Journal of the Korean School Mathematics Society (한국학교수학회논문집)

The Korean School Mathematics Society (한국학교수학회)
권호 표지

Mathematics Preservice Teachers' Conception of Teacher Discourse

예비 수학 교사의 교사 담화에 대한 인식 분석

  • 이지현 (인천대학교 수학교육과)
  • Received : 2017.11.14
  • Accepted : 2017.12.20
  • Published : 2017.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

Teachers' conceptions about teaching are important driving and also interfering forces which might affect their actual practice and training. This research explores preservice mathematics teachers' conceptions of teacher discourse, through tasks analyzing and evaluating teachers' moment-to-moment discourse moves which occur in authoritative and dialogical classroom discourse. Some facets of the preservice teachers' conceptions were congruent with dialogical discourse: they criticized teacher's one-way communication and ignoring students' voices; they supported teacher's questions probing students' thinking and receptive attitude to ward students' wrong answers. However, some deep and subtle facets of their conceptions were more congruent with authoritative discourse rather than dialogical discourse: they positively perceived teacher's closed, information seeking questions that funnel students' thinking to the predetermined procedure; they emotionally resisted teacher's questions which might facilitate dialogical engagement by allowing students to judge mathematical correctness of ideas from their peers. Preservice teachers' conceptions of teacher discourse explored in this research provide useful foundations on which to build continuous and coherent teacher professional development programs about classroom discourse.

본 연구에서는 권위적 및 대화적 담화 사례의 교사 담화 평가에서 드러난 예비 수학 교사들의 인식을 질적 내용 분석으로 탐색하였다. 예비교사들은 교사의 일방적 설명이나 학생 대답을 적극적으로 수용하지 않는 폐쇄적 발화에 비판적이었으며, 학생의 이유를 탐색하는 질문과 오답에 대한 개방적 태도를 지지했다는 측면에서 표면적으로 대화적 담화를 지향하고 있었다. 그러나 교사가 대부분의 인지활동을 대행하는 테스트 질문에 무비판적이었고, 학생들에게 제기된 답에 대한 수학적 판단 기회를 부여하여 대화적 상호작용을 촉진하는 교사 발문에 대해 심리적 저항을 보였다는 점에서, 예비교사들의 심층적인 권위적 담화 지향성도 확인할 수 있었다. 본 연구에서 보고한 교사교육 입문 초기 예비교사들의 담화인식은, 교실 담화에 대한 교사 전문성 교육 과정 설계에 유용한 기초를 제공할 수 있을 것이다.

