The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

Interaction patterns between teachers-students and teacher's discourse structures in mathematization processes

수학화 과정에서 교사와 학생 간의 상호작용 양상과 교사의 담론 구조

  • Received : 2019.12.23
  • Accepted : 2020.01.22
  • Published : 2020.02.29
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this study is to analyze the teacher's discourse structure of teachers according to the interaction pattern between teacher and student in the process of mathematization. To achieve this goal, we observed a semester class (44 lessons) of an experienced teacher who had practiced teaching methods for promoting student engagement for more than 20 years. Among them, one lesson case would be match the teacher's intention and the student's response and the other one lesson case would be to mismatch between the teacher's intention and the student's response was analyzed. In other words, in the process of mathematization based on students' engagement, the intention of the teacher and the reaction of the student was determined according to the cases where students did not make an error and when they made an error. A methodology used to develop a theory based on data collected through classroom observations(grounded theory). Because the purpose of the study is to identify the teacher's discourse structure to help students' mathematization, observe the teacher's discourse and collect data based on student engagement. Based on the teacher's discourse, conceptualize it as a discourse structure for students to mathematization. As a result, teacher's discourse structure had contributed to the intention of the teacher and the reaction of the student in the process of mathematization. Based on these results, we can help the development of classroom discourse for mathematization by specifying the role of the teacher to help students experience the mathematization process in the future.

본 연구의 목적은 수학화 과정에서 교사와 학생 간의 상호작용 양상에 따른 교사의 담론 구조를 분석하는 것이다. 이러한 목적 달성을 위해 학생들의 참여를 촉진하는 교수법을 20년 이상 실행한 경력 교사의 한 학기 수업 44차시 중에서 수학화 과정에서 교사와 학생 간의 서로 다른 상호작용 양상을 보이는 대표적인 경우 각각 1차시 수업을 비교분석하였다(근거 이론). 분석 결과, 학생들의 참여 양상을 고려한 교사의 담론 구조는 수학화 과정 경험에 도움을 준 것으로 볼 수 있었다. 이러한 결과를 바탕으로 향후 학생들과의 상호작용 양상에 따라 수학화 과정을 경험할 수 있도록 도움을 주기 위한 교사의 역할을 구체화함으로써 수학화를 위한 교실 담론 개발에 도움을 줄 수 있을 것이다.

