The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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An analysis of mathematical tasks in the middle school geometry

중학교 수학 교과서에 제시된 기하영역의 수학 과제 분석

  • Received : 2013.01.17
  • Accepted : 2013.02.15
  • Published : 2013.02.28
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Abstract

The purpose of this study was to examine and analyze the cognitive demand of the mathematical tasks suggested in the middle school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks in the strand of geometry in the textbooks. We adopted the framework for mathematical task analysis suggested by Stein & Smith(1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at high level and the rest at low level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures. In particular, the high level tasks were presented at the end of each chapter or unit for wrap up rather than as key resources.

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References

  1. 권나영, 김래영, 김구연 (2011). 초, 중등 수학과 교육과정 연구의 주제별 동향분석, 수학교육 50(4), 507-520.(Kwon, N. Y., Kim, R. Y., & Kim, G. (2011). Trends in research on mathematics curriculum: An analysis of research topics, The Mathematical Education 50(4) 507-520.)
  2. 교육과학기술부 (2012). 수학교육 선진화 방안. 교육과학기술부 보도자료.(Ministry of Education, Science and Technology (2012). Strategies for Mathematics Education Advancement. Press Release: Author.)
  3. 교육인적자원부 (2007). 중학교 교육과정해설. 서울: 저자.(Ministry of Education & Human Resources Development (2007). A curriculum guide for middle school. Seoul: Author.)
  4. 김구연 (2010). The analysis of a mathematics curriculum material: Addition and subtraction in grade 3, 교육과정평가연구 13(2), 59-78.(Kim, G. (2010). The analysis of a mathematics curriculum material: Addition and subtraction in grade 3, The Journal of Curriculum and Evaluation 13(2), 59-78.)
  5. 김민혁 (2012). 수학교사의 교과서 및 교사용 지도서 활용도 조사. 석사학위 논문, 서강대학교.(Kim, M. H. (2012). Secondary mathematic teachers' use of curriculum materials. Master's thesis: Sogang University.)
  6. 박경미, 김동원 (2011). 우리나라 수학교육의 문제점 진단을 위한 조사 연구, 수학교육 50(1), 89-102.(Park, K. M., & Kim, D. W. (2011). A survey research to diagnose the problems of mathematics education in Korea, The Mathematical Education 50(1), 89-102.)
  7. 박선영, 김원경 (2011). 국내외 수학교육 연구 동향 비교 분석, 수학교육 50(3), 285-308.(Park, S. Y., & Kim, W. K. (2011). A comparative analysis on research trends of secondary mathematics, The Mathematical Education 50(3), 285-308.)
  8. 우정호, 박교식, 박경미, 이경화, 김남희, 임재훈, 박 인, 이영란, 고현주, 김은경 (2009a). 중학교 수학 1, 서울: 두산동아.(Woo, J. H., Park, K. S., Park, K., Lee, K. H., Kim, N. H., Lim, J. H., Park, I., Lee, Y. R., Kho, H. J., & Kim, E. K. (2009a). Mathematics 1, grade 7, Seoul: Doosan-Dongah.)
  9. 우정호, 박교식, 박경미, 이경화, 김남희, 임재훈, 박 인, 이영란, 고현주, 김은경 (2009b). 중학교 수학 익힘책 1, 서울: 두산동아.(Woo, J. H., Park, K. S., Park, K. M., Lee, K. H., Kim, N. H., Lim, J. H., Park, I., Lee, Y. R., Kho, H. J., & Kim, E. K. (2009b). Mathematics workbook 1, grade 7, Seoul: Doosan-Dongah.)
  10. 우정호, 박교식, 박경미, 이경화, 김남희, 임재훈, 박 인, 이영란, 고현주, 김은경 (2010a). 중학교 수학 2, 서울: 두산동아.(Woo, J. H., Park, K. S., Park, K. M., Lee, K. H., Kim, N. H., Lim, J. H., Park, I., Lee, Y. R., Kho, H. J., & Kim, E. K. (2010a). Mathematics 2, grade 8, Seoul: Doosan-Dongah.)