Keywords

References

  1. 권나영. (2014). 중등 수학 예비교사의 교수-학습 개념 연구. 한국학교수학회논문집, 17(3), 321-335.
  2. 김상화, 방정숙 (2010). 담화 중심 수학적 의사소통 수업의 분석. 한국초등수학교육학회지, 14(3), 523-545.
  3. 김진호 (2009). 수학 수업 중 원활한 의사소통이 이루어지는 교실문화 형성하기. C-초등수학교육, 12(2), 99-115.
  4. 나귀수, 최승현 (2003). 초등학교 수학교육 실제의 이해. 학교수학, 5(3), 275-295.
  5. 박미혜, 방정숙 (2009). 개정 교육과정의 실험 적용에서 나타나는 수학적 의사소통 분석. 수학교육학연구, 19(1), 163-183.
  6. 방정숙, 정희진 (2006). 학습자 중심 교수법에 대한 초등 교사의 이해와 실행형태: 수학적 의사소통을 중심으로. 학습자중심교과교육연구, 6(1), 297-321.
  7. 이광호. (2009). 중등 수학 예비 교사들의 다양한 교수, 학습 방법에 대한 성향. 한국학교수학회논문집, 12(1), 1-25.
  8. 신보미 (2014). 교사들의 수업 분석 특징에 대한 연구. 학교수학, 16(3), 519-542.
  9. 홍서영, 서태열 (2014). 지리교육 연구의 대안적 연구 방법으로서 QCA (Qualitative Content Analysis)의 적용. 한국지리환경교육학회지, 22(3), 103-120.
  10. Aguirre, J., & Speer, N. M. (1999). Examining the relationship between beliefs and goals in teacher practice. The Journal of Mathematical Behavior, 18(3), 327-356. https://doi.org/10.1016/S0732-3123(99)00034-6
  11. Bakker, A., Smit, J., & Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM, 47(7), 1047-1065. https://doi.org/10.1007/s11858-015-0738-8
  12. Bakhtin, M. (1984). Problems of Doestoevsky's poetics. C. Emerson, Trans. Minneapolis: University of Minnesota Press.
  13. Ball, D. L. (1991). What's all this talk about "discourse"? The Arithmetic Teacher, 39(3), 44-48.
  14. Barwell, R. (2015). Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic. Educational Studies in Mathematics, 92(3), 331-345.
  15. Blanton, M. L., Berenson, S. B., & Norwood, K. S. (2001). Using classroom discourse to understand a prospective mathematics teacher's developing practice. Teaching and Teacher Education, 17(2), 227-242. https://doi.org/10.1016/S0742-051X(00)00053-6
  16. Boaler, J., & Greeno, J. G. (2000). Identity, agency, and knowing in mathematics worlds. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning(pp. 171-200). Westport, CT: Ablex Publishing.
  17. Bray, W. S. (2011). A collective case study of the influence of teachers' beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics Education, 42(1), 2-38. https://doi.org/10.5951/jresematheduc.42.1.0002
  18. Brendefur, J., & Frykholm, J. (2000). Promoting mathematical communication in the classroom: Two preservice teachers' conceptions and practices. Journal of Mathematics Teacher Education, 3(2), 125-153. https://doi.org/10.1023/A:1009947032694
  19. Bruner, J. S. (1996). The culture of education. Cambridge, MA: Harvard University Press.
  20. Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American educational research journal, 26, 499-531. https://doi.org/10.3102/00028312026004499
  21. Carpenter, T. P., Hiebert, J., Fennema, E., Fuson, K. C., Wearne, D., & Murray, H. (1997). Making sense: Teaching and learning mathematics with understanding. 김수환, 박영희, 이경화, 한대희 역. 어떻게 이해하지?. 서울: 경문사.
  22. Cazden, C. B. (1988). Classroom discourse: the language of teaching and learning. Portsmouth, NH: Heinemann.
  23. Chapin, S. H., O'Connor, C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn, Grades K-6. Sausalito, CA: Math Solutions Publications.
  24. Cobb, P., Wood, T., & Yackel, E. (1993). Discourse, mathematical thinking, and classroom practice. In N. Minick, E. Forman, & A. Stone (Eds.), Education and mind: Institutional, social, and developmental processes(pp. 91-119). New York: Oxford University Press.
  25. Edwards-Groves, C. J., & Hoare, R. (2012). "Talking to Learn": Focusing teacher education on dialogue as a core practice for teaching and learning. Australian Journal of Teacher Education, 37(8). 82-100.
  26. Eley, M. G. (2006). Teachers' conceptions of teaching, and the making of specific decisions in planning to teach. Higher education, 51(2), 191-214. https://doi.org/10.1007/s10734-004-6382-9
  27. Engle, R. A., & Conant, F. R. (2010). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20(4), 399-483. https://doi.org/10.1207/S1532690XCI2004_1
  28. Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning(Vol.1)(pp.225-256). Reston, VA: NCTM.
  29. Hiebert, J., Gallimore, R., Garnier, H., Givvin Bogard, K., Hollingsworth, H., Jacobs, J., & al., e. (2003). Teaching mathematics in seven countries-Results from the TIMSS 1999 video study. U. S. Department of Education, Washington, DC: National Center for Education Statistics.
  30. Holt-Reynolds, D. (1991). The dialogues of teacher education: Entering and influencing preservice teachers' internal conversations. (Research Report 91-4). East Lansing: Michigan State University, National Center for Research for Teacher Learning.
