School Mathematics (대한수학교육학회지:학교수학)

The Korea Society of Educational Studies in Mathematics (대한수학교육학회)
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Characteristics of Teachers' Questioning to Formulate an Effective Mathematics Discourse

효과적인 수학적 담론을 구축하기 위한 교사 질문활동의 특성

  • Received : 2016.02.10
  • Accepted : 2016.03.11
  • Published : 2016.03.31
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Abstract

Teachers' questioning plays an important role in mathematics teaching and learning by asking students to react or to participate in mathematical discourse. Previous studies on teachers' questioning have not focused on how to questioning to formulate an effective mathematical discourse which is contributed by students because studies mostly analyzed and categorized teachers' questions according to cognitive levels of questions without consideration of context. Therefore, this study explored characteristics of teachers' questioning to formulate an effective characteristics of teachers' questioning to formulate an effective mathematical discourse in mathematics classrooms. By reviewing and analyzing mathematics discourse and studies on teachers' questioning theoretically, we presented openness, sharedness, and productivity as characteristics of teachers' questioning. Through a middle school mathematics teacher's case, we examined three characteristics were necessary to formulate an effective mathematical discourse. Based on results from theoretical analysis and case analysis, we discussed that openness, sharedness, and productivity would be useful as a framework to analyze teachers' questioning.

교사의 질문은 학생들이 구체적인 반응과 함께 수학적 담론에 참여하도록 한다는 점에서 수학 교수-학습에서 중요한 역할을 한다. 교사의 질문에 관한 기존 연구들은 주로 맥락에 대한 고려 없이 질문을 인지적 수준에 따라 범주화하여 분석하였기에, 효과적인 수학적 담론을 구축하기 위해 교사가 어떻게 질문해야 하는지에 대해서는 크게 주목하지 못하였다. 이에 본 연구는 수학 교실에서 효과적인 수학적 담론을 구축하는 교사의 질문활동이 어떤 특성을 가지고 있어야 하는지를 탐색하고자 하였다. 수학적 담론 및 교사의 질문활동에 관한 선행연구 검토와 이론적 분석을 통해, 교사 질문활동의 특성으로서 개방성, 공유성, 생산성을 도출하였다. 중학교 수학교사 한 명의 수업 사례를 통해 효과적인 수학적 담론 구축을 위해 교사 질문활동의 세 가지 특성이 필요함을 확인하였다. 이론적 분석과 수업 사례 분석을 통해 확인한 결과를 바탕으로 개방성, 공유성, 생산성이 교사의 질문활동을 분석하기 위한 틀로써 유용할 수 있음을 논의하였다.