  11. 우정호, 박교식, 박경미, 이경화, 김남희, 임재훈, 박 인, 이영란, 고현주, 김은경 (2010b). 중학교 수학 익힘책 2, 서울: 두산동아.(Woo, J. H., Park, K. S., Park, K. M., Lee, K. H., Kim, N. H., Lim, J. H., Park, I., Lee, Y. R., Kho, H. J., & Kim, E. K. (2010b). Mathematics workbook 2, grade 8, Seoul: Doosan-Dongah.)
  12. 우정호, 박교식, 박경미, 이경화, 김남희, 임재훈, 박 인, 이영란, 고현주, 김은경 (2011a). 중학교 수학 3, 서울: 두산동아.(Woo, J. H., Park, K. S., Park, K. M., Lee, K. H., Kim, N. H., Lim, J. H., Park, I., Lee, Y. R., Kho, H. J., & Kim, E. K. (2011a). Mathematics 3, grade 9, Seoul: Doosan-Dongah.)
  13. 우정호, 박교식, 박경미, 이경화, 김남희, 임재훈, 박 인, 이영란, 고현주, 김은경 (2011b). 중학교 수학 익힘책 3. 서울: 두산동아.(Woo, J. H., Park, K. S., Park, K. M., Lee, K. H., Kim, N. H., Lim, J. H., Park, I., Lee, Y. R., Kho, H. J., & Kim, E. K. (2011b). Mathematics workbook 3, grade 9, Seoul: Doosan-Dongah.)
  14. 정상권, 이재학, 박혜숙, 홍진곤, 서혜숙, 박부성, 강은주 (2009a). 중학교 수학 1, 서울: 금성출판사.(Cheong, S. W., Lee, J. H., Park, H. S., Hong, J. K., Seo, H. S., Park, B. S., & Kang, E. J.(2009a). Mathematics 1, grade 7, Seoul: Kumsung.)
  15. 정상권, 이재학, 박혜숙, 홍진곤, 서혜숙, 박부성, 강은주 (2009b). 중학교 수학 익힘책 1, 서울: 금성출판사.(Cheong, S. W., Lee, J. H., Park, H. S., Hong, J. K., Seo, H. S., Park, B. S., & Kang, E. J. (2009b). Mathematics workbook 1, grade 7, Seoul: Kumsung.)
  16. 정상권, 이재학, 박혜숙, 홍진곤, 서혜숙, 박부성, 강은주 (2010a). 중학교 수학 2, 서울: 금성출판사.(Cheong, S. W., Lee, J. H., Park, H. S., Hong, J. K., Seo, H. S., Park, B. S., & Kang, E. J. (2010a). Mathematics 2, grade 8, Seoul: Kumsung.)
  17. 정상권, 이재학, 박혜숙, 홍진곤, 서혜숙, 박부성, 강은주 (2010b). 중학교 수학 익힘책 2, 서울: 금성출판사.(Cheong, S. W., Lee, J. H., Park, H. S., Hong, J. K., Seo, H. S., Park, B. S., & Kang, E. J.(2010b). Mathematics workbook 2, grade 8, Seoul: Kumsung.)
  18. 정상권, 이재학, 박혜숙, 홍진곤, 서혜숙, 박부성, 강은주 (2011a). 중학교 수학 3, 서울: 금성출판사.(Cheong, S. W., Lee, J. H., Park, H. S., Hong, J. K., Seo, H. S., Park, B. S., & Kang, E. J. (2011a). Mathematics 3, grade 9, Seoul: Kumsung.)
  19. 정상권, 이재학, 박혜숙, 홍진곤, 서혜숙, 박부성, 강은주 (2011b). 중학교 수학 익힘책 3, 서울: 금성출판사.(Cheong, S. W., Lee, J. H., Park, H. S., Hong, J. K., Seo, H. S., Park, B. S., & Kang, E. J. (2011b). Mathematics workbook 3, grade 9, Seoul: Kumsung.)
  20. 최용준, 한대희, 박진교, 김강은, 신태양, 배명주 (2009a). 중학교 수학 1, 서울: 천재문화.(Choe. Y. J., Han, D. H., Park, J. K., Kim, K. E., Shin, T. Y., & Bae, M. J. (2009a). Mathematics 1, grade 7, Seoul: ChunjaeMunhwa.)
  21. 최용준, 한대희, 박진교, 김강은, 신태양, 배명주 (2009b). 중학교 수학 익힘책 1, 서울: 천재문화.(Choe. Y. J., Han, D. H., Park, J. K., Kim, K. E., Shin, T. Y., & Bae, M. J. (2009b). Mathematics workbook 1, grade 7, Seoul: ChunjaeMunhwa.)
  22. 최용준, 한대희, 박진교, 김강은, 신태양, 배명주 (2010a). 중학교 수학 2, 서울: 천재문화. Choe. Y. J., Han, D. H., Park, J. K., Kim, K. E., Shin, T. Y., & Bae, M. J.(2010a). Mathematics 2, grade 8, Seoul:ChunjaeMunhwa.
  23. 최용준, 한대희, 박진교, 김강은, 신태양, 배명주 (2010b). 중학교 수학 익힘책 2, 서울: 천재문화.(Choe. Y. J., Han, D. H., Park, J. K., Kim, K. E., Shin, T. Y., & Bae, M. J.(2010b). Mathematics workbook 2, grade 8, Seoul: ChunjaeMunhwa.)
  24. 최용준, 한대희, 박진교, 김강은, 신태양, 배명주 (2011a). 중학교 수학 3, 서울: 천재문화.(Choe. Y. J., Han, D. H., Park, J. K., Kim, K. E., Shin, T. Y., & Bae, M. J. (2011a). Mathematics 3, grade 9, Seoul: ChunjaeMunhwa.)