  31. Holt-Reynolds, D. (1992). Personal history-based beliefs as relevant prior knowledge in course work. American educational research journal, 29(2), 325-349. https://doi.org/10.3102/00028312029002325
  32. Huang, R., & Li, Y. (2012). What matters most: A comparison of expert and novice teachers' noticing of mathematics classroom events. School science and mathematics, 112(7), 420-432. https://doi.org/10.1111/j.1949-8594.2012.00161.x
  33. Ilic, M., & Bojovic, Z. (2016). Teachers' folk pedagogies. Journal of Arts and Humanities, 5(9), 41-52. https://doi.org/10.18533/journal.v5i9.987
  34. Ingram, J., Pitt, A., & Baldry, F. (2015). Handling errors as they arise in whole-class interactions. Research in Mathematics Education, 17(3), 183-197. https://doi.org/10.1080/14794802.2015.1098562
  35. Jang, H. (2010). Measuring teacher beliefs about mathematics discourse: An item response theory approach. Doctoral dissertation. University of California, Berkeley.
  36. Kaplan, R.G. (1991). Teacher beliefs and practices: A square peg in a square hole. In R.G. Underhill (Ed.), Proceedings of the PME-NA 13 Conference, Vol. 2 (pp. 119-125). Blacksburg, VA: Virginia Tech.
  37. Kazak, S., Wegerif, R., & Fujita, T. (2015). The importance of dialogic processes to conceptual development in mathematics. Educational Studies in Mathematics, 90(2), 105-120. https://doi.org/10.1007/s10649-015-9618-y
  38. Knuth, E., & Peressini, D. (2001). Unpacking the nature of discourse in mathematics classrooms. Mathematics teaching in the middle school, 6(5), 320-325.
  39. Krull, E., Oras, K., & Sisask, S. (2007). Differences in teachers' comments on classroom events as indicators of their professional development. Teaching and Teacher Education, 23(7), 1038-1050. https://doi.org/10.1016/j.tate.2006.02.001
  40. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American educational research journal, 27(1), 29-63. https://doi.org/10.3102/00028312027001029
  41. "Lay Theories." International Encyclopedia of the Social Sciences. Retrieved October 08, 2017 from Encyclopedia.com: http://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/lay-theories
  42. Lee, J. E., & Kim, K. T. (2016). Pre-service teachers' conceptions of effective teacher talk: their critical reflections on a sample teacher-student dialogue. Educational Studies in Mathematics, 93(3), 363-381. https://doi.org/10.1007/s10649-016-9710-y
  43. Lefstein A., & Snell, J. (2011). Classroom discourse: The promise and complexity of dialogic practice. In S. Ellis, E. McCartney, & J. Bourne (Eds.), Applied linguistics and primary school teaching(pp. 165-185). Cambridge: Cambridge University Press.
  44. Lehesvuori, S., Viiri, J., & Rasku-Puttonen, H. (2011). Introducing dialogic teaching to science student teachers. Journal of Science Teacher Education, 22(8), 705-727. https://doi.org/10.1007/s10972-011-9253-0
  45. Lortie, D. C. (1975). School teacher: A sociological study. 진동섭 역. 교직사회 : 교직과 교사의 삶. 서울: 良書院.
  46. Lotman, Y. M. (1988). Text within a text. Soviet psychology, 26(3), 32-51. https://doi.org/10.2753/RPO1061-0405260332
  47. Lotman, Y. (2000). Universe of the mind: A semiotic theory of culture. A. Shukman, Trans. New York: I. B. Tauris Publishers.
  48. Mehan, H. (1979). 'What time is it, Denise?": Asking known information questions in classroom discourse. Theory Into Practice, 18(4), 285-294. https://doi.org/10.1080/00405847909542846
  49. Munby, H., & Russell, T. (1994). The authority of experience in learning to teach: Messages from a physics methods class. Journal of Teacher Education, 45(2), 86-95. https://doi.org/10.1177/0022487194045002002
  50. Nassaji, H., & Wells, G. (2000). What's the use of 'triadic dialogue'?: An investigation of teacher-student interaction. Applied Linguistics, 21(3), 376-406. https://doi.org/10.1093/applin/21.3.376
  51. Nystrand, M., Wu, L. L., Gamoran, A., Zeiser, S., & Long, D. A. (2003). Questions in time: Investigating the structure and dynamics of unfolding classroom discourse. Discourse Processes, 35(2), 135-198. https://doi.org/10.1207/S15326950DP3502_3
  52. Otten, S., Engledowl, C., & Spain, V. (2015). Univocal and dialogic discourse in secondary mathematics classrooms: The case of attending to precision. ZDM, 47(7), 1285-1298. https://doi.org/10.1007/s11858-015-0725-0
  53. Pajares, M. F. (1992). Teachers' beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62, 307-332. https://doi.org/10.3102/00346543062003307
