The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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An action research on a middle school mathematics teacher's lesson reflection: Focused on the teacher's discourse capability to promote students' participation

중학교 수학 교사의 수업 성찰 실행 연구: 학생의 참여를 촉진하는 교사의 담론 역량을 중심으로

  • Received : 2022.01.03
  • Accepted : 2022.02.14
  • Published : 2022.02.28
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Abstract

The aim of this study was to analyze the changing process in a middle school teacher's discourse capability through reflection to lessons, thereby providing the implications for activities to improve the quality of lessons. To that end, this study explored the characteristics of change in the teacher's discourse capability of promoting students' participation while the teacher repeated instruction implementation and meeting for reflecting the implementation. Through the reflection, the teacher noticed his own matters about dealing with the students' responses and presentations. By attempting to address the matters in the instructions and reflecting the attempt, the teacher was able to accelerate the students' participation in the lesson discourse through enhancing productivity and openness of the discourse. The result of this study demonstrated that lesson reflection beneficially influenced development of teaching profession related to discourse capability.

본 연구는 교사의 수업 성찰이 담론 역량 변화에 작용하는 양상을 분석하여 교사 수업 전문성 개발에의 시사점을 얻는 데 목표를 두었다. 이에 중학교 수학 교사가 실제 수업을 실행한 다음, 연구자와의 협의회를 통해 수업을 성찰하는 과정에서 학생의 참여를 촉진하는 담론 역량이 어떻게 변화하는지 살펴보았다. 본 연구에서 교사는 수업 실행과 성찰을 통해, 수업 중 학생의 발표와 반응을 다루는 2가지 국면에서 자신의 담론 역량에 문제가 있음을 인식하였으며, 이를 개선하기 위한 시도를 수업에서 실행하고 재성찰하는 과정을 반복함으로써 담론 생산성과 개방성을 높여 학생의 참여를 촉진하는 변화를 보였다. 이상의 연구 결과는 교사의 수업 성찰이 담론 역량 개발과 관련되는 수업 전문성 신장에 기여함을 보여준다.

