East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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Teacher Education for Mathematical Modeling: a Case Study

수학적 모델링의 구현을 위한 교사 교육: 사례 연구

  • Received : 2019.10.28
  • Accepted : 2020.02.22
  • Published : 2020.02.29
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Abstract

Mathematical modeling has been emphasized because it offers important opportunities for students to both apply their learning of mathematics to a situation and to explore the mathematics involved in the context of the situation. However, unlike its importance, mathematical modeling has not been grounded in typical mathematics classes because teachers do not have enough understanding of mathematical modeling and they are skeptical to implement it in their lessons. The current study analyzed the data, such as video recordings, slides, and surveys for teachers, collected in four lessons of teacher education in terms of mathematical modeling. The study reported different kinds of tasks that are authentic with regards to mathematical modeling. Furthermore, in teacher education, teachers' identities have separated a mode as learners and a mode as teachers and conflicts and intentional transition were observed. Analysis of the surveys shows what teachers think about mathematical modeling with their understanding of it. In teacher education, teachers achieved different kinds of modeling tasks and experience them which are helpful to enact mathematical modeling in their lessons. However, teacher education also needs to specifically offer what to do and how to do it for their lessons.

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References

  1. 김민경, 민선희, 강선미(2009). 초등교사들의 수학적 모델링에 대한 인식 조사 연구. 한국학교수학회논문집, 12(4), 411-431.
  2. 박경미, 박선화, 권점례, 윤상혁, 강현영, 이경진, . . . 전인태(2015). 2015 개정 수학과 교육과정 시안 개발 연구 (연구보고 BD15110002). 서울, 한국: 한국과학창의재단.
  3. 박선영, 한선영(2018). 수학적 모델링 과정을 반영한 교과서 문제 재구성 예시 및 적용. 수학교육, 57(3), 289-309.
  4. 서지희, 윤종국, 이광호(2013). 중학교 3학년 수학 영재 학생들을 위한 수학적 모델링 교수 학습 자료의 개발 및 적용: 쓰나미를 소재로. 학교수학, 15(4), 785-799.
  5. 신은주, & 이종희(2004). 모델링 과정에서 지각적, 인지적, 메타인지적 활동의 상호작용에 관한 사례연구. 학교수학, 6(2), 153-179.
  6. 오영열, 박주경(2019). 초등수학에 적용된 수학적 모델링 과제 유형 탐색, 한국초등교육, 30(10), 87-99.
  7. 조원주, 권오남(2002). 중학교 함수영역에서 수학적 모델링을 활용한 수행과제와 구체적 평가기준안 개발. 수학교육 논문집, 14, 349-370.
  8. 최지선(2017). 수학적 모델링 수업에 대한 초등 교사의 인식. 수학교육학연구, 27(2), 313-328.
  9. 최희선, 한혜숙(2018). 수학적 모델링 기반 수업이 중학교 1학년 학생들의 수학적 문제제기 능력에 미치는 영향. 학습자중심교과교육연구, 18(14), 755-782.
  10. 황혜정(2007). 수학적 모델링의 이해: 국내 연구 결과 분석을 중심으로. 학교수학, 9(1), 65-97.
  11. Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19(6), 523-545. https://doi.org/10.1007/s10857-015-9309-8
  12. 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
  13. Beijaard, D., Meijer, P. C., & Verloop, N. (2004). Reconsidering research on teachers' professional identity. Teaching and Teacher Education, 20(2), 107-128. https://doi.org/10.1016/j.tate.2003.07.001
  14. Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
  15. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects: State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68. https://doi.org/10.1007/BF00302716
  16. Boaler, J. (2001). Mathematical modelling and new theories of learning. International Journal of the IMA, 20(3), 121-128.
  17. Boaler, J., & Brodie, K. (2004). The importance, nature, and impact of teacher questions. Paper presented at the Proceedings of the twenty-sixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
  18. Borko, H., Liston, D., & Whitcomb, J. A. (2007). Genres of empirical research in teacher education. Journal of Teacher Education, 58(1), 3-11. https://doi.org/10.1177/0022487106296220
  19. Chan, E. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47-66.
  20. Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119-142. https://doi.org/10.3102/01623737025002119
  21. Connelly, F. M., & Clandinin, D. J. (1999). Shaping a professional identity: Stories of educational practice. London, ON: The Althouse Press.
  22. Doerr, H. M., & Lesh, R. (2003). A modeling perspective on teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 125-140). Mahwah, NJ: Lawrence Erlbaum Associates.
  23. English, L. (2003). Mathematical modelling with young learners. In S. J. Lamon, W. A. Parker, & K. Houston (Eds.), Mathematical modelling (pp. 3-17). West Sussex, England: Woodhead Publishing.
  24. Ferri, R. B. (2013). Mathematical modeling-The teacher's responsibility. In B. Dickman & A. Sanfratello (Eds.), Proceedings of Converence on Mathematical Modeling (pp. 26-31). New York, NY: Teachers College Columbia University.