  54. Peterson, P. L., Fennema, E., Carpenter, T. P., & Loef, M. (1989). Teacher's pedagogical content beliefs in mathematics. Cognition and instruction, 6(1), 1-40. https://doi.org/10.1207/s1532690xci0601_1
  55. Pierson, J. L. (2008).The relationship between patterns of classroom discourse and mathematics learning. Doctoral dissertation. The University of Texas at Austin.
  56. Reddy, M. (1979). The conduit metaphor: A case of frame conflict in our language about language. In A. Ortony (Ed.), Metaphor and thought (pp. 284-324). Cambridge: Cambridge University Press.
  57. Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21(5), 491-508. https://doi.org/10.1016/j.tate.2005.03.004
  58. Schoenfeld, A. H. (1996). In fostering communities of inquiry, Must it matter that the teacher knows "the answer"?. For the learning of mathematics, 16(3), 11-16.
  59. 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
  60. Scott, P. H., Mortimer, E. F., & Aguiar, O. G. (2006). The tension between authoritative and dialogic discourse: A fundamental characteristic of meaning making interactions in high school science lessons. Science Education, 90(4), 605-631. https://doi.org/10.1002/sce.20131
  61. Sedova, K., Sedlacek, M., & Svaricek, R. (2016). Teacher professional development as a means of transforming student classroom talk. Teaching and Teacher Education, 57, 14-25. https://doi.org/10.1016/j.tate.2016.03.005
  62. Shoham, E., Penso, S., & Shiloah, N. (2003). Novice teachers' reasoning when analysing educational cases. Asia-Pacific Journal of Teacher Education, 31(3), 195-211. https://doi.org/10.1080/0955236032000149346
  63. Sinclair, J. M., & Coulthard, M. (1975). Towards an analysis of discourse: The English used by teachers and pupils. London: Oxford University Press.
  64. Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers' ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125. https://doi.org/10.1007/s10857-007-9063-7
  65. Tharp, R. G., & Gallimore, R. (1991). Rousing minds to life: Teaching, learning, and schooling in social context. Cambridge: Cambridge University Press.
  66. Thompson, A. G. (1984). The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105-127. https://doi.org/10.1007/BF00305892
  67. Truxaw, M. P. (2004). Mediating mathematical meaning through discourse: An investigation of discursive practices of middle grades mathematics teachers. Doctoral dissertation. University of Connecticut.
  68. Truxaw, M. P., & DeFranco, T. C. (2008). Mapping mathematical classroom discourse and its implication for model of teaching. Journal for Research in Mathematics Education, 39(5), 489-525.
  69. Tulis, M. (2013). Error management behavior in classrooms: Teachers' responses to student mistakes. Teaching and Teacher Education, 33, 56-68. https://doi.org/10.1016/j.tate.2013.02.003
  70. van Zee, E. H., & Minstrell, J. (1997a). Reflective discourse: Developing shared understandings in a physics classroom. International Journal of Science Education, 19(2), 209-228. https://doi.org/10.1080/0950069970190206
  71. van Zee, E. H., & Minstrell, J. (1997b). Using questioning to guide student thinking. Journal of the Learning Sciences, 6(2), 227-269. https://doi.org/10.1207/s15327809jls0602_3
  72. Wells, G. (1993). Reevaluating the IRF sequence: A proposal for the articulation of theories of activity and discourse for the analysis of teaching and learning in the classroom. Linguistics and Education, 5(1), 1-37. https://doi.org/10.1016/S0898-5898(05)80001-4
  73. Wells, G. (1996). Using the tool-kit of discourse in the activity of learning and teaching. Mind, Culture, and Activity, 3(2), 74-101. https://doi.org/10.1207/s15327884mca0302_2
  74. Wells, G., & Arauz, R. M. (2006). Dialogue in the classroom. The Journal of the Learning sciences, 15(3), 379-428. https://doi.org/10.1207/s15327809jls1503_3
  75. Wilen, W. W. (2004). Refuting misconceptions about classroom discussion. The Social Studies, 95(1), 33-39. https://doi.org/10.3200/TSSS.95.1.33-39
  76. Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or focusing. In H. Steinbring, M. G. B. Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167-178). Reston, VA: National Council of Teachers of Mathematics.
  77. Wood, T., Williams, G., & McNeal, B. (2006). Children's mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222-253.
  78. Yadav, A., & Koehler, M. (2007). The role of epistemological beliefs in preservice teachers' interpretation of video cases of early-grade literacy instruction. Journal of Technology and teacher Education, 15(3), 335-361.