Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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An Analysis of Understanding Level of High School Students Shown in Trigonometric Functions

삼각함수에 대한 고등학생들의 이해 층위 분석

  • Received : 2019.07.19
  • Accepted : 2019.08.27
  • Published : 2019.09.30
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Abstract

In this study, using the tasks related trigonometric functions, the degree of high school students' understanding of the function concept was examined through the level of Hitt(1998). First, the degree of the students' understanding was classified by level, then the concept understanding was reclassified by the process or the object. As a result, high school students' concept understanding showed incompleteness in three stages. It was possible to know that the process in the interpretation of the graph is the main perspective, and the operation of algebraic representation is regarded as important. Based on these results, it seems necessary to study the teaching-learning method which can understand trigonometric functions from various perspectives. It seems necessary to study a lesson model that can reach function concept's understanding level 5 that maintains consistency between problem solving and representation system.

본 연구는 삼각함수와 관련된 과제를 통해 고등학교 학생들의 함수 개념 이해 정도를 Hitt(1998)의 층위 분석을 통해 살펴보았다. 우선 학생들의 함수 이해 정도를 층위 분석을 통해 단계를 구분한 후 이해 관점을 과정과 대상 관점으로 다시 분류하였다. 그 결과 고등학교 학생들의 함수 개념 이해의 정도 층위는 3단계에서 불완전성을 보였다. 그리고 함수의 이해의 관점은 그래프 해석에서 과정 관점이 주를 이루고 있으며 대수적 표상의 조작이 중요시되고 있음을 알 수 있었다. 이러한 결과를 바탕으로 삼각함수를 다양한 관점으로 이해할 수 있는 교수-학습 방법에 대한 연구와 함께 문제 해결과 그에 따른 표상 체계 사이의 일관성이 유지되는 함수 개념 이해 층위 5단계에 도달할 수 있는 수업모델의 연구가 필요할 것으로 보인다.

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References

  1. Bannister, V. R. P. (2014). Flexible conceptions of perspectives and representations: an examination of pre-service mathematics teachers' knowledge. International Journal of Education in Mathematics, Science and Technology, 2(3), 223-233.
  2. Despina, A. S. (2011). An examination of middle school students' representation practices in mathematical problem solving through the lens of expert work: towards an organizing scheme. Educational Studies Mathematics, 265-280.
  3. Dreyfus, T. & Vinner, S. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356-366. https://doi.org/10.2307/749441
  4. Dubinsky, E. & Harel, G. (1992). The nature of process of function. In E. Dubinsky, & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (MAA Notes No. 25, pp. 85-106). Washington, DC: Mathematical Association of America.
  5. Eisenberg, T. (1992). On the development of a sense for functions. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 153-174). Mathematical Association of America.
  6. Even, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17(1), 105-121. https://doi.org/10.1016/S0732-3123(99)80063-7
  7. Friedlender, A. & Tabach, M. (2001). Promoting multiple representation in algebra, In A. A. Cuoco (Ed.), The roles of representation in school mathematics. Reston, VA: NCTM.
  8. Goldin, G. A. (1987). Cognitive representational systems for mathematical problem solving. In Claude Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 125-146). Hillsdale, New Jersey: Lawrence Erlbaum Associates.
  9. Hitt, F. (1998). Difficulties in the articulation of different representations linked to the concept of function. The Journal of Mathematical Behavior, 17(1), 123-134. https://doi.org/10.1016/S0732-3123(99)80064-9
  10. Hitt, F. & Gonzalez-Martin, A, S. (2015). Covariation between variables in a modelling process: The ACODESA(collaborative learning, scientific debate and self-reflection) method. Educational Studies Mathematics, 201-219.
  11. Janvier, C. (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Erlbaum.
  12. Kleiner, I. (1989). Evolution of the function concept: A brief survey. College Mathematics Journal, 20, 282-300. https://doi.org/10.1080/07468342.1989.11973245
  13. Lamon, S. J. (2001). Presenting and representing: From fractions to rational numbers. In A. Cuoco (Ed.), The roles of representation in school mathematics. 2001 Yearbook of the National Council of Teachers of Mathematics (pp. 41-52). Reston, VA: National Council of Teachers of Mathematics.
  14. Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In Claude Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, New Jersey: Lawrence Erlbaum Associates.
  15. Monk, G. S. (1988). Students' understanding of functions in calculus courses. Humanistic Mathematics Network Newsletter, 2.
  16. Moschkovich, J., Schoenfeld, A., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations and connections among them. In T. Romberg, E. Fennema, & T. Carpenter (Eds.), Integrating research on the graphical representation of function (pp. 69-100). Hillsdale, NJ: Lawrence Erlbaum Associates.
  17. NCTM. (2000). Principles and standards for school mathematics. Reston, VA: The Author.
  18. Romberg, T., Fennema, E., & Carpenter, T. (1993). Toward a common research perspective. In T. Romberg, E. Fennema & T. Carpenter (Eds.), Integrating research on the graphical representation of function. Hillsdale, NJ: Lawrence Erlbaum Associates.
  19. Schnotz, W. & Bannert, M. (2003). Construction and interference in learning from multiple representations. Learning and Instruction, 13, 141-156. https://doi.org/10.1016/S0959-4752(02)00017-8
  20. Selden, A. & Selden, J. (1992). Research perspectives on conceptions of fuction summary and overview. In E. Dubinsky, & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (MAA Notes No. 25, pp. 133-150). Washington, DC: Mathematical Association of America.
  21. Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification-the case of function. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspect of epistemology and pedagogy (pp. 59-84). Washington DC: MAA.
  22. Tall, D. (2013). How humans learn to think mathematically: Exploring the three worlds of mathematics. Cambridge University Press.
  23. Yerushalmy, M. & Schwartz, J. (1993). Seizing the opportunity to make algebra mathematically and pedagogically interesting. In T. Romberg, E. Fennema, & T. Carpenter (Eds.), Integrating research on the graphical representation of function (pp. 69-100). Hillsdale, NJ: Lawrence Erlbaum Associates.
  24. Yerushalmy, M. & Swidan, O. (2012). Signifying the accumulation graph in dynamic and multi-representation environment. Educational Studies Mathematics, 80, 287-306. https://doi.org/10.1007/s10649-011-9356-8