The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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An Analysis of Students' Understanding on Unit Fraction : Focusing on Teaching Context and Visual Representation

단위분수에 대한 초등학교 3학년 학생들의 이해 분석 : 지도 맥락과 시각적 표현의 관점에서

  • Received : 2018.01.11
  • Accepted : 2018.02.25
  • Published : 2018.02.28
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Abstract

Despite the significance of fraction in elementary mathematics education, it is not easy to teach it meaningfully in connection with real life in Korea. This study aims to investigate and analyze 3rd grade students' understanding on unit fraction concepts and on comparison of unit fractions and to identify the parts which need to be supplemented in relation to unit fraction. For these purposes, I reviewed previous studies and extracted chapters which cover unit fractions in elementary mathematics textbooks based on 2009 revised curriculums and analyzed teaching contexts and visual representations of unit fractions. From this point of view, I constructed a test which consists of three problems based on Chval et al(2013) to investigate students' understanding on unit fraction. To apply this test, I selected forty-one 3rd grade students and examined that students' aspects of understanding on unit fraction. The results were analyzed both qualitatively and quantitatively. In this study, I present the analysis results and provide implications and some didactical suggestions for teaching contexts and visual representations of unit fraction based on the discussion.

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References

  1. 강완(2014). 분수 개념 지도 내용과 방법 분석, 수학교육학연구 24(3), 467-480.(Kang, W. (2014). An analysis on concepts and methods of teaching fractions, Journal of Educational Research in Mathematics 24(3), 467-480.)
  2. 강흥규 (2013). 한국의 초등수학 교과서에 나타나는 분수의 개념과 모델의 양상 분석, 한국초등수학교육학회지 17(3), 431-455.(Kang, H. K. (2013). An analysis on aspects of concepts and models of fraction appeared in Korea elementary mathematics textbook, Journal of Elementary Mathematics Education in Korea 17(3), 431-455.)
  3. 교육과학기술부 (2009). 수학 2-2. 서울: 두산동아.(Ministry of Education, Science, and Technology (2009).Elementary mathematics textbook 2-2. Seoul: Doosan Donga.)
  4. 교육부 (2015a). 수학 3-1. 서울: 천재교육.(Ministry of Education (2015a). Elementary mathematicstextbook 3-1. Seoul: Chunjae Education.)
  5. 교육부 (2015b). 수학 3-1 교사용 지도서. 서울: 천재교육.(Ministry of Education (2015b). Elementary mathematics teacher's guide book 3-1. Seoul: Chunjae Education.)
  6. 교육부 (2015c). 수학 5-1. 서울: 천재교육.(Ministry of Education (2015c). Elementary mathematicstextbook 5-1. Seoul: Chunjae Education.)
  7. 김명운, 장경윤 (2009). 맥락화를 통한 분수의 곱셈과 나눗셈 지도, 학교수학 11(4), 685-706.(Kim, M. W. & Chang, K. Y. (2009). Teaching multiplication & division of fractions through contextualization, School Mathematics 11(4), 685-706.)
  8. 박경미, 이환철, 박선화, 강은주, 김선희, 임해미, 김성여,장혜원, 강태석, 권점례, 김민정, 방정숙, 이화영, 임미인, 이만근, 김화경, 윤상혁, 이광상, 이경은, 조혜정, 권영기, 권오남, 신동관, 강현영, 김재영, 도종훈, 박정숙,서보억, 안현정, 오택근, 이경진, 이광연, 이문호, 이승훈, 이은정, 이지윤, 전태인, 최지선, 황선미, 박문환, 김환일, 강성권, 여미주 (2015). 2015 개정 수학과 교육과정 시안 개발 연구 II. 교육부, 한국과학창의재단.(Park, K., Lee, H., Park, S., Kang, E., Kim, S., Lim, H., Kim, S., Chang, H., Kang, T., Kwon, J., Kim, M., Pang, J., Lee, H., Lim, M., Lee, M., Kim, H., Yun, S., Lee, K., Lee, K., Jo, H., Kwon, Y., Kwon, O., Shin, D., Kang, H., Kim, J., Do, J., Park, J., Seo, B., An, H., Oh, T., Lee, K., Lee, K., Lee, M., Lee, S., Lee, E., Lee, J., Jeon, T., Choi, J., Hwang, S., Park, M., Kim, H., Kang, S., & Yeo, M. (2015). A development of a draft for the 2015 revised mathematics curriculum. Kofac Research Reprot BD15120005.)
