The Case Study of High School Students' Understanding of the Concept of Parameter In A Computer Algebra Environment

컴퓨터 대수 환경에서 매개변수 개념에 대한 고등학생의 이해에 관한 사례 연구

  • Received : 2010.09.10
  • Accepted : 2010.11.25
  • Published : 2010.11.30

Abstract

The purpose of the study was to investigate how students' understanding was formed for solving the algebra problems involving parameters in a computer algebra environment. The teaching experiment has been conducted with 6 high school students. As a result, students studied the parameter in different roles such as placeholder, changing quantity, unknown and generalizer. The results indicate that a computer algebra environment offers opportunities for algebra activities that may support the development of understanding of the concept of parameter.

본 연구의 목적은 고등학생 6명을 대상으로 교수실험을 통해 컴퓨터 대수 환경에서 매개변수 개념에 대한 학생들의 이해 과정에서 나타난 특정들을 알아보는 것이다. 본 연구에서는 Drijvers(2003)의 매개변수 개념의 구분에 따라 매개변수 개념을 "자리지기로서의 매개변수", "변하는 양으로서의 매개변수", "미지수로서의 매개변수", "일반화로서의 매개변수"로 세분화하여 컴퓨터 대수 환경에서 각 매개변수 개념에 대한 학생들의 이해의 특징을 조사하고, 컴퓨터 대수 환경이 각 매개변수의 개념 이해에 어떠한 역할을 하는지에 대해 알아보았다.

Keywords

References

  1. 김남희 (2004). 매개변수 개념의 교수-학습에 관한 연구. 대한수학교육학회지 <수학교육학연구> 14(3), 305-325.
  2. 김성준 (2002). 학교수학에서의 매개변수의 역할 고찰. 대한수학교육학회지 <학교수학> 4(3), 495-511.
  3. 이종영 (1999). 컴퓨터 환경에서의 수학 학습-지도에 관한 교수학적 분석. 서울대학교 대학원 박사학위논문.
  4. 이종희 (2003). 중학생들의 매개변수개념 분석과 교수-학습방안 탐색. 대한수학교육학회지 <학교수학> 5(4), 477-506.
  5. 황우형 (1993). 한국과 미국학생의 대수 문장제 풀이 비교 연구. 대한수학교육학회 논문집 3(2), 105-109.
  6. Bills, L. (2001). Shifts in the meanings of literal symbols. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education, Vol 2 (pp.161-168). Utrecht, Netherlands: Freudenthal Institute.
  7. Bloedy-Vinner, H. (2001). Beyond unknowns and variables-parameters and dummy variables in high school algebra. In R. Sutherland, T. Rojano, A. Bell & R. Lins (Eds.), Perspectives on school algebra (pp.177-189). Dordrecht, Netherlands: Kluwer Academic Publishers.
  8. Boyer, C. B. (1968). A history of mathematics. New York: Wiley.
  9. Drijvers P. (2003) Learning Algebra in a Computer Algebra Environment: design research on the understanding of the concept of parameter. Utrecht: CD-$\beta$ Press.
  10. Drijvers, P. (2000). Students encountering obstacles using a CAS. International Journal of Computers for Mathematical Learning 5, 189-209. https://doi.org/10.1023/A:1009825629417
  11. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, Netherlands: Reidel.
  12. Furinghetti, F., & Paola, D. (1994). Parameters, unknowns and variables: A little difference? In J. P. Da Ponte & J. F. Matos (Eds.), Proceedings of the 18th international conference for the psychology of mathematics education, Vol2 (pp.368-375). Lisbon: University of Lisbon.
  13. Giessen, van de (2002). The visualisation of parameters. In M. Borovcnik & H. Kautschitsch (Eds.), Technology in mathematics teaching. Proceedings of ICTMT5 (pp.97-100). Mienna Oebv&hpt Verlagsgesellschaft.
  14. Kaput, J. J. (1992). Technology and mathematics education. In D. A Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.515-556). New York: Macmillan.
  15. Kindt, M. (1980). Als een kat om de hete algebrij, [As a cat around the algebra.] De Wiskrant Tijdschrift voor Nederlands Wiskundeonderwijs 5(21), 155-157.
  16. Malle, G. (1993). Didactical problems of elementary algebra. Wiesbaden, Germany: Vieweg.
  17. Parkhurst, S. (1979). Hand-held Calculators in the classroom: A review of the research. ERIC Document Reproduction Service No. ED200416.
  18. Rojano, T. (1996) The role of problems and problem solving in the development of algebra. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra, perspectives for research and teaching (pp.55-62). Dordrecht, Netherland: Kluwer Academic Publisgers.
  19. Schoenfeld, A. H. (1985). Metacognitive and epistemological issues in mathematical understanding. In E. A. Silver (Ed), Teaching and learning mathematical problem solving: Multiple research perspectives (pp.361-379). Hillsdale, NJ: Lawrence Erlbaum Associates.
  20. Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification-the case of algebra. Educational Studies in Mathematics 26, 191-228. https://doi.org/10.1007/BF01273663
  21. Tall, D., Thomas, M., Davis, G., Gray, E., & Simpson, A. (2000). What is the object of the encapsulation of a process? Jaournal of Mathematical Behavior 18, 223-241.
  22. Waerden, B. L. (1983). Geometry and algebra in andent civilisation. Berlin: Springer Verlag.
  23. Wagner, S. (1983). What are these things called variables? The Mathematics Teacher 76, 474-479.