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변수 개념에 대한 중등 예비교사들의 노티싱

Prospective Teachers' Noticing about Concept of Variables

  • 투고 : 2021.07.21
  • 심사 : 2021.09.23
  • 발행 : 2021.09.30

초록

본 연구는 예비교사가 변수와 관련된 학생의 사고를 어떻게 파악하고 대응하는지를 조사하는 것을 목적으로 하였다. 변수와 관련된 학생들의 사고를 추론하여 그에 따른 지도방안을 제시해 보게 하는 문항에서 예비교사의 주목하기와 해석하기의 특징을 동시에 살펴보았으며 주목하기와 해석하기에 따라 예비교사의 대응하기가 어떻게 제안되었는지 그 특징을 조사하였다. 예비교사 26명의 응답을 분석한 결과, 예비교사들이 학생들의 응답에서 나타나는 변수에 대한 오개념에 주목하기가 쉽지 않음을 보여주었으며, 주목은 하였으나 적절한 해석을 해내지 못한 경우를 확인할 수 있었다. 주목하지 못하고 해석하지 못한 대부분 예비교사는 변수에 대한 전반적인 이해의 부족으로 인해 적절한 대응을 제시하지 못한 것으로 나타났으며, 주목하기와 해석하기가 성공적으로 이루어졌다 하더라도 경험적 지식의 부족으로 인해 적절한 대응을 제시하지 못하였다. 연구 결과를 바탕으로, 예비교사 교육에 주는 시사점을 논의하였다.

This study investigated the prospective teacher's noticing of students' mathematical thinking from the perspective of how the prospective teacher pays attention to, interprets, and responds to the student's responses related to variables. The prospective teachers were asked to infer the students' thinking from the variables related to the tasks and suggest feedback accordingly. An analysis of the responses of 26 prospective teachers showed that it was not easy for prospective teachers to pay attention to the misconception of variables and that some of them did not make proper interpretations. Most prospective teachers who did not attend and interpret were found to have failed to provide an appropriate response due to a lack of overall understanding of variables. even though prospective teachers who did proper attend and interpret were found to have failed to respond appropriately due to a lack of empirical knowledge, even with proper attention and interpretation.