Keywords

References

  1. Alice F. Artzt., Eleanor Armour-Thomas., & Frances R. Curio. (2015). Becoming a reflective mathematics teacher. Seoul: Kyungmoon Publishers.
  2. Boaler, J. (2016). Mathematical mindsets. Unleashing students' potential through creative math, inspiring messages & innovative teaching. San Francisco: Wiley.
  3. Brousseau, G. (2002). Theory of didactical situations in mathematics: Didactique des mathematiques, 1970-1990. Dordrecht: Kluwer Academic Publishers.
  4. Charalambous, Y. C. (2009). Mathematical knowledge for teaching and providing explanations: An exploratory study. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proc. 33rd Conf. of the Int. Group for the Psychology of Mathematics Education (Vol. 2, pp. 305-312). Thessaloniki, Greece: PME.
  5. Cho, J. W. (2017). A triangular analysis of mathematics classroom discourse Doctoral dissertation. Graduate School in Seoul National University, Seoul, Korea.
  6. Cho, J. W., & Lee, K. H. (2015). The later wittgenstein' philosophy and mathematics learning. The journal of educational research in mathematics, 25(1), 59-74.
  7. Cho, J. W., Park, M. S., Lee, K. H., & Lee, E. J. (2016). Characteristics of teachers' questioning to formulate an effective mathematics discourse. School Mathematics, 18(1), 193-214.
  8. Choi, H. S., & Han, H. S. (2020). A study on the reflective thinking of pre-service mathematics teachers. Journal of Learner-Centered Curriculum and Instruction, 20(5), 999-1028. https://doi.org/10.22251/jlcci.2020.20.5.999
  9. Choi, S. H. (2018). Mathematics teachers' discursive competency : Based on the formation process of social norm and sociomathematical norm Doctoral dissertation. Graduate School in Korea University, Seoul, Korea.
  10. Choi, S. H. (2020a). Interaction patterns between teachers-students and teacher's discourse structures in mathematization processes. The Mathematical Education 59(1), 17-29. https://doi.org/10.7468/MATHEDU.2020.59.1.17
  11. Choi, S. H. (2020b). Quantitative and qualitative analysis of teacher-student interaction in student engagement mathematics classes. Journal of Educational Research in Mathematics 30(2), 227-244. https://doi.org/10.29275/jerm.2020.05.30.2.227
  12. Choi, S. H., & Kim, D. J. (2019). A mathematics teacher's discursive competence on the basis of mathematical competencies. Communications of mathematical education, 33(3), 377-394. https://doi.org/10.7468/JKSMEE.2019.33.3.377
  13. Choi, S. I. (2009). The development of mathematics teachers' professionalism through learning community activities for class analysis Doctoral dissertation. The Graduate School Seoul National University, Seoul, Korea.
  14. Jeong, B., & Shin J. H. (2010). A study on the instructional supervision climate of elementary schools. The Education Research Institute, 8(3), 65-86.
  15. Kang, J. G. (2016). Difficulties and alternative ways to learn irrational number concept in terms of notation. Journal of the Korean School Mathematics, 19(1), 63-82.
  16. Keum, H. J. (2016). The basic theoretical research for a practice of university faculty member's teaching reflection. Journal of Digital Convergence, 14(2), 57-63. https://doi.org/10.14400/JDC.2016.14.2.57
  17. Kim, D. J., Shin, J. H., Lee, J. E., Lim, W., Lee, Y. H., & Choi, S. H. (2019). Conceptualizing discursive teaching capacity: A case study of a middle school mathematics teacher. School Mathematics, 21(2), 291-318. https://doi.org/10.29275/sm.2019.06.21.2.291
  18. Kim, D. W. (2009). A mathematics teacher's reflective practice as a process of professional development. Communications of mathematical education, 23(3), 735-760.
  19. Kim, H. S. (2016). A case study on the changing of school culture through instructional coaching-focused on s middle school. Journal of Studies on Schools and Teaching, 1(1), 47-73. https://doi.org/10.23041/JSST.2016.1.1.002
  20. Kim, H. S., & Jin, Y. S. (2017). A case study on the improvement of unit school instructional discussion culture through instructional sharing. The Journal of Korean Teacher Education 34(3), 81-107. https://doi.org/10.24211/TJKTE.2017.34.3.81
  21. Kim, H. W. (2018). Understanding of the lesson study for reflective teaching of elementary school teachers. Journal of Learner-Centered Curriculum and Instruction, 18(17), 673-695. https://doi.org/10.22251/jlcci.2018.18.17.673
  22. Kim, J. H., & Kim, H. B. (2016). A qualitative study on the class culture of 'saetbyeol elementary school'. The Journal of Humanities, 42, 131-154. https://doi.org/10.22947/IHMJU.2021.42.1.005
  23. Kim, T. H. (2012). Teacher meets me in class. Seoul: Good Teacher Publishers.
  24. Lee, E. J., & Lee, K. H. (2016). A study on teacher's pre-noticing and actual noticing in mathematics classroom. School Mathematics, 18(4), 773-791.
  25. Lee, S. Y., & Han, S. Y. (2020). Systematic review on the research of mathematical beliefs in Korean mathematical education. The Mathematical Education, 59(4). 331-355. https://doi.org/10.7468/MATHEDU.2020.59.4.331
  26. Lee, Y. M., & Lee, S. J. (2018). Prospective secondary mathematics teachers' noticing in lesson evaluation and lesson reflection. School Mathematics, 20(1), 185-207. https://doi.org/10.29275/sm.2018.03.20.1.185
  27. Loughran, J. (2007). A history and context of self-study of teaching and teacher education practice. In J. Loughran, M. Hamilton, V. Laboskey, & T. Russell (Eds.), International handbook of self-study of teaching and teacher education practice (pp. 7-39). NY: Springer.
  28. Maher, C. A. (2008). Video recordings as pedagogical tools in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education (pp. 65-83). The Netherlands: Sense.
  29. Maher, C. A., Landis, H. J., & Palius, F. M. (2010). Teachers attending to students' reasoning: Using videos as tools. Journal of Mathematics Education, 3(2), 1-24.
  30. Markovits, Z., & Smith, M. (2008). Cases as tools in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education (pp. 39-64). The Netherlands: Sense.
  31. Oh, K. H., Park, J. S., & Kwon, O. N. (2017). A textbook analysis of irrational numbers unit: Focus on the view of process and object. The Mathematical Education, 6(2), 131-145.
  32. Oh, T. K. (2016). For the reflective practice of math classes - case study on the learning community of math teachers in a school -. School Mathematics, 18(1), 105-126.
  33. Ozmantar, F., Akkoc, H., & Bingolbali, E. (2008). Voices in shaping the subjectivity of pedagogical content knowledge. In O. Figueras, J. L. Cortina, S., Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proc. of the Joint Meeting of PME 32nd and PME-NA XXX (Vol. 4, pp. 81-88). Mexico: Cinvestav-UMSNH.
  34. Park, Y. E., & Pang, J. S. (2016). Exploring self-study and its application to enhance instructional expertise in mathematics. Journal of Educational Research in Mathematics, 26(3), 467-488.
  35. Posner, G. J., & Vivian, C. (2010). Field experience: A guide to reflective teaching. Boston: Pearson.
  36. Samaras, A. (2002). Self-study for teacher educators: Crafting a pedagogy for educational change. NY: Peter Lang Pub Inc.
  37. Samaras, A. (2011). Self-study teacher research : Improving your practice through collaborative inquiry. LA: Sage Publications.
  38. Schon, D. (1983). The reflective practitioner: How professionals think in action. London: Temple Smith.
  39. Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4-13. https://doi.org/10.2307/1176193
  40. 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
  41. Sherin, G., Jacobs, V., & Philipp, R. (2011). Situating the study of teacher noticing. In G. Sherin, V. Jacobs & R. Philipp (Eds.), Mathematics teacher noticing (pp. 3-13). NY: Routledge.
  42. Sirotic, N., & Zazkis, R. (2007). Irrational numbers: The gap between formal and intuitive knowledge. Educational Studies in Mathematics, 65, 49-76. https://doi.org/10.1007/s10649-006-9041-5
  43. Smith, M. S., & Stein, M. K. (2013). 5 Practices for orchestration productive mathematics discussions. Seoul: Kyungmoon Publishers.
  44. Son, T. K., & Hwang, S. H. (2021). Examining teachers' noticing competency on students' problem-solving strategies: Focusing on errors in fraction addition and subtraction with uncommon denominators problems. The Mathematical Education, 60(2), 229-247. https://doi.org/10.7468/MATHEDU.2021.60.1.229
  45. Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development (2nd ed.). New York: Columbia University.
  46. Voskoglou, M. G. (2013). An application of the APOS/ACE approach in teaching the irrational numbers. Journal of Mathematical Sciences and Mathematics Education, 8(1), 30-47.
  47. Yang, K. L., Hsu, H. Y., Lin, F. L., Chen, J. C., & Cheng, Y. H. (2015). Exploring the educative power of an experienced mathematics teacher educator-researcher. Educational Studies in Mathematics, 89(1), 19-39. https://doi.org/10.1007/s10649-014-9589-4