive learning at work: Toward an activity theoretical reconceptualization. Journal of Education and Work, 14(1), 133-156.
  11. Goldin, G. A., & Shteingold, N. (2001). System of representations and the development of mathematical concepts. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (pp. 1-23). Reston, VA: National Council of Teachers of Mathematics, Inc.
  12. Goldin, G. A. (2008). Perspectives on representation in mathematical learning and problem solving, In L. D. English (Ed.) Handbook of international research in mathematics education. Routledge, NY: New York.
  13. Hillel, J. (1993). Computer algebra systems as cognitive technologies: Implication for the practice of mathematics education. In C. Keitel, & K. Ruthven (Eds.), Learning from computers:Mathematics education and technology (pp. 18-48). Springer Verlag.
  14. Hitt, F. (2003). The functional nature of the representations. Annales de Didactique et des Sciences Cognitives, 8, 255-271.
  15. Hitt F. (2007). Use of CAS in a method of collaborative learning, scientific debateand self reflection. In M. Baron, D. Guin, & L. Trouche (Eds.), Environments informatises et ressources numEriques pour l'apprentissage (pp. 65-88). Editorial Hermes.
  16. Hitt, F., & Morasse, C. (2009). Developing the concept of covariation and function in 3rd year of secondary school in the context of mathematical modelling and problem solving situations.
  17. Kamii, C., Kirkland, L., & Lewis, B. A. (2001). Representation and abstraction in young children's numerical reasoning. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (pp.24-34). Reston, VA: National Council of Teachers of Mathematics, Inc.
  18. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
  19. Pugalee, D. K. (2004). A comparison of verbal and written descriptions of students' problem solving process. Educational Studies in Mathematics, 55, 27-47.
  20. Seeger, F. (1997). Representations in the mathematics classroom: Reflections and constructions. In J. Voigt (Ed.), The culture of the mathematics classroom (pp. 308-343). NY:Cambridge University Press.
  21. Slavit, D. (1997). An alternate route to the reification of function. Educational Studies in Mathematics, 33, 259-281.
  22. Swafford, J. O., & Langrall, C. W. (2000). Grade 6 students' preinstructional use of equations to describe and represent problem situations. Journal for Research in Mathematics Education, 31(1) , 89-112.
  23. Zawojewski, J. S., Lesh, R., & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism (pp. 317-336). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  24. Zou, X. (2000). The use of introductory physics: An example for work and energy. Unpublished doctoral dissertation, The Ohio State University, Mansfield.