키워드

참고문헌

  1. Kim, N. H. (1997a). A study of the notion of variable and the understanding of algebraic expressions, Journal of Educational Research in Mathematic, 1(1), 93-105.
  2. Kim, N. H. (1997b). Didactical analysis of variable concept and search for the direction of its learning-teaching(Doctoral dissertation). Seoul National University, Seoul. Korea.
  3. Kim, N. H. (1999). On some teaching problem related to the learning of variable concept in school mathematics, School Mathematics, 1(1), 19-37.
  4. Kim, D.-J., Choi, S.-H., & Lee, J.-H. (2020). An analysis of pre-service teachers' cognition in curriculum for developing their discursive competency, Communications of Mathematical Education, 34(2), 41-68.
  5. Sunwoo, J., & Pang, JS. (2020). How do prospective elementary school teacher response to students' mathematical thinking? The journal of educational research in mathematics. 30(4), 751-772. https://doi.org/10.29275/jerm.2020.11.30.4.751
  6. Song, U. B. (2003). A study on understanding concerning the concept of variable and cognitive obstacles in middle school third year students, Master's thesis, Korea national university of education, Chung-buk, Korea.
  7. Yang, H. J. (2003). (A) Study on the teaching of the concepts of variables using excel, Master's thesis, Korea national university of education, Chung-buk, Korea.
  8. Lee Y. M., & Lee, S. J. (2018). Prospective secondary mathematics teachers' noticing in lesson evaluation and lesson reflection. School Mathematics, 20(1), 185-207. https://doi.org/10.29275/sm.2018.03.20.1.185
  9. Lee, E-J., & Park, M. (2018). Exploring Prospective Elementary Teachers' Ability to Notice, The journal of educational research in mathematics, 28(4), 417-435. https://doi.org/10.29275/jerm.2018.11.28.4.417
  10. Lee, J. M. (2010). An analysis of middle school teacjers' knowledge of student understanding about equal sign concept and variable concept,. Master's thesis, Korea national university of education, Chung-buk, Korea.
  11. Lee J. A., & Lee, S. J. (2019). Mathematical noticing of two prospective secondary mathematics teachers in the course of planning, implementin, and reflecting on lessons. School Mathematics, 21(3), 561-589. https://doi.org/10.29275/sm.2019.09.21.3.561
  12. Woo. J. H. (2017). Educational principle for School mathematics(I). Seoul: SNU press.
  13. Lee, J. K., & Rhee, J. S. (2008). Investigation of understanding avility for the high school first grade students in the variable concept, Journal of natural science research institute for natural science, 9, 25-45.
  14. Yim, M-S. (2007). A study on the actual sate of middle school 2nd and 3rd garder understanding of the concept of variables, Master's thesis, Korea national university of education, Chung-buk, Korea.
  15. Che, E. J. (1995). A study of notice the errors within the use of letters, Master's thesis, Ewha women university, Seoul, Korea.
  16. Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, P. (2007) Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272. https://doi.org/10.1080/10986060701360910
  17. Ball, D. (2011). Foreword. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.), Mathematics teacher noticing (pp. 35-50). New York: Routledge.
  18. Boz, N. (2002). Prospective teachers' subject matter and pedagogical content knowledge of variables. Proceedings of British Society for Research into Learning Mathematics, 22(3), Retrieved from http://www.bsrlm.org.uk/informalproceedings.html.
  19. Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers' noticing of students' understandings of pattern generalization. Journal of Mathematics Teacher Education, 20, 309-333. https://doi.org/10.1007/s10857-016-9343-1
  20. Dogbey, J. (2015). Using Variables in School Mathematics: Do School Mathematics Curricula Provide Support for Teachers? International Journal of Science and Mathematics Education, 14(6), 1175-1196. https://doi.org/10.1007/s10763-015-9643-4
  21. Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94-116. https://doi.org/10.2307/749215
  22. Fernandez, C., Llinares, C., & Valls, J. (2011). Development of prospective mathematics teachers" professional noticing in a specific domain: proportional reasoning. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 329-336). Ankara, Turkey: PME.
  23. Fernandez, C., Llinares, S., & Valls, J. (2013). Primary school teacher's noticing of students' mathematical thinking in problem solving. The Mathematics Enthusiast, 10, 441-467 https://doi.org/10.54870/1551-3440.1274
  24. Freudenthal, H. (1983) Didactical phenomenology of mathematical structures. Defunct: D. Reidel Publishing.
  25. Graham, A., & Thomas, M. (2000). Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics, 41, 265-282. https://doi.org/10.1023/A:1004094013054
  26. Jacobs, V. R., Lamb, L. C., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41, 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
  27. Knuth, E. J., Alibali, M. W., Weinberg, A., McNeil, N. M., & Stephens, A. C. (2005). Middle school students' understanding of core algebraic concepts: Equivalence and variable. ZDM, 37, 68-76.
  28. Lee, M. Y. (2021). Using a technology tool to help pre-service teachers notice students' reasoning and errors on a mathematics problem. ZDM Mathematics Education, 53, 135-149. https://doi.org/10.1007/s11858-020-01189-z
  29. Mason, J. (2011). Noticing: roots and branches. In M. G. Sherin, V. R. Jacobs & R. A. Philipp. (Eds.) Mathematics teacher noticing (pp. 17-34). New York: Routledge.
  30. Mohr, D. J. (2008). Pre-service elementary teachers make connections between geometry and algebra through the use of technology. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 3. Retrieved from http://www.k-12prep.math.ttu.edu/journal/journal.shtml.
  31. Sanchez-Matamoros, G., Fernandez, C., & Llinares, S. (2019). Relationships among prospective secondary mathematics teachers' skills of attending, interpreting and responding to students' understanding. Educational Studies in Mathematics, 100, 83-99. https://doi.org/10.1007/s10649-018-9855-y
  32. Sherin, G. M., Jacobs, V. R., & Philipp, R. A. (2011). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.) Mathematics teacher noticing (pp. 3-13). New York: Routledge.
  33. Star, J. R., & Lynch, K., & Perova, N. (2011). Using video to improve preservice mathematics teachers' abilities to attend to classroom teachers: a replication study. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.) Mathematics teacher noticing (pp. 117-133). New York: Routledge.
  34. Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers'ability to notice. Journal of Mathematics Teacher Education, 11, 107-125. https://doi.org/10.1007/s10857-007-9063-7
  35. Usiskin, Z. (1999). Conceptions of school algebra and use of variables. In M. Barbara (Ed.) Algebraic Thinking, Grades K-12: Readings from NCTM's School-Based Journals and Other Publications (pp. 7-13). Reston, Va.: National Council of Teachers of Mathematics,
  36. van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.), Mathematics teacher noticing (pp. 134-151). New York: Routledge.
  37. van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers "learning to notice" in the context of a video club. Teaching and Teacher Education, 24, 244-276. https://doi.org/10.1016/j.tate.2006.11.005