Education of Primary School Mathematics (한국수학교육학회지시리즈C:초등수학교육)

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

DOI QR Code

Teaching Practices Emphasizing Mathematical Argument for Fifth Graders

초등학교 5학년 학생들의 수학적 논증을 강조한 수업의 실제

  • Received : 2023.10.04
  • Accepted : 2023.10.16
  • Published : 2023.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, we designed and implemented a instruction emphasizing mathematical argument for fifth-grade students and analyzed the teaching practices. Through a literature review related to instruction emphasizing mathematical argument, we organized a teaching model of five phases that explain why the general claim that the sum of consecutive odd numbers equals a square number is true: 1) noticing patterns, 2) articulating conjectures, 3) representing through visual model, 4) arguing based on representation, 5) comparing and contrasting. Then, we analyzed the argumentation stream by phases to observe how the instruction emphasizing mathematical argument is implemented in the elementary classroom. Based on the results of this study, we discuss the implications of teaching a mathematical argument in elementary school.

본 연구는 초등학교 5학년 학생들을 대상으로 수학적 논증을 강조한 수업을 설계 및 구현하여 수업의 실제를 분석하였다. 문헌 연구를 통해 수학적 논증을 강조한 수업을 1) 패턴 주목하기, 2) 추측 분명히 나타내기, 3) 시각적 모델로 표현하기, 4) 표현에 근거한 논증하기, 5) 비교 및 대조하기 5단계로 구성한 다음, 연속된 홀수의 합은 제곱수임을 주제로 수업을 설계하였다. 그리고 실제 수업 과정에서 수학적 논증을 강조한 수업이 어떻게 구현되는지 수업의 흐름을 단계별로 분석하였다. 본 연구의 결과를 바탕으로 초등학교에서 수학적 논증을 강조한 수업의 시사점을 논의하였다.

Keywords

References

  1. 강완, 백석윤, 전인호, 이경화, 김연, 이미연, 윤동선, 백종숙, 강태석, 송정환, 이정, 도주원, 이주영, 김봉준, 정희선, 김경미, 이정민, 권혜현, 임다원, ... 이윤경(2023). 수학 4-1. 대교.
  2. 교육부(2022). 수학과 교육과정. 교육부 고시 제 2022-33호.
  3. 방정숙, 선우진(2016). 초등학교 수학 교과서에 제시된 패턴 지도방안에 대한 분석. 초등수학교육, 19(1), 1-18.
  4. Campbell, T. G., Boyle, J. D., & King, S. (2020). Proof and argumentation in K-12 mathematics: A review of conceptions, content, and support. International Journal of Mathematical Education in Science and Technology, 51(5), 754-774. https://doi.org/10.1080/0020739X.2019.1626503
  5. Cervantes-Barraza, J., Cabanas-Sanchez, G., & Reid, D. (2019). Complex argumentation in elementary school. PNA, 13(4), 221-246. https://doi.org/10.30827/pna.v13i4.8279
  6. Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Retrieved from https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf
  7. Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students' engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401-429. https://doi.org/10.1007/s10649-014-9532-8
  8. Department for Education. (2013). Mathematics: programmes of study: key Stages 1 and 2 (national curriculum in England). Retrieved from https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239129/PRIMARY_national_curriculum_-_Mathematics.pdf
  9. Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3-21. https://doi.org/10.1007/s10649-006-9059-8
  10. Knipping, C., & Reid, D. (2019). Argumentation analysis for early career researchers. In G. Kaiser & N. Presmeg (Eds.), Compendium for early career researchers in mathematics education (pp. 3-31). Springer.
  11. Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb, & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229-269). Lawrence Erlbaum Associates.
  12. Lannin, J., Ellis, A. B., & Elliott, R. (2011). Developing essential understanding of mathematical reasoning for teaching mathematics in prekindergarten-grade 8. In R. M. Zbiek (Ed.), Essential understandings series. National Council of Teachers of Mathematics.
  13. Reuter, F. (2023). Explorative mathematical argumentation: A theoretical framework for identifying and analysing argumentation processes in early mathematics learning. Educational Studies in Mathematics, 112(3), 415-435. https://doi.org/10.1007/s10649-022-10199-5
  14. Russell, S. J., Schifter, D., Kasman, R., Bastable, V., & Higgins, T. (2017). But why does it work? Mathematical argument in the elementary grades. Heinemann.
  15. Schifter, D., & Russell, S. J. (2020). A model for teaching mathematical argument at the elementary grades. Journal of Educational Studies in Mathematics, Special Issue, 15-28.
  16. Shinno, Y., Miyakawa, T., Iwasaki, H., Kunimune, S., Mizoguchi, T., Ishii, T., & Abe, Y. (2018). Challenges in curriculum development for mathematical proof in secondary school: Cultural dimensions to be considered. For the Learning of Mathematics, 38(1), 26-30.
  17. Spinillo, A. G., Lautert, S. L., & Borba, R. (2021). Mathematical reasoning of children and adults. Springer.
  18. Stylianides, A. J. (2016). Proving in the elementary classroom. Oxford University Press.
  19. Stylianides, G. J. (2008). An analytic framework of reasoning-and-proving. For the Learning of Mathematics, 28(1), 9-16.
  20. Stylianides, G. J., & Silver, E. A. (2010). Reasoning-and-proving in school mathematics: The case of pattern identification. In D. A. Stylianou, M. L. Blanton, & E. J. Knuth (Eds.), Teaching and learning proof across the grades: A K-16 perspective (pp. 235-249). Routledge.
  21. Toulmin, S. (2003). The uses of argument. Cambridge University Press.
  22. Van Eemeren, F. H., Grootendorst, R., & Henkemans, F. S. (1996). Fundamentals of argumentation theory. A handbook of historical backgrounds and contemporary developments. Lawrence Erlbaum Associates.
  23. Van Ness, C. K., & Maher, C. A. (2019). Analysis of the argumentation of nine-year-olds engaged in discourse about comparing fraction models. The Journal of Mathematical Behavior, 53, 13-41. https://doi.org/10.1016/j.jmathb.2018.04.004
  24. Zhuang, Y., & Conner, A. (2022). Secondary mathematics teachers' use of students' incorrect answers in supporting collective argumentation. Mathematical Thinking and Learning, 1-24. https://doi.org/10.1080/10986065.2022.2067932