DOI QR코드

DOI QR Code

Exploring the Relationships Among Teacher Questions, Turn-Taking Patterns, and Student Talks in Mathematics Classrooms

수학 교실에서 교사 질문, 말하기 차례 규칙, 학생 발화 사이의 관계 분석

  • Received : 2019.11.15
  • Accepted : 2019.12.16
  • Published : 2019.12.30

Abstract

In this study, we examined classroom interaction to explore the relationships among teacher questions, turn-taking patterns, and student talks in mathematics classrooms. We analyzed lessons given by three elementary teachers (two first-grade teachers and one second-grade teacher) who worked in the same school using a conversation-analytic approach. We observed individual classrooms three times in a year. The results revealed that when teachers provided open-ended questions, such as "why and how" questions and "agree and disagree" questions, and used a non-IRE pattern (teacher initiation-student response-teacher feedback; Mehan, 1979), students more actively engaged in classroom discourse by justifying their ideas and refuting others' thinking. Conversely, when teachers provided closed-ended questions, such as "what" questions, and used an IRE pattern, students tended to give short answers focusing on only one point. The findings suggested teachers should use open-ended questions and non-IRE turn-taking patterns to create an effective math-talk learning community. In addition, school administrators and mathematics educators should support teachers to acquire practical knowledge regarding this approach.

본 연구는 교사 질문, 말하기 차례 규칙, 학생 발화 사이의 관계를 파악하고자 수학 교실 내의 언어적 상호작용을 분석하였다. 이를 위해 같은 학교에 근무하고 있는 세 명의 초등학교 교사들(1학년 교사 2명과 2학년 교사 1명)의 수학 수업을 대화분석 기법을 사용해서 분석하였다. 각 교사들의 수업은 일 년에 걸쳐 총 3회 관찰되었다. 분석 결과, 교사가 열린 질문(예를 들어 "왜" 그리고 "어떻게" 질문들과 "동의합니까" 그리고 "동의하지 않습니까" 질문들)을 사용하고 비전통적인 말하기 차례 규칙(교사발문-학생답변-교사 피드백; Mehan, 1979)을 사용하였을 때는 학생들이 자신의 생각을 정당화하고 다른 사람의 생각을 반박하기 위해 교실 담화에 보다 적극적으로 참여하여하는 것으로 나타났다. 하지만, 교사가 닫힌 질문(예를 들어 "무엇" 질문들)을 사용하고 전통적인 말하기 차례 규칙을 사용하였을 때 학생들은 정답을 말하는 것에만 관심을 갖고 짧은 발화만을 사용하는 것으로 드러났다. 본 연구의 시사점은 다음과 같다. 첫째, 교사들은 효과적인 수학-대화 학습공동체를 만들기 위해 열린 질문을 사용하고 비전통적인 말하기 차례 규칙을 사용해야 한다. 둘째, 교사들이 발화기법에 관한 실질적인 지식을 얻을 수 있도록 교육 행정가와 수학 교육자들이 지원해야 한다.