  25. Ferri, R. B., & Blum, W. (2009). Mathematical modelling in teacher education-Experiences from a modelling seminar. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of CERME 6 (pp. 2046-2055). Lyon, France: European Society for Research in Mathematics Education.
  26. Ferri, R. B., & Blum, W. (2013). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons. Paper presented at the Congress of European Research in Mathematics Education.
  27. Flores, M. A., & Day, C. (2006). Contexts which shape and reshape new teachers' identities: A multi-perspective study. Teaching and Teacher Education, 22(2), 219-232. https://doi.org/10.1016/j.tate.2005.09.002
  28. Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199-219. https://doi.org/10.1007/s10857-007-9070-8
  29. Gee, J. P. (2000). Identity as an analytic lens for research in education. Review of Research in Education, 25(1), 99-125. https://doi.org/10.3102/0091732X025001099
  30. Guest, G., MacQueen, K., & Namey, E. (2012). Applied thematic analysis. Thousand Oaks, CA: Sage.
  31. Hewson, P. W., & A'B. Hewson, M. G. (1988). An appropriate conception of teaching science: A view from studies of science learning. Science Education, 72(5), 597-614. https://doi.org/10.1002/sce.3730720506
  32. Jung, H., & Brady, C. (2016). Roles of a teacher and researcher during in situ professional development around the implementation of mathematical modeling tasks. Journal of Mathematics Teacher Education, 19(2-3), 277-295. https://doi.org/10.1007/s10857-015-9335-6
  33. Lesh, R., & Doerr, H. M. (2000). Symbolizing, communicating, and mathematizing: Key components of models and modeling. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 361-383). Mahwah, NJ: Lawrence Erlbaum Associates.
  34. Lesh, R., & Doerr, H. M. (2003a). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum Associates.
  35. Lesh, R., & Doerr, H. M. (Eds.). (2003b). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum Associates.
  36. Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2&3), 157-189. https://doi.org/10.1080/10986065.2003.9679998
  37. Lytle, S. L., & Cochran-Smith, M. (1994). Inquiry, knowledge, and practice. Teacher research and educational reform, 93, 22-51.
  38. MacLure, M. (1993). Arguing for your self: Identity as an organising principle in teachers' jobs and lives. British Educational Research Journal, 19(4), 311-322. https://doi.org/10.1080/0141192930190401
  39. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  40. National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington D.C.: National Governors Association Center for Best Practices, Council of Chief State School Officers.
  41. Olsen, B. (2008). Teaching what they learn, learning what they live. Boulder, CO: Paradigm Publishers.
  42. Pollak, H. (2007). Mathematical modelling - a conversation with Henry Pollak. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics Education: The 14th ICMI Study (pp. 109-120). Boston, MA: Springer.
  43. Saldana, J. (2013). The coding manual for qualitative researchers (2 ed.). Los Angeles: SAGE
  44. Schorr, R. Y., & Lesh, R. (2003). A modelling approach for providing teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivismen - Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 141-157). Mahwah, NJ: Lowrence Erlbaum Associates.
  45. Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14-22. https://doi.org/10.3102/0013189X034004014
  46. Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.
  47. 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(2), 455-488. https://doi.org/10.3102/00028312033002455
  48. Swetz, F., & Hartzler, J. S. (1991). Mathematical modeling in the secondary school curriculum. Reston, VA: National Council of Teachers of Mathematics.
  49. Thomas, L., & Beauchamp, C. (2007). Learning to live well as teachers in a changing world: Insights into developing a professional identity in teacher education. The Journal of Educational Thought, 41(3), 229-243.
  50. Zawojewski, J. (2013). Problem solving versus modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students'mathematical modeling competencies: ICTMA 13 (pp. 237-243). Dordrecht: Springer Netherlands.
  51. Zbiek, R. M., & Conner, A. (2006). Beyond motivation: exploring mathematical modeling as a context for deepening students' understandings of curricular mathematics. Educational Studies in Mathematics, 63(1), 89-112. https://doi.org/10.1007/s10649-005-9002-4