Keywords

References

  1. 강완, 장윤영, 정선혜(2011). 수학 수업 발문유형 분석 및 대안 탐색 -신임 교사 사례 연구-. 초등수학교육, 14(3), 293-302.
  2. 김상화, 방정숙(2010). 담화 중심 수학적 의사소통 수업의 분석. 한국초등수학교육학회지, 14(3), 523-545.
  3. 문지혜, 박만구(2012). 열린 발문이 초등학생들의 수학적 창의력에 미치는 영향. 한국초등교육, 23(4), 1-25.
  4. 박만구, 김진호(2006). 학습자 중심의 수학 수업에서 교사의 발문 분석. 한국학교수학회논문집, 9(4), 425-457.
  5. 백소영, 김도현, 이경언(2014). 수업 시연에 나타나는 예비 수학교사의 발문 유형과 특성 분석. 교사교육연구, 53(3), 400-415.
  6. 변재현, 김민경(2004). 교사의 단계적 발문이 학습자의 수학적 사고에 미치는 효과. 교과교육연구, 8(2), 199-217.
  7. 이기숙, 김원경(2006). 중학교 수학교사의 발문행동에 관한 분석. 교원교육, 22(4), 111-133.
  8. 이정모(2010). '체화된 인지(Embodied Cognition)' 접근과 학문간 융합 - 인지과학 새 패러다임과 철학의 연결이 주는 시사. 철학사상, 38, 27-66.
  9. 조광희(2002). 경험이나 직관을 강조한 발문학습이 수학학습태도 및 학업성취도에 미치는 영향. 한국학교수학회논문집, 5(1), 123-134.
  10. 조진우, 이경화(2015). 후기 비트겐슈타인 철학과 수학 학습. 수학교육학연구, 25(1), 59-74.
  11. Barnes, D. (1990). Language in the secondary classroom: a study of language interaction in twelve lessons in the first term of secondary education. In D. Barnes, B. James, & R. Harold (Eds.), Language, the Learner and the School. Baltimore: Penguin Books.
  12. Boaler, J., & Brodie, K. (2004). The importance, nature, and impact of teacher questions. In D. E. McDougall, & J. A. Ross (Eds.), Proceedings of the 26th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2, (pp. 773-781). Toronto: Ontario Institute of Studies in Education/University of Toronto.
  13. Bridges, D. (1979). Education, Democracy and Discussion. Oxford: NFER.
  14. Capraro, M. M,, Carter, T., & Harbaugh, A. (2010). Understanding, questioning, and representing mathematics: what makes a difference in middle school classrooms? Research in Middle Level Education, 34(4), 1-19.
  15. Carlsen, W. S. (1991). Questioning in Classrooms. Review of Educational Research, 61(2), 157-178. https://doi.org/10.3102/00346543061002157
  16. Chazan, D., & Ball, D. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2-10.
  17. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175-190. https://doi.org/10.1080/00461520.1996.9653265
  18. Dillon, J. T. (1984). Research on Questioning and Discussion. Educational Leadership, 42, 50-56.
  19. Dillon, J. T. (1985). Using questions to foil discussion. Teaching & Teacher Education, 1(2), 109-121. https://doi.org/10.1016/0742-051X(85)90010-1
  20. Dillon, J. T. (1991). Questioning the use of questions. Journal of Educational Psychology, 83(1), 163-163. https://doi.org/10.1037/0022-0663.83.1.163
  21. Franke, M. L., Webb, N. M., Chan, A., Battey, D., Ing, M., Freund, D., & De, T. (2007). Eliciting Student Thinking in Elementary School Mathematics Classroom. CRESST REPORT 725, L.A.: National Center for Research on Evaluation, Standards, and Student Testing.
  22. Gall, M. D. (1970). The use of questions in teaching. Review of Educational Research, 40(5), 707-721. https://doi.org/10.3102/00346543040005707
  23. Leatham, K. R., Peterson, B. E., Stockero, S. L., & Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education. 46(1), 88-124. https://doi.org/10.5951/jresematheduc.46.1.0088
  24. Manouchehri, A., & Lapp, D. A. (2003). Unveiling student understanding: The role of questioning in instruction. Mathematics Teacher, 96(8), 562-566.
  25. Mason, J. (2000). Asking mathematical questions mathematically. International Journal of Mathematics Education in Science and Technology, 31, 97-111. https://doi.org/10.1080/002073900287426
  26. Moyer, P. S., & Milewicz, E. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293-315. https://doi.org/10.1023/A:1021251912775
  27. National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.
  28. Nilsson, P., & Ryve, A. (2014). The nature and role of common ground in the learning of mathematics in small-group discussions. Scandinavian Journal of Educational Research, 58(5), 609-623. https://doi.org/10.1080/00313831.2013.821087
  29. Olson, C. J., & Knott, L. (2013). When a problem is more than a teacher's question. Educational Studies in Mathematics, 83, 27-36. https://doi.org/10.1007/s10649-012-9444-4
