Measuring and Analyzing Prospective Secondary Teachers' Mathematical Knowledge for Teaching [MKT]

예비교사들의 수학교수지식(MKT) 측정 및 분석 연구

  • Received : 2015.10.12
  • Accepted : 2015.11.15
  • Published : 2015.11.30

Abstract

This study explored preservice secondary mathematics teachers' mathematical knowledge for teaching [MKT]. In order to measure preservice teachers' MKT, we developed items according to Ball, Thames & Phelps (2008)'s domains and conducted to 53 preservice teachers. Also, we interviewed 1 preservice teacher with the items and a set of interview questions. The findings from the data analysis suggested as follows: a) overall, the preservice teachers scored average 30.2 out of 100; b) the preservice teachers appeared to be unable to explain students' difficulties in learning a specific mathematical idea and how they would respond to and resolve such difficulties.

이 연구에서는 중등 예비교사들의 교수를 위한 수학적 지식(Mathematical Knowledge for Teaching, 이하 MKT) 수준을 검증할 수 있는 문항 개발을 확장하여서 이를 적용한 측정을 통해 중등 예비수학교사들의 MKT 수준이 어떠한지 알아보고자 한다. 이를 위해 중학교 수준의 수학 영역에 대한 검사 문항을 개발하여 예비교사 54명을 상대로 검사를 실시하여 자료를 수집하여 분석하였다. 자료 분석 결과 예비교사들이 얻은 점수를 백점 만점으로 환산 시 검사지 총점의 평균은 30.2점으로 나타났는데, 예비교사들은 대체로 문항에서 나타내는 학습 내용에 관한 지식을 정확히 이해하지 못하는 것으로 나타났으며 중등학생들이 어려워하는 부분과 이에 대한 정확한 설명 방법을 구체적으로 도입하지 못하는 것으로 나타났다. 교수 방법을 제시하고 설명하는 과정에서도 내용의 본질을 충분히 담지 못하며 학습자에 대해서도 일반적으로 관찰할 수 있는 특성을 기술하는 것으로 나타났다.

