Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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Teachers' Decision and Enactment of Their Content Knowledge Assessed Through Problem Posing - A U.S. Case

문제 만들기를 통해 알아본 교사의 내용지식 사용에 대한 결정과 수행 - 미국 사례를 중심으로

  • Received : 2017.03.28
  • Accepted : 2017.04.25
  • Published : 2017.05.15
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Abstract

164 preservice elementary teachers' decision and enactment of their knowledge of fraction multiplication were examined in a context where they were asked to write a story problem for a multiplication problem with two proper fractions. Participants were selected from an entry level course and an exit level course of their teacher preparation program to reveal any differences between the groups as well as any recognizable patterns within each group and overall. Patterns and tendencies in writing story problems were identified and analyzed. Implications of the findings for teaching and teacher education are discussed.

본 연구에서는 예비교사가 문제 만들기 과제를 위해 분수곱셈지식을 사용하는 과정에서 드러나는 이해의 정도와 유형을 미국사례를 중심으로 조사하였다. 이를 위하여, 미국 대학 교사교육과정의 입문단계와 종료단계에 있는 총 164명의 예비초등교사를 대상으로 분수곱셈에 대한 문장제 문제를 작성하게 하고, 이를 수학적 정교성과 작성한 문제에 사용한 분수곱셈의 의미의 유형으로 분석하였다. 분석결과는 교육과정 입문단계와 종료단계의 예비교사 그룹 간의 차이점, 각 그룹, 그리고 전체적인 경향에 대해 기술하였고, 분수곱셈 지도와 교사교육에 대한 시사점을 제공하였다.

Keywords

References

  1. Ball, D.L. (1990). Prospective elementary and secondary teachers' understanding of division, Journal for Research in Mathematics Education, 21, 132-144. https://doi.org/10.2307/749140
  2. Ball, D., Hill, H.C., & Bass, H. (2005). Knowing mathematics for teaching: who knows mathematics well enough to teach third grade and how can we decide? American Educator, 29, 14-22, 43-46.
  3. Ball, D.L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  4. Barlow, A.T. & Cates, J.M. (2006). The impact of problem posing on elementary teachers' beliefs about mathematics and mathematics teaching, School Science and Mathematics, 106(2), 64-73. https://doi.org/10.1111/j.1949-8594.2006.tb18136.x
  5. Charalambous, C.Y., Hill, H.C., & Mitchell, R.B. (2012). Two negative don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality, Journal of Curriculum Studies, 44(4), 489-513. https://doi.org/10.1080/00220272.2012.716974
  6. Common Core State Standards Initiative. (2010). The common core state standards for mathematics, Washington DC: National Governors Association Center for Best Practices and Council of Chief State School Officers.
  7. Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers, Washington, DC: Mathematical Association of America.
  8. Conference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II,. Washington, DC: Author.
  9. Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in pre-service teachers' practices, Educational Studies in Mathematics, 52(3), 243-270. https://doi.org/10.1023/A:1024364304664
  10. Hill, H.C., Rowan, B., & Ball, D.L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement, American Educational Research Journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
  11. Krathwohl, D.R. (1998). Methods of educational and social science research: An integrated approach (2nd ed.), New York: Addison Wesley Longman.
  12. Lampert, M, (1998). Study teaching as thinking practice. In J. Greeno & S.G. Goldman (Eds.), Thinking practice (53-78). Hillsdale, NJ: Erlbaum.
  13. Landis, J.R. & Koch, G.G. (1977). The measurement of observer agreement for categorical data, Biometrics, 33(1), 159-174. https://doi.org/10.2307/2529310
  14. Lee, S., Brown, R.E., & Orrill, C.H. (2011) Mathematics teachers' reasoning about fractions and decimals using drawn representations, Mathematical Thinking and Learning, 13(3), 198-220. https://doi.org/10.1080/10986065.2011.564993
  15. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understandings of fundamental mathematics in China and the United States., Mahwah, NJ: Erlbaum.
  16. McAllister, C. & Beaver, C. (2012). Identification of error types in preservice teachers' attempts to create fraction story problems for specified operations, School Science and Mathematics, 112(2), 88-98. https://doi.org/10.1111/j.1949-8594.2011.00122.x
  17. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics, Reston, VA: Author.
  18. National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Pane,. Washington, DC: U.S. Department of Education. Retrieved from http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf
  19. National Research Council. (2001). Adding it up: Helping children learn mathematics, Washington, DC: National Academy Press.
  20. Newton, K.J. (2008). An extensive analysis of pre-service elementary teachers' knowledge of fractions, American Educational Research Journal, 45(4), 1080-1110. https://doi.org/10.3102/0002831208320851
  21. Noh, J. & Sabey, K. (2014). What does multiplying two candy bars really mean? Educational Leadership 71(7). http://www.ascd.org/publications /educational-leadership/apr14/vol71/num07/abstract. aspx#What_Does_Multiplying_Two_Candy_Bars_Really_Mean.
  22. Noh, J. & Webb, M. (2014). Teacher learning of subject matter knowledge through an educative curriculum, Journal of Educational Research, 108(4), 292-305. https://doi.org/10.1080/00220671.2014.886176
  23. Rea, L.M. & Parker, R.A (1992). Designing and conducting survey research, San Francisco: Jossey-Boss.
  24. Remillard, J.T., Herbel-Eisenmann, B.A., & Lloyd, G.M. (2009). Mathematics teachers at work: Connecting curriculum materials and classroom instructio,. New York: Routledge.
  25. Rittle-Johnson, B. & Koedinger, K.R. (2005). Designing knowledge scaffolds to support mathematical problem solving. Cognition and Instruction, 23(3), 313-349. https://doi.org/10.1207/s1532690xci2303_1
  26. Smith, J.P., diSessa, A.A., & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition, The Journal of the Learning Sciences, 3(2), 115-163. https://doi.org/10.1207/s15327809jls0302_1
  27. Son, J.W., & Crespo, S. (2009). Prospective teachers' reasoning and response to a student's non-traditional strategy when dividing fractions, Journal of Mathematics Teacher Education, 12, 235-261. https://doi.org/10.1007/s10857-009-9112-5
  28. Thompson, P.W., & Saldanha, L.A. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, W.G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (95-113). Reston, VA: NCTM.
  29. Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions, Journal for Research in Mathematics Education, 31, 5-25. https://doi.org/10.2307/749817
  30. Tirosh, D., & Graeber, A.O. (1990). Evoking cognitive conflict to explore preservice teachers' thinking about division, Journal for Research in Mathematics Education, 21, 98-108. https://doi.org/10.2307/749137
  31. Toluk-Ucar, Z. (2009). Developing preservice teachers understanding of fractions through problem posing, Teaching and Teacher Education, 25(1), 166-175. https://doi.org/10.1016/j.tate.2008.08.003
  32. Whitin, D.J. (2004). Building a mathematical community through problem posing. In R.N. Rubenstein (Ed.), Perspectives on the teaching of mathematics: Sixty-sixth yearbook (129-140). Reston, VA: NCTM.
  33. Young, E. & Zientek, L. (2011). Fractions operations: An examination of prospective teachers' errors, confidence, and bias, Investigations in Mathematics Learning, 4(1), 1-23. https://doi.org/10.1080/24727466.2011.11790307