Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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A Case Study on Teaching the Sum of the Interior Angles of a Triangle Using Measurement Errors

측정 오차를 활용한 삼각형의 내각의 합 지도 방안 사례 연구

  • Received : 2021.11.29
  • Accepted : 2021.12.29
  • Published : 2021.12.31
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Abstract

In this study, under the assumption that the goal pursued in measurement area can be reached through the composition of the measurement activity considering the mathematical process, the method of summing the interior angles of a triangle using the measurement error was applied to the 4th grade class of the elementary school. Results of the study, first, students were able to recognize the possibility of measurement error by learning the sum of the interior angles of a triangle using the measurement error. Second, the discussion process based on the measurement error became the basis for students to attempt mathematical justification. Third, the manipulation activity using the semicircle was recognized as a natural and intuitive way of mathematical justification by the students and led to generalization. Fourth, the method of guiding the sum of the interior angles of a triangle using the measurement error contributed to the development of students' mathematical communication skills and positive attitudes toward mathematics.

본 연구는 수학적 과정을 고려한 측정 활동의 구성을 통해 측정 영역에서 추구하는 목표에 도달할 수 있다는 가정 아래 초등학교 4학년 학급에 측정 오차를 활용한 삼각형의 내각의 합 지도 방안을 적용하고 결과를 분석하였다. 연구 결과 첫째, 학생들은 측정 오차를 활용하여 삼각형의 내각의 합을 학습함으로써 측정 오차의 발생 가능성을 인식할 수 있었다. 둘째, 측정 오차에 기반한 토론 과정은 학생들이 수학적 정당화를 시도할 수 있는 바탕이 되었다. 셋째, 반원을 활용한 조작 활동은 학생들에게 자연스럽고 직관적인 수학적 정당화의 방법으로 인식되었고 일반화를 이끌었다. 넷째, 측정 오차를 활용한 삼각형의 내각의 합 지도 방안은 학생들의 수학적 의사소통 능력과 수학에 대한 긍정적인 태도의 함양에 기여하였다.

Keywords

Acknowledgement

이 연구는 2021년도 서울교육대학교 교내연구비에 의하여 연구되었음.

References

  1. Kang, H. K. (2019). A study on angle and angle measurement concepts in elementary mathematics education. The Journal of Education Studies, 56(1), 1-15.
  2. Ministry of Education (2015). Mathematics curriculum. Ministry of Education Report 2015-74.
  3. Ku, M. Y. & Lee, K. H. (2015). Analyzing and restructuring mathematical tasks of length measurement in elementary school mathematics - Focused on 2nd graders -. Journal of Elementary Mathematics Education in Korea, 19(3), 387-408.
  4. Kwon, S. Y. (2003). A study on mathematical justification activities in elementary school. Education of Primary School Mathematics, 7(2), 85-99.
  5. Kim, D. H. & Kim, M. K. (2020). A study on understanding and misconception a out Angle of elementary 4th grade students. School Mathematics, 22(2), 183-203. https://doi.org/10.29275/sm.2020.06.22.2.183
  6. Kim, S. Y. & Kang, W. (2005). An analysis of teaching areas of triangles and quadrilaterals in elementary school mathematics textbooks. Journal of Elementary Mathematics Education in Korea, 9(2), 161-180.
  7. Kim, E. J. & Kang, H. K. (2014). A construction of 'Decimal Fraction' unit of elementary mathematics textbook and analysis of students' state of understanding based on measurement activity. Journal of Elementary Mathematics Education in Korea, 18(1), 37-62.
  8. Kim, J. H. (2019). A study on teaching method and textbook analysis of the sum of internal angles of triangle. Journal of Learner-Centered Curriculum and Instruction, 19(7), 141-159.
  9. Kim, J. H. & Kang, M. B. (201). A study on mathematical justification of elementary school teachers. Journal of EJementary Mathemaucs Education in Korea, 15(3), 509-531.
  10. Park, K. S. (2010). An analysis and criticism on contents related on angular measure in Korean elementary mathematics subject. School Mathematics, 12(1), 45-60.
  11. Pang, J. S., Kim, J. W. & Kim, H. J. (2012). An analysis of good mathematics instruction by key instructional elements of measurement. Education of Primary School Mathematics, 15(2), 77-89. https://doi.org/10.7468/JKSMEC.2012.15.2.077
  12. Song, M. J. & Park, J. S. (2005). An analysis of mathematics learning achievements of elementary students in measurement, The Research of Science Education, 28, 39-58.
  13. Oh, Y. Y. (2021). A study on teaching method for sum of the internal angles of a triangle. The Journal of Korea Elementary Education, 32(1), 123-135.
  14. Lee, K. H. (1999). A study on teaching measurement in grade 4. Education of Primary School Mathematics, 3(1), 55-62.
  15. Lim, M. I. & Chang, H. W. (2018). An analysis of second-grade students' mathematical activities using broken rulers. The Journal of Educational Research in Mathematics, 28(1), 97-112. https://doi.org/10.29275/jerm.2018.02.28.1.97
  16. Lim, J. H. (2009). An analysis of activities to explore the sum of the interior angles of a triangle. Studies on Constitutional Cases, 22(1), 23-35.
  17. Hong, G. J. & Oh, S. H. (2018). A study on the introduction and explanation of the sum of the angles of a triangle in elementary school mathematics. Education of Primary School Mathematics, 21(1), 75-91. https://doi.org/10.7468/JKSMEC.2018.21.1.75
  18. Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.
  19. Hiebert, J. (1984). Why do some children have trouble learning measurement concepts?. The Arithmetic Teacher, 31(7), 19-24. https://doi.org/10.5951/AT.31.7.0019
  20. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston. VA: National Council of Teachers of Mathematics.
  21. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: National Council of Teachers of Mathematics.
  22. Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2009). Helping children learn mathematics. Hoboken, NJ: John Wiley & Sons.
  23. Smith, J. P., van den Heuvel-Panhuizen, M., & Teppo, A. R. (2011). Learning, teaching, and using measurement: Introduction to the issue. ZDM, 43(5), 617-620. https://doi.org/10.1007/s11858-011-0369-7
  24. Tall, D. (1995). Cognitive developments, representations and proof. Paper presented at the conference Justifying and Proving in School Mathematics Institute of Education, London, pp. 27-38.
  25. Wilson, P. S., & Adams, V. M. (1992). A dynamic way to teach angle and angle measure. The Arithmetic Teacher, 39(5), 6-13. https://doi.org/10.5951/AT.39.5.0006
  26. Yin, R. K. (2011). Qualitative research from start to finish (2nd ed.). 박지연, 이숙향, 김남희 역 (2013). 질적 연구: 시작부터 완성까지. 서울: 학지사.