Keywords

References

  1. 고희정.고상숙(2013). 고등학교 미적분 수업에서 나타나는 초임교사의 교수를 위한 전문화된 수학내용 지식(SCKT). 한국학교수학회논문집, 16(1), 157-185.
  2. 권지현.김구연(2013). 중학교 수학 교과서에 제시된 기하영역의 수학 과제 분석. 수학교육, 52(1), 111-128.
  3. 김구연(2011). How teachers use mathematics curriculum materials in planning and implementing mathematics lessons. 학교수학, 13(3), 485-500.
  4. 김미희.김구연(2013). 고등학교 교과서의 수학과제 분석. 학교수학, 15(1), 37-59.
  5. 김대영.김구연(2014). 중등 수학교사의 교과서 수학과제 이해 및 변형 능력. 학교수학, 16 (3), 45-469.
  6. 김민혁(2013). 수학 교사의 교과서 및 교사용 도서 활용도 조사. 학교수학, 15(3), 503-531.
  7. 김영천(201). 질적연구방법론. 서울: 문음사.
  8. 노선숙, 김래영, 김구연, 김민경, 고정숙, 권혜란, 김기영, 김도희, 김민연, 박미영, 박석순, 박지원, 이민희, 이선비, 이아름, 이일웅, 이현희, 전지훈, 정빛나(2013a). 수학과 서술형 논술형 평가의 실제 중학교 2학년. 서울: 경문사.
  9. 노선숙, 김구연, 김래영, 김민경, 고정숙, 권혜란, 김기영, 김도희, 김민연, 박미영, 박석순, 박지원, 이민희, 이선비, 이아름, 이일웅, 이현희, 전지훈, 정빛나(2013b). 수학과 서술형 논술형 평가의 실제 중학교 3학년. 서울: 경문사.
  10. 문진수.김구연(2015). 중등 수학교사의 함수에 대한 지식(MKT) 측정 및 분석. 학교수학, 17(3), 469-492.
  11. 방정숙.Yeping Li(2008). 예비 초등 교사들의 분수 나눗셈에 대한 지식. 수학교육, 47(3), 291-301.
  12. 서관석.전경순(2000). 예비 초등 교사들의 분순연산에 관한 내용적 지식과 교수학적 지식수준에 대한 연구: 교사교육적 관점. 수학교육학연구, 10(1), 103-114.
  13. 이승훈.조완영(2013). 수학교사의 이차곡선에 관한 내용지식의 분석. 학교수학, 15(4), 995-1013.
  14. 이혜림.김구연(2013). 수학교과서 문제에 대한 예비중등교사의 이해 및 변형 능력. 수학교육학연구, 23(3), 353-371.
  15. 홍창준.김구연(2012). 중학교 함수 단원의 수학과제 분석. 학교수학, 14(2), 213-232.
  16. Ball, D. L., Hill, H. C., Rowan, B., & Schilling, S. (2002). Measuring teachers' content knowledge for teaching: Elementary mathematics release items, 2002. Ann Arbor, MI: Study of Instructional Improvement.
  17. Ball, D. L., Hill, H. C., & Schilling, S. G. (2004). Developing measures of teachers' mathematics knowledge for teaching. Elementary School Journal, 105(1), 11-30. https://doi.org/10.1086/428763
  18. Ball, D. L., Lewis, J., & Thames, M. H. (2008). Making mathematics work in school. Journal for Research in Mathematics Education, Monograph 14, 13-44.
  19. Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers' mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433-456). Washington, DC: American Educational Research Association.
  20. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  21. Collopy, R. (2003). Curriculum Materials as a professional development tool: How a mathematics textbook affected two teachers' learning. Elementary School Journal, 103, 287-311. https://doi.org/10.1086/499727
  22. Cooney, T. J., Wittman, E. C., Schrage, G., Dossey, J., & Brawn, S. I. (1996). Mathematics, pedagogy, and secondary teacher education. Portsmouth, NH: Heinemann.
  23. Cooney, T. J., Beckmann, S., & Lloyd, G. M. (2010). Developing essential understanding of functions for teaching mathematics in grade 9-12. Reston, VA.: National Council of Teachers of Mathematics.
  24. Copur-Gencturk, Y. (2015). The effects of changes in mathematical knowledge on teaching: A longitudinal study of teachers' knowledge and instruction. Journal for Research in Mathematics Education, 46, 280-330. https://doi.org/10.5951/jresematheduc.46.3.0280
  25. Cramer, K. (2004). Facilitating teachers' growth in content knowledge. In R. Rubenstein (Ed.), Implementing the teacher principle: 2004 yearbook. Reston, VA: National Council of Teachers of Mathematics.
  26. Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.
  27. Grouws, G. A., Tarr, J. E., Chavez, O., Sears, R., Soria, V. M., & Taylan, R. D. (2013). Curriculum and implementation effects on high school students' mathematics learning from curricula representing subject-specific and integrated content organizations. Journal for Research in Mathematics Education, 44, 416-463. https://doi.org/10.5951/jresematheduc.44.2.0416
  28. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524-549. https://doi.org/10.2307/749690
  29. Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 377-406.
  30. Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers'mathematics knowledge for teaching. Elementary School Journal, 105, 11-30. https://doi.org/10.1086/428763
  31. Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers'mathematical knowledge: What knowledge matters and what evidence counts? In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111-155). Charlotte, NC: Information Age.
  32. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400.
  33. Izsak, A., Jacobson, E., de Araujo, Z., & Orrill, C. H. (2012). Mathematical Knowledge for Teaching Fractions with Drawn Quantities. Journal for Research in Mathematics Education, 43(4), 391-427. https://doi.org/10.5951/jresematheduc.43.4.0391
  34. Keiser, J. M. (2000). The role of definition. Mathematics Teaching in the Middle School, 506-11.
  35. Kvale, S. (1996). Interviews: An introduction to qualitative research interviewing. Thousand Oaks, CA: Sage.
  36. Lamon, S. J. (2012). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. New York: Routledge.
  37. Lloyd, G. M., Herbel-Eisenmann, B., & Star, J. R. (2011). Developing essential understanding of functions for teaching mathematics in grade 6-8. Reston, VA.: National Council of Teachers of Mathematics.
  38. McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S. L. (2012). Knowledge of algebra for teaching: A framework of knowledge and practices. Journal for Research in Mathematics Education, 43(5), 584-615. https://doi.org/10.5951/jresematheduc.43.5.0584
  39. Mertler, C. A. (2009). Teachers' assessment knowledge and their perceptions of the impact of classroom assessment professional development. Improving Schools, 12(2), 101-113. https://doi.org/10.1177/1365480209105575
  40. National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: Author.
  41. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA.: Author.
  42. Posamentier, A. S., Smith, B. S., & Stepelman, J. (2010). Teaching secondary mathematics: techniques and enrichment. Boston, MA: Allyn & Bacon.
  43. Remillard, J. T., & Bryans, M. B. (2004). Teachers' orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35, 352-388. https://doi.org/10.2307/30034820
  44. Sanchez, W. B. (2013). Open-ended questions and the process standards. Mathematics Teacher, 107(3), 206-211. https://doi.org/10.5951/mathteacher.107.3.0206
  45. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.2307/1175860
  46. Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33, 455-488. https://doi.org/10.3102/00028312033002455
  47. Stein, M. K., & Smith, M. S. (2010) The influence of curriculum on students' learning. In B. J. Reys, R. E. Reys & R. Rubenstein (Eds.), Mathematics curriculum: Issues, trends, and future directions (pp. 351-362). Reston, VA: National Council of Teachers of Mathematics.