Connecting Research and Practice: Teaching for Robust Understanding of Mathematics Framework in a Korean Mathematics Classroom Context

수학 교사교육 연구와 실천과제: 효과적인 수학 수업의 다섯 가지 필수 측면 프레임으로 분석한 고등학교 수열 단원 수업과 교사 전문성 신장에 대한 소고

  • Received : 2017.09.25
  • Accepted : 2017.11.10
  • Published : 2017.11.30

Abstract

This article reviews several classroom observational frameworks and introduces one of them, Teaching for Robust Understanding of Mathematics (TRU Math) framework, in more detail. The TRU Math framework has unique features, especially of which it helps researchers and practitioners analyze lessons with a focus on opportunities to learn and on how students access to the learning opportunities in mathematics classrooms rather than focusing on teacher behaviors. In this article, using this TRU Math framework, a Korean high school mathematics lesson was analyzed. The analysis illustrates the aspects of good mathematics teaching according to the five dimensions that we theorized. It provides implications on how to better use the tool for both research and practice in Korean school culture and teacher professional development contexts.

본 논문에서는 수학 교실 수업 관찰 프레임인 "효과적인 수학 수업의 다섯 가지 필수 측면 프레임"을 한국어로 소개하고, 이 프레임을 이용하여 한국의 고등학교 수업을 분석한 결과를 논의한다. 교사의 교수 행동에 초점을 맞추어 교사를 평가를 하였던 기존의 많은 수업 관찰 프레임에서 보여졌던 것과는 달리, "효과적인 수학 수업의 다섯 가지 필수 측면 프레임"은 교실 수업에서 학생들에게 어떤 질 좋은 배움의 기회를 제공하고 그 기회에 학생들이 참여하게 하는 지에 초점을 맞추고 있는 것이 큰 특징이다. 본 고에서는 단순히 이 프레임을 번역하여 소개하는 것이 아닌, 연구 수업 및 교사 공동체가 학교와 교사의 문화로 자리매김한 한국 상황에 맞게 적용하여 한국 고등학교 수업을 케이스 스터디로 분석한 것으로, 한국의 학교 문화에 적용할 수 있는 시사점을 제시하고 있다. 또한, 본 고의 말미에서는 "효과적인 수학 수업의 다섯 가지 필수 측면 프레임"의 다른 버전인 교사 전문성 신장 가이드를 이용하여 교사들과 교사 연수자들이 수학 교실 수업 개선을 목표로 하는 교사 전문성 신장에 관한 실천적 측면의 함의점을 논한다.

