The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

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

DOI QR Code

Teacher-student interaction patterns and teacher's discourse structures in understanding mathematical word problem

학생들의 수학 문장제 이해 과정에서 교사와 학생 간의 상호 작용 양상과 교사의 담론 구조

  • Received : 2020.02.25
  • Accepted : 2020.03.23
  • Published : 2020.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this study is to analyze the structures of teacher's discourse according to the pattern of interaction between teachers and students in the understanding mathematical word problem. The structures of teacher's discourse could be conceptualized as a process in which the teacher starts, develops and organizes the discourse based on prior research. For this purpose, the fourth class(example, a problem of the same type as the example, formative assessment, and final assessment) was extracted from one semester of experienced teachers who have been practicing teaching methods to facilitate student participation for many years. A methodology used to develop a theory based on data collected through classroom observations. Because the purpose of the study is to identify the structures of teacher's discourse to help the problem understanding, observe the teacher's discourse and collect data based on student engagement. Results show that the structure of teacher's discourse, which consults on important aspects of interaction between teachers-students and creates mathematical meanings, helped students understand the mathematics word problem by promoting their engagement in class. Based on the structures of teacher's discourse to understand problems based on the interaction patterns between teachers and students, it can be said that teachers provided specific methodologies on how to communicate with students in order to understand problems in the future.

본 연구의 목적은 문장제 이해 과정에서 교사와 학생 간의 상호 작용 양상에 따른 교사의 담론 구조를 분석하는 것이다. 이를 위해 학생들의 참여를 촉진하는 교수법을 다년간 실행해 온 경력교사의 한 학기 수업 중에서 문제 해결 과정을 대표할 수 있는 수업 4차시를 추출하였다. 4차시 수업에서 교사와 학생 간에 중요하게 생각하는 부분에 대한 일치 여부에 따라 교사 담론의 구조는 어떠한 특징이 있는지를 분석하였다. 분석 결과, 교사와 학생 간의 상호 작용 양상에 따라 문장제에서 중요하게 생각하는 부분을 협의하고 수학적인 의미를 만들어 가는 교사 담론의 구조는 학생들의 수업 참여를 촉진함으로써 문장제 이해에 도움을 주는 것으로 볼 수 있었다. 교사와 학생 간의 상호 작용 양상에 따라 학생들의 문제 이해를 위한 교사 담론의 구조를 바탕으로 향후 교사들이 문제 이해를 위해 학생들과 어떻게 소통해야 하는지에 대한 구체적인 방법론을 제공하였다고 볼 수 있다.

Keywords

References

  1. Ahn, B. (2018). A study on the improvement of problem-solving in elementary mathematics textbooks. Journal of Elementary Mathematics Education in Korea, 22(4), 405-425.
  2. Baxter, P., & Jack, S. (2008). Qualitative case study methodology: Study design and implementation for novice researchers. The Qualitative Report, 13(4), 544-559.
  3. Choi, S. (2018). Mathematics teachers' discursive competency. Doctoral dissertation, Korea University, Seoul.
  4. Choi, S. (2020). 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
  5. Choi, S., Ha, J., & Kim, D. (2016a). A communicational approach to mathematical process appeared in a peer mentoring teaching method. Communications of Mathematical Education, 30(3), 375-392. https://doi.org/10.7468/jksmee.2016.30.3.375
  6. Choi, S., Ha, J., & Kim, D. (2016b). 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. Choi, S., & Kim, D. (2019). A mathematics teacher's discursive competence on the basis of mathematical competencies. Communications of Mathematical Education, 33(3), 377-394.
  8. Choi, S., Lee, D., & Kim, D. (2017). Teacher-friendly education for process-focused assessment and teacher cognition. Korean Journal of Teacher Education, 33(2), 1-23.
  9. Creswell, J. (2015). Qualitative inquiry and research design(translated by Cho, Jeong, Kim, & Kwon). Seoul: Hakjisa(originally published in 2013)
  10. Hwang, H., Na, G., Choe, S., Park, K., Yim, J., & Seo, D. (2016). Theory of mathematics education. Seoul: moonumsa.
  11. Ji, C., & Oh, S. (2000). The study on the influence that the understanding degree about the sentence stated math. problems reach the extension of the problem solving capacity. Journal of the Korean School Mathematics Society, 3(1), 189-200.
  12. Kang, O., Hwang, S., Kwon, E., Jeong, K., Kim, Y. (2014). Middle school mathematics 1. Seoul: Doosandonga.
  13. 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
  14. Lee, J., & Ahn, B. (2013). The effects of writing activities based on Polya's problem solving stages on learning accomplishment and attitudes. Journal of Elementary Mathematics Education in Korea, 17(1), 87-103.
  15. Lee, K., & Shin, H. (2009). Exemplary teachers' teaching strategies for teaching word problems. Journal of the Korean School Mathematics Society, 12(4), 433-452.
  16. 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(pp. 235-240). Cambridge, UK: Cambridge University Press.
  17. Ministry of Education (2015). The second comprehensive plan of mathematics education. Ministry of Education.
  18. NCTM(2000). Principles and standards for school mathematics. Reston, VA: Author.
  19. Park, H., & Lee, C. (2006). An analysis of similarities that students construct in the process of problem solving. Journal of Educational Research in Mathematics, 16(2), 115-138.
  20. Park, J., Ryu, S., & Lee, J. (2012). The analysis of mathematics error type that appears from the process of solving problem related to real life. Journal of the Korean School Mathematics Society, 15(4), 699-718.
  21. Polya, G. (2008). How to solve it?(translated by Woo, J.). Seoul: Kyowoosa(Originally published in 1954)
  22. Ra, W., & Paik, S. (2009). Teaching the comprehension of word problems through their mathematical structure in elementary school mathematics. Journal of Elementary Mathematics Education in Korea, 13(2), 247-268.
  23. 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
  24. Sfard, A. (2008). Thinking as communicating. New York: Cambridge university press.
  25. Vygotsky, L. S. (1986). Thought and language. Cambridge, M. A.: MIT Press.
  26. Wittgenstein, L. (1953/2003). Philosophical investigations: The German text, with a revised English translation(3rd ed., G. E. M. Anscombe, Trans.). Malden, MA: Blackwell.
  27. Woo, J., & Jeong, E. (1995). A study on the Polya's mathematical heuristics. The Journal of Educational Research in Mathematics, 5(1), 99-117.
  28. 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(pp. 167-178). Reston, VA: NCTM.
  29. Yin, R. (2005). Case study research(translated by Shin & Seo). Seoul: Hankyungsa(originally published in 2003)