Keywords

References

  1. Barwell, R. (2005). Integrating language and content: Issues from the mathematics classroom. Linguistics and Education, 16(2), 205-218. https://doi.org/10.1016/j.linged.2006.01.002
  2. Boaler, J., & Brodie, K. (2004). The importance of depth and breadth in the analysis of teaching: A framework for analysing teacher questions. In the Proceedings of the 26th Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education. Toronto, Ontario
  3. Bucholtz, M., & Hall, K. (2005). Identity and interaction: A sociocultural linguistic approach. Discourse Studies, 7, 585-614. https://doi.org/10.1177/1461445605054407
  4. Cazden, C. B. (2001). The language of teaching and learning. Portsmouth, NH: Heinemann.
  5. Chi, M. T. H. (2000). Self-explaining: the dual processes of generating inferences and repairing mental models. In R. Glaser (Ed.), Advances in instructional psychology, (pp. 161-238). Mahwah, NJ: Lawrence Erlbaum Associates.
  6. Choi, S. H., Ha, J. M., & Kim, D. J. (2016). An analysis of student engagement strategy and questioning strategy in a peer mentoring teaching method. Journal of the Korean School Mathematics Society, 19(2), 153-176.
  7. 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/10.1207/s15326985ep3103&4_3
  8. Franke, M. L., Webb, N. M., & Chan, A. G. (2009). Teacher questioning to elicit students' mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60, 380-392 https://doi.org/10.1177/0022487109339906
  9. Graesser, A. C., & Person, N. K. (1994). Question asking during tutoring. American Educational Research Journal, 31(1), 104-137. https://doi.org/10.3102/00028312031001104
  10. Herbal-Eisenmann, B. A., & Breyfogle, M. L. (2005). Questioning our patterns of questioning. Mathematics Teaching in the Middle School, 10(9), 484-489. https://doi.org/10.5951/MTMS.10.9.0484
  11. Hong, W. J., & Pang, J. S. (2008). An analysis of teacher-student communication and students' mathematical thinking in six grade mathematics classrooms. Journal of the Korean School Mathematics Society, 11(2), 201-219.
  12. Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81-116. https://doi.org/10.2307/30034933
  13. Hwang, S. H. (2018). Teachers' beliefs, classroom norms and discourse, and equity in mathematics classrooms. Journal of Korean Society of Mathematics Education. Series C: Education of Primary School Mathematics, 21(2), 163-192.
  14. Ingram, J., & Elliott, V. (2014). Turn taking and 'wait time' in classroom interactions. Journal of Pragmatics, 62, 1-12. https://doi.org/10.1016/j.pragma.2013.12.002
  15. Ko, J. H., Kim, T. E., & No, W. K. (2015). An analysis of the actual status about the connection of teaching and learning mathematics between elementary school and junior high school. Journal of Korea Society Educational Studies in Mathematics: School Mathematics, 17(1), 135-156.
  16. Lerman, S. (2001). Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics, 46, 87-113. https://doi.org/10.1023/A:1014031004832
  17. McHoul, A. (1978). The organization of turns at formal talk in the classroom. Language in Society, 7(2), 183-213. https://doi.org/10.1017/S0047404500005522
  18. Mehan, H. (1979). Learning lessons. Cambridge, MA: Harvard University Press.
  19. Meyer, D. K., & Turner, J. C. (2002). Using instructional discourse analysis to study the scaffolding of student self-regulation. Educational Psychologist, 37(1), 17-25. https://doi.org/10.1207/S15326985EP3701_3
  20. Ministry of Education (2015). Mathematics curricula. Seoul: The Ministry of Education.
  21. Moschkovich, J. (1999). Supporting the participation of English language learners in mathematical discussions. For the Learning of Mathematics, 19(1), 11-19.
  22. Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/international-results/
  23. Nathan, M. J., & Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21(2), 175-207. https://doi.org/10.1207/S1532690XCI2102_03
  24. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
  25. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author Reston, VA.
  26. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Author Reston, VA.
  27. Radford, J., Blatchford, P., & Webster, R. (2011). Opening up and closing down: How teachers and TAs manage turn-taking, topic and repair in mathematics lessons. Learning and Instruction, 21(5), 625-635. https://doi.org/10.1016/j.learninstruc.2011.01.004
  28. Sacks, H., Schegloff, E. A., & Jefferson, G. (1974). A simplest systematics for the organization of turn-taking for conversation. Language, 50, 696-735. https://doi.org/10.1353/lan.1974.0010
  29. Seedhouse, P. (2004). The interactional architecture of the language classroom: A conversation analysis perspective. Malden, MA: Blackwell.
  30. 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
  31. 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.
  32. Sinclair, J., & Coulthard, M. (1975) Towards an analysis of discourse. Oxford: Oxford University Press.
  33. United Kingdom Qualifications and Curriculum Authority. (1999). The national curriculum: Handbook for primary teachers in England. Crown copyright & Qualifications and Curriculum Authority: London.
  34. Vygotsky, L. S. (1980). Mind in society: The development of higher psychological processes. Cambridge: Harvard university press.
  35. Vygotsky, L. S. (1986). Thought and language. Cambridge: MIT Press.
  36. Walshaw, M., & Anthony, G. (2008). The teacher's role in classroom discourse: A review of recent research into mathematics classrooms. Review of Educational Research, 78(3), 516-551. https://doi.org/10.3102/0034654308320292
  37. Warford, M. K. (2011). The zone of proximal teacher development. Teaching and Teacher Education, 27(2), 252-258. https://doi.org/10.1016/j.tate.2010.08.008
  38. Webb, N., Franke, M., Ing, M., Wong, H., Fernandez, C., Shin, N., & Turrou, A. (2014). Engaging with other's mathematical ideas: Interrelationships among student participation, teachers' instructional practice, and learning. International Journal for Educational Research, 63, 79-93. https://doi.org/10.1016/j.ijer.2013.02.001
  39. Webb, N. M., & Palincsar, A. S. (1996). Group processes in the classroom. In D. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 841-873). New York: Simon Schuster/Macmillan.
  40. Wood, T. (1998). Funneling or focusing? Alternative patterns of communication in mathematics class. In H. Steinbring, M. G. BartoliniBussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167-178). Reston, VA: National Council of Teachers of Mathematics.
  41. Wortham, S. (2004). From good student to outcast: The emergence of a classroom identity. Ethos, 32(2), 164-187. https://doi.org/10.1525/eth.2004.32.2.164
  42. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. https://doi.org/10.2307/749877