Keywords

References

  1. 구미영, 이광호(2015). 인지적 요구 수준 및 사고 수준의 발달방향에 따른 초등학교 길이 측정 단원의 수학과제 분석. 한국초등수학교육학회지, 19(3), 387-408.
  2. 김동원(2010). 우리나라 수학 수업 연구의 현황과 전망. 수학교육학연구, 20(2), 121-143.
  3. 김희정, 한채린, 배미선, 권오남(2017). 수학 교사의 주목하기와 반응적 교수의 관계: 모든 학생의 수학적 사고 계발을 지향하는 수업 상황에서. 수학교육, 56(3), 341-363.
  4. 방정숙(2012). 초등학교 수학 수업 어떻게 분석 할 것인가?-수학 수업 평가 기준의 활용 사례. 초등교과교육연구, 15, 109-140.
  5. 이경화(2002). 초등 수학 수업의 이해를 위한 관찰과 분석. 학교수학, 4(3), 435-461.
  6. 이은정, 이경화(2016). 교사의 사전 주목하기와 수학수업에서 실제 주목하기에 대한 연구. 학교수학, 18(4), 773-791.
  7. 주삼환(1998). 수업관찰과 분석: 장학과 교사의 수업의 질 향상을 위한. 서울: 원미사.
  8. 최승현, 임찬빈(2006). 수업평가 매뉴얼: 수학과 수업평가 기준. 한국교육과정평가원 연구자료. ORM 2006-24-5.
  9. 한국교육개발원(2000). 학교평가대상학교 교직원 연수 자료집. 한국교육개발원.
  10. Baldinger, E. Louie, N., and the Algebra Teaching Study and Mathematics Assessment Project. (2016). TRU Math conversation guide: A tool for teacher learning and growth (mathematics version). Berkeley, CA & E. Lansing, MI: Graduate School of Education, University of California, Berkeley & College of Education, Michigan State University.
  11. Borko, H., Eisenhart, M., Brown, C., Underhill, R., Jones, D., & Agard, P. (1992). Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give up Too Easily? Journal for Research in Mathematics Education 23(3). 194-222. https://doi.org/10.2307/749118
  12. Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B. and Perlwitz, M.: 1991, 'Assessment of a problem-centered second-grade mathematics project', Journal for Research in Mathematics Education 22(1), 3-29. https://doi.org/10.2307/749551
  13. Cohen, D., Raudenbush, S., & Ball, D. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 1-24. https://doi.org/10.3102/01623737025001001
  14. Council of Chief State School Officers. (2013). Interstate Teacher Assessment and Support Consortium InTASC Model Core Teaching Standards and Learning Progressions for Teachers 1.0: A Resource for Ongoing Teacher Development. Washington, DC: Author.
  15. Danielson, C. (2011). The Framework for Teaching evaluation instrument, 2011 Edition. http://www.danielsongroup.org/article.aspx?page=FfTEvaluationInstrument. http://www.danielsongroup.org/download/?download=448.
  16. Engle, R. A. (2011). The productive disciplinary engagement framework: Origins, key concepts and developments. In D. Y. Dai (Ed.), Design research on learning and thinking in educational settings: Enhancing intellectual growth and functioning (pp. 161-200). London: Taylor & Francis.
  17. Engle, R. A., & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20(4), 399-483 Franke, https://doi.org/10.1207/S1532690XCI2004_1
  18. Institute for Research on Policy Education and Practice. (2011). PLATO (Protocol for language arts teaching observations). Stanford, CA: Institute for Research on Policy Education and Practice.
  19. Junker, B., Matsumura, L. C., Crosson, A., Wolf, M. K., Levison, A., Weisberg, Y., & Resnick, L. (2004). Overview of the Instructional Quality Assessment. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.
  20. Kane, T. J. & Staiger, D. O. (2012). Gathering feedback for teaching: Combining high-quality observations with student surveys and achievement gains. Research Paper. MET Project. Bill & Melinda Gates Foundation.
  21. Kim, D. (2010). Current state and prospect of research about mathematics instruction in Korea. Journal of Educational Research in Mathematics. 20(2). 121-143.
  22. Kim, H. J. (2015). Teacher learning through practices: How mathematics teachers change in practices with innovative curriculum materials. Unpublished doctoral dissertation. University of California, Berkeley, Berkeley, CA.
  23. Kim, H., Han, C., Bae, M. S., & Kwon, O. N. (2017). The relationship between mathematics teachers' noticing and responsive teaching: In the context of teaching for all students' mathematical thinking. Journal of Korean Society of Mathematics Education Series A: The Mathematical Education. 56(3), 341-363.
  24. Ku, M. & Lee, K. (2015). Analyzing and restructuring mathematical tasks of length measurement in elementary school mathematics: Focused on 2nd Graders. Journal of Elementary Mathematics Education in Korea. 19(3), 387-408.