Keywords

References

  1. Baek, I., & Choi, C. (2015). Effects on mathematical thinking ability of mathematising learning with RME. Journal of Elementary Mathematics Education in Korea, 19(3), 323-345.
  2. Blum, W. (2011). Can modelling be taught and learnt, some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (15-30). New York: Springer.
  3. Blum, W., & Ferri, R. B. (2016). Advancing the teaching of mathematical modeling: research-based concepts and examples. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (65-76). Reston, VA: NCTM.
  4. Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. Proceedings of the 26th North American Chapter of the International Group for the Psychology of Mathematics Education (774-783). Toronto, Canada.
  5. Chapin, S. H., O'Connor, C., & Anderson, N. C. (2003). Classroom discussions: Using math talk to help students learn, grades 1-6. Sausalito, Calif.: Math Solutions.
  6. Cho, W. (2006). A study on mathematizing teaching and learning in highschool calculus. School Mathematics, 8(4), 417-439.
  7. Choi, J., & Kim, H. (2008). Development and application of learning materials for Freudenthal's mathematising activities in the middle school geometry. Journal of the Korean School Mathematics Society, 11(1), 69-96.
  8. Choi, K. (2017). A design of teaching units for experiencing mathematising of elementary gifted students. Communications of Mathematical Education, 31(2), 223-239. https://doi.org/10.7468/jksmee.2017.31.2.223
  9. Choi, S. (2018). Mathematics teachers' discursive competency. Korea University Graduate School Doctoral thesis.
  10. Choi, S., Ha, J., & Kim, D. (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.
  11. Choi, S., & Kim, D. (2017). Effects of a communicational approach to teacher education on cognitive changes in mathematical beliefs. Korean Journal of Teacher Education, 33(4), 25-50.
  12. Choi-Koh, S., & Choi, K. (2006). Student's mathematization of equations in the middle school using the history of mathematics. Mathematical Education, 45(4), 439-457.
  13. Creswell, J. W. (2002). Educational research: Planning, conducting, and evaluating qualitative and qualitative research. Upper Saddle River, NJ: Pearson Education.
  14. Freudenthal H. (1973). Mathematics as an Educational Task. Dordrecht: Kluwer Academic Publishers.
  15. Glaser, B. F., & Strauss, A. L. (1967). The discovery of grounded theory. New York: Aldine de Gruyter.
  16. Katano, Z. (2011). Sugakushi wo katsuyo shita kyozai kenkyu(translated by Kim, B., & Jeong, Y.). Seoul: kyungmoonsa(originally published in 1992)
  17. Kim, D., Shin, J., Lee, J., Lim, W., Lee, Y., & Choi, S. (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. Kwon, O., Ju, M., Park, J., Park, J., Oh, H., & Jo, H. (2013). The study on the development principles for the mathematics textbook based on storytelling and the possibility of implementation. Communications of Mathematical Education, 27(3), 249-266. https://doi.org/10.7468/jksmee.2013.27.3.249
  19. Lee, D., & Choe, S. (2006). A qualitative analysis on the characteristics of "Best Practice" in mathematics. Journal of the Korean School Mathematics Society, 9(3), 249-263.
  20. Lee, K., & Kim, W. (2006). An analysis on mathematics teachers' questioning behaviour. Korean Journal of Teacher Education, 22(4), 111-133.
  21. Mehan, H. (1997). Students' interactional competence. In M. Cole, Y. Engestrom, & O. Vasquez(Eds.), Mind, Culture, and activity: Seminal papers from the laboratory of comparative human cognition (235-240). Cambridge, UK: Cambridge University Press.
  22. NCTM (1991). Professional standards for teaching mathematics. Reston, VA: Author.
  23. NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  24. NCTM (2007). Mathematics teaching today. Reston, VA: Author.
  25. Oh, H. (2018). A study on understanding of differentiation. Communications of Mathematical Education, 32(2), 131-146. https://doi.org/10.7468/JKSMEE.2018.32.2.131
  26. Pyo, Y., & Lee, J. (2007). Development and application of real-life problems for uplifting problem solving skills. Communications of Mathematical Education, 21(2), 177-197.
  27. Schwartz, C. (2015). Developing the practice of teacher questioning through a K-2 elementary mathematics field experience. Investigations in Mathematics Learning, 7(3), 30-50. https://doi.org/10.1080/24727466.2015.11790344
  28. 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
  29. Sfard, A. (2008). Thinking as communicating. New York: Cambridge university press.
  30. Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussion. Reston, VA: NCTM.
  31. Stender, P., & Kaiser, G. (2016). Fostering modeling competencies for complex situations. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (107-115). Reston, VA: NCTM.
  32. Treffers, A. (1987). Three dimension. Dordrecht, Holland: Reidel Publishing Company.
  33. Um, S., & Lee, K. (2006). The attitude and the features of learning process in a math history applied lesson. Korean Journal of Teacher Education, 22(4), 135-150.
  34. Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or focusing? H. Steinbring, M. Bussi, & A. Sierpinska(Eds.), Language and communication in the mathematics classroom (167-178). Reston, VA: NCTM.
  35. Yim, Y., & Hong, J. (2015). Primary gifted students" mathematical thinking and attitude related to problem solving of triangular array. School Mathematics, 17(3), 377-390.

Cited by

  1. 수학교육에서 진보주의와 구성주의 적용에 대한 성찰 vol.60, pp.3, 2021, https://doi.org/10.7468/mathedu.2021.60.3.387