  9. 서동엽 (2005). 분수의 역사발생적 지도 방안, 수학교육학연구 15(3), 233-249.(Seo, D. Y. (2005). The historico-genetic instruction on fractions, Journal of Educational Research in Mathematics 15(3), 233-249.)
  10. 우정호 (2000). 수학 학습-지도 원리와 방법. 서울대학교출판부.(Woo, J. H. (2000). The principle and method of teaching and learning in mathematics. Seoul National University Press.)
  11. 임미인, 장혜원 (2017). 산술적 사고 수준의 분석 및 검사도구 개발, 한국초등수학교육학회지 21(4), 575-598.(Lim, M. I., & Chang, H. W. (2017). An analysis on levels of the arithmetical thinking and development of thearithmetical thinking level test, Journal of Elementary Mathematics Education in Korea 21(4), 575-598.)
  12. 장혜원 (1997). 수학 학습에서의 표현 및 표상에 관한 연구: 표상 모델 개발을 중심으로. 박사학위논문, 서울대학교.(Chang, H. W. (1997). A study on the representations in mathematics learning : focused on the development of a representation model. Doctoral dissertation, Seoul National University.)
  13. 정은실 (2006). 분수 개념의 의미 분석과 교육적 시사점탐구, 학교수학 8(2), 123-138.(Jeong, E. S. (2006). An educational analysis on fraction concept, Journal of Korea Society of Educational Studies in Mathematics 8(2), 123-138.)
  14. 최근배 (2015). 한국과 미국(Harcourt Math)의 초등수학 교과서 비교 분석, 한국초등수학교육학회지 19(1), 17-37.(Choi, K. B. (2015). A comparative study of elementary school mathematics textbooks of Korea(2007 curriculums) and America(Harcourt math), J ournal of Elementary Mathematics Education in Korea 19(1), 17-37.)
  15. 최창우 (2017). 한국과 뉴질랜드, 싱가포르에서의 분수지도에 관한 고찰, 영남수학회 33(2), 235-255.(Choi, C. W. (2017). On teaching fraction of elementary mathematics textbooks in Korea, New Zealand and Singapore, East Asian Mathematical Journal 33(2), 235-255.)
  16. Battista, M. T. (2012). Cognition-based assessment at teaching of fractions: Building on student's reasoning. portsmouth. NH: Heinemann.
  17. Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A.(1983). Rational number concepts. In Lesh, R., &Landau, M. (Eds.), Aquisition of mathematics concepts and process, 91-125. NY: Academic Press.
  18. Chval, K., Lannin, J., Jones, D., & Dougherty, B. J.(2013). Putting essential understanding of fractions into practice in grades 3-5. VA: NCTM.
  19. Empson, S. B. (1995). Research into practice: Using sharing situations to help children learn fractions, Teaching Children Mathematics 2, 110-114.
  20. Fosnot, C. & Dolk, M. (2002). Young mathematicians at work: Constructing fractions, decimals, and percents. NH: Heinemann.
  21. Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. Second handbook of research on mathematics teaching and learning. VA: NCTM.
  22. NCTM (2007). 학교수학을 위한 원리와 규준 (류희찬, 조완영, 이경화, 나귀수, 김남균, 방정숙 역), 서울: 경문사.
  23. Tall, D. O. & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limit and continuity, Educational Studies in Mathematics 12(2), 151-169. https://doi.org/10.1007/BF00305619
  24. Tall, D. O. (2003). 고등수학적 사고 (류희찬, 조완영, 김인수 역), 서울: 경문사.
  25. Usiskin, Z. (2011). Performance with fractions: A demonstration of cultural differences within the United States and overseas. In Reys, B. J. & Reys, R. E. (Eds.), We need another revolution, 97-105. VA: NCTM.