  25. Learning for Mathematics for Teaching (2006). A Coding Rubric for Measuring the Mathematical Quality of Instruction (Technical Report LMT1.06). Ann Arbor, MI: University of Michigan, School of Education.
  26. Lee, E. J. & Lee, K-H. (2016). A study on teacher's pre-noticing and actual noticing in mathematics classroom. Journal of Korean Society Educational Studies in Mathematics School Mathematics, 18(4). 773-791.
  27. Lee, K-H. (2002). Observation and analysis of elementary mathematics classroom discourse. Journal of Korean Society Educational Studies in Mathematics School Mathematics, 4(3). 435-461.
  28. MacQueen, K. M., McLellan, E., Kay, K., & Milstein, B. (1998). Codebook development for team-based qualitative analysis. Cultural Anthropology Methods, 10(2), 31-36.
  29. Marder, M., & Walkington, C. (2012) UTeach Teacher Observation Protocol. https://wikis.utexas.edu/pages/viewpageattachments.action?pageId=6884866&sortBy=date&highlight=UTOP_Physics_2009.doc.&.
  30. Measures of Effective Teaching Project (2012). Gathering Feedback for Teaching. http://metproject.org/downloads/MET_Gathering_Feedback_Research_Paper.pdf
  31. Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage Publications.
  32. National Governors Association Center for Best Practices and Councile of Chief State School Officiers (NGA & CCSSO). (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.
  33. PACT Consortium (2012) Performance Assessment for California Teachers. (2012) A brief overview of the PACT assessment system. http://www.pacttpa.org/_main/hub.php?pageName=Home.
  34. Peressini, D., & Knuth, E. (1998). 'Why are you talking when you could be listening? The role of discourse in the professional development of mathematics teachers', Teaching and Teacher Education. 14(1), 107-125. https://doi.org/10.1016/S0742-051X(97)00064-4
  35. Pianta, R., La Paro, K., & Hamre, B. K. (2008). Classroom assessment scoring system. Baltimore: Paul H. Brookes.
  36. Richardson, V. (2003). The dilemmas of professional development. Phi Delta Kappan, (January), 401-406.
  37. Schoenfeld, A. H. (2011). How we think: A theory of goal-oriented decision making and its educational applications. New York: Routledge.
  38. Schoenfeld, A. H. (2013). Classroom observations in theory and practice. ZDM, 45(4), 607-621. https://doi.org/10.1007/s11858-012-0483-1
  39. Schoenfeld, A. H. (2014). What makes for powerful classrooms, and how can we support teachers in creating them? Educational Researcher, 43(8), 404-412. https://doi.org/10.3102/0013189X14554450
  40. Schoenfeld, A. H. (2015). Thoughts on scale. ZDM, 47(1), 161-169. https://doi.org/10.1007/s11858-014-0662-3
  41. Schoenfeld, A. H. (July 23, 2017). Personal communication.
  42. Schoenfeld, A. H. (November 2, 2017). Personal communication.
  43. Schoenfeld, A. H. (in press). In C. Y. Charalambous and A.-K. Praetorius (Eds.), Studying Instructional Quality in Mathematics through Different Lenses: In Search of Common Ground. An issue of ZDM: Mathematics Education.
  44. Schoenfeld, A. H., & the Teaching for Robust Understanding Project. (2016a). An Introduction to the Teaching for Robust Understanding (TRU) Framework. Berkeley, CA: Graduate School of Education. Retrieved from http://map.mathshell.org/trumath.php or http://tru.berkeley.edu.
  45. Schoenfeld, A. H., and the Teaching for Robust Understanding Project. (2016b). The Teaching for Robust Understanding (TRU) observation guide for mathematics: A tool for teachers, coaches, administrators, and professional learning communities. Berkeley, CA: Graduate School of Education, University of California, Berkeley.
  46. Smith, M. S., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.
  47. Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development. Second Edition. Reston, VA: Teachers College Press.
  48. Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. New York: The Free Press.
  49. University of Michigan (2006). Learning mathematics for teaching. A coding rubric for measuring the mathematical quality of instruction (Technical Report LMT1.06). Ann Arbor, MI: University of Michigan, School of Education.
  50. Yin, R. K. (2009). Case study research: Design and Methods. SAGE publications. Thousand oaks.