  30. Ong, E. G., Lim, C. S., & Ghazali, M. (2010). Examining the changes in novice and experienced mathematics teachers' questioning techniques through the lesson study process. Journal of Science and Mathematics Education in Southeast Asia. 33(10), 86-109.
  31. Perry, M., Vanderstoep, S. W., & Yu, S. L. (1993). Asking questions in first-grade mathematics classes: Potential influences on mathematical thought. Journal of Educational Psychology, 85(1), 31-40. https://doi.org/10.1037/0022-0663.85.1.31
  32. Purdum-Cassidy, B., Nesmith, S., Meyer, R. D., & Cooper, S. (2015). What are they asking? An analysis of the questions planned by prospective teachers when integrating literature in mathematics. Journal of Mathematics Teacher Education. 18(1), 79-99. https://doi.org/10.1007/s10857-014-9274-7
  33. Radford, L. (2011). Book review: Classroom interaction: Why is it good, really? Educational studies in mathematics, 76, 101-115. https://doi.org/10.1007/s10649-010-9271-4
  34. Sahin, A., & Kulm, G. (2008). Sixth grade mathematics teachers' intentions and use of probing, guiding, and factual questions. Journal of Mathematics Teacher Education, 11(3), 221-241. https://doi.org/10.1007/s10857-008-9071-2
  35. Scott, P. (1998). Teacher talk and meaning making in science classrooms: A Vygotskian analysis and review. Studies in Science Education, 32(1), 45-80. https://doi.org/10.1080/03057269808560127
  36. Seeger, F. (1998). Discourse and beyond: On the ethnography of classroom discourse. In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and Communication in the Mathematics Classroom (pp. 85-101). Reston, VA: National Council of Teachers of Mathematics.
  37. Sfard, A. (2008). Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing. Cambridge: Cambridge University Press.
  38. Sfard, A. (2014). Discursive approaches to learning mathematics. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. (pp. 405-408). New York: Springer.
  39. Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions. Mind, Culture, and Activity, 8(1), 42-76. https://doi.org/10.1207/S15327884MCA0801_04
  40. Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, J. (1998). Learning mathematics through conversation: Is it as good as they say? For the Learning of Mathematics, 18(1), 41-51.
  41. Smith, M. S., & Stein, M. K. (2014). 효과적인 수학적 논의를 위해 교사가 알아야 할 5가지 관행, (방정숙 역). 서울: 경문사 (영어초판은 2013년 출판).
  42. Sorto, M. A., Mccabe, T., Warshauer, M., & Warshauer, H. (2009). Understanding the value of a question: An analysis of a lesson. Journal of Mathematical Sciences and Mathematics Education, 4(1), 50-60.
  43. Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2), 161-217. https://doi.org/10.1080/07370000701301125
  44. Tsui, A. B. M., Marton, F., Mok, I. A. C., & Ng, D. F. P. (2004). Questions and the space of learning. In F. Marton, & A. B. M. Tsui (Eds.), Classroom Discourse and the Space of Learning (pp. 113-137). Mahwah, NJ: Lawrence Erlbaum Associates.
  45. Vacc, N. N. (1993). Implementing the professional standards for teaching mathematics: Questioning in the mathematics classroom. The Arithmetic Teacher, 41(2), 88-91.
  46. Voigt, J. (1996). Negotiation of mathematical meaning in classroom processes: Social interaction and learning mathematics. In L. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of Mathematical Learning (pp. 21-50). Mahwah, NJ: Lawrence Erlbaum Associates.
  47. White, D. Y. (2003). Promoting productive mathematical classroom discourse with diverse students. The Journal of Mathematical Behavior, 22(1), 37-53. https://doi.org/10.1016/S0732-3123(03)00003-8
  48. Wong, E. D. (1991). Beyond the question/nonquestion alternative in classroom discussion. Journal of Educational Psychology, 83(1), 159-162. https://doi.org/10.1037/0022-0663.83.1.159
  49. Wood, T. (1998). Funneling or focusing? Alternative patterns of communication in mathematics class. In H. Steinbring, M. G. Bartolini Bussi, A. Sierpinska (Eds.), Language and Communication in the Mathematics Classroom (pp. 167-178). Reston, VA: National Council of Teachers of Mathematics.