  25. 최용준, 한대희, 박진교, 김강은, 신태양, 배명주 (2011b). 중학교 수학 익힘책 3, 서울: 천재문화.(Choe. Y. J., Han, D. H., Park, J. K., Kim, K. E., Shin, T. Y., & Bae, M. J.(2011b). Mathematics workbook 3, grade 9, Seoul: ChunjaeMunhwa.)
  26. 홍창준, 김구연 (2012). 중학교 함수 단원의 수학과제 분석, 학교수학 14(2), 213-232.(Hong, C. J., & Kim, G. (2012). Functions in the middle school mathematics: The cognitive demand of mathematical tasks. School Mathematics 14(2), 213-232.)
  27. Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is-or might be-the role of curriculum materials in teacher learning and instructional reform? Educational Researcher 25(9), 6-8.
  28. Battista, M. T. (2007). Highlights of research on learning school geometry. In F. Lester, Jr.(Ed.), Second handbook of research on mathematics teaching and learning(pp. 91-108). Charlotte, NC: Information Age.
  29. Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers' learning, Elementary School Journal 103, 287-311. https://doi.org/10.1086/499727
  30. Doyle, W. (1983) Academic work. Review of Educational Research 53(2), 159-199. https://doi.org/10.3102/00346543053002159
  31. Henningsen, M., & Sten, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning, Journal for Research in Mathematics Education 28, 524-549. https://doi.org/10.2307/749690
  32. Hiebert, J., & Wearne, D. (1993). Instructional, classroom discourse, and student's learning in second-grade arithmetic. American Educational Research Journal 30, 393-425. https://doi.org/10.3102/00028312030002393
  33. National Council of Teachers of Mathematics (1995). Assessment Standards for school mathematics, Reston, VA: Author.
  34. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics, Reston, VA: Author.
  35. Rezat, S. (2006). A Model of Textbook Use. In J. Novotna, H. Moraova, M. Kratka & N. A. Stehlikova(Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 409-416). Prague, Czech Republic.
  36. Robitaille, D. F., & Travers, K. J. (1992). International studies of achievement in mathematics. In D. A. Grouws (Ed.), Handbook of Research on mathematics Teaching and Learning (pp. 687-709). New York: Macmillan.
  37. Smith, M. S., & Stein. M. K. (1998) Selecting and creating mathematical: from research to practice, Mathematics Teaching in the Middle School 3, 344-350.
  38. Stein, M. K., & Kim, G. (2009). The role of mathematics curriculum materials in large-scale urban reform. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 37-55). New York: Routledge.
  39. Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning. An analysis of mathematical used in reform classrooms, American Educational Research Journal 33, 455-488. https://doi.org/10.3102/00028312033002455
  40. Stein, M. K., Remillard, J. T., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Charlotte, NC: Information Age.
  41. Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice, Mathematics Teaching in the Middle School 3, 268-275.
  42. Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. (2000). Implementing Standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.
  43. Trafton, P. R., Reys, B. J., & Wasman, D. G. (2001). Standards-based mathematics curriculum materials: A phrase in search of a definition, Phi Delta Kappan 83(3), 259-264. https://doi.org/10.1177/003172170108300316

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