Education of Primary School Mathematics (한국수학교육학회지시리즈C:초등수학교육)

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

DOI QR Code

An Analysis of Pre-service Teachers' Pedagogical Content Knowledge about Story Problem for Division of Fractions

분수 나눗셈 스토리 문제 만들기에 관한 예비교사 지식 조사 연구

  • Noh, Jihwa (Department of Mathematics Education, Pusan National University) ;
  • Ko, Ho Kyoung (Graduate School of Education, Ajou University) ;
  • Huh, Nan (Graduate School of Education, Kyonggi University)
  • Received : 2015.12.31
  • Accepted : 2016.01.24
  • Published : 2016.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

This study examined pre-service teachers' pedagogical content knowledge of fraction division in a context where they were asked to write a story problem for a symbolic expression illustrating a whole number divided by a proper fraction. Problem-posing is an important instructional strategy with the potential to create meaningful contexts for learning mathematical concepts, especially when real-world applications are intended. In this study, story problems written by 135 elementary pre-service teachers were analyzed with respect to mathematical correctness. error types, and division models. Patterns and tendencies in elementary pre-service teachers' knowledge of fraction division were identified. Implicaitons for teaching and teacher education are discussed.

본 연구는 초등 예비교사의 교사지식 중 분수 나눗셈 스토리 문제 제기(problem posing) 수행 정도를 파악하고자 하였다. 나눗셈에 관한 스토리 문제 제기 능력은 나눗셈의 개념을 실생활 맥락에서 유연하게 사용하는 능력과도 관련이 있기 때문에 초등 예비교사들이 향후 교실에서 실생활 소재를 통해 나눗셈 교수 내용을 구성하고 가르치는데 있어 중요한 능력이라 할 수 있다. 이를 위하여 초등 예비교사 135명을 대상으로 자연수 나누기 분수 문제에 대한 설문조사를 실시하고, 분석틀 기준에 따라 '수학적 정교성'과 '주요 오류 유형' 그리고 '나눗셈 연산 모델'의 세 부분으로 나누어 자료를 분석함에 따라 초등 예비교사의 나눗셈 교사 지식에 대한 시사점을 제공하였다.

Keywords

References

  1. 방정숙.이지영 (2009a). 사례연구를 통한 분수 나눗셈의 연산 감각 분석. 학교수학 11(1), 71-91.(Park, J. S. & Lee, J. Y. (2009a). An Analysis of Operation Sense in Division of Fraction Based on Case Study. School Mathematics 11(1), 71-91.)
  2. 방정숙.이지영 (2009b). 분수의 곱셈과 나눗셈에 관한 초등학교 수학과 교과용 도서 분석. 학교수학 11(4), 723-743(Park, J. S. & Lee, J. Y. (2009b). An Analysis of the Multiplication and Division of Fractions in Elementary Mathematics Instructional Meterials. School Mathematics 11(4). 723-743)
  3. 서관석.전경순 (2000). 예비 초등 교사들의 분수 연산에 관한 내용적 지식과 교수학적 지식 수준에 대한 연구 - 교사교육적 관점. 수학교육학연구 10(1), 103-113.(Seo, K. S. & Jeon K. (2000). A Study on Elementary Preservice Teachers' Subject Matter Knowledge and Pedagogical Content Knowledge in Fraction-related Operations: A Teacher Education Perspective. Journal of Educational Research in Mathematics 10(1), 103-113.)
  4. 이미경 외 (2004). PISA 2003 결과 분석 연구-수학적 소양, 읽기 소양, 과학적 소양 수준 및 배경변인 분석. 연구보고RRE 2004-2-1. 한국교육과정평가원.(Lee, M. K., et al. (2004). The PISA 2003 Results-An Analysis of performances and influences on Mathematical Literacy, Reading Proficiency, Scientific Literacy. Report, RRE 2004-2-1. Korea Institute for Curriculum and Education.)
  5. 이미경 외 (2007). OECD/PISA 평가틀 및 공개 문항 분석. 한국교육과정평가원. 연구자료 ORM 2007-24.(Lee, M. K., et al. (2007). An Analysis of the Assessment Rubric for and Released Items of OECD/PISA. Report, ORM 2007-24. Korea Institute for Curriculum and Education.)
  6. 이재학.정상권.김선희.최민식.원유미.김영진, 고호경 (2013). 스토리텔링을 활용한 중학교 기하영역 자료 개발 연구. 한국수학교육학회지 시리즈E <수학교육 논문집> 27(3), 341-356.(Lee, J. H., Chung, S. K., Kim, S. H., Choi, M. S., Won,, Y. M., Kim, Y. J., & Ko, H. K. (2013). Development of Meterial for Middle School Geometry using Storytelling. Communications of Mathematical Education 27(3). 235-249.)
  7. 임청환 (2003). 과학 교과교육학 지식의 본질과 발달. 한국지구과학회지 24(4), 235-249.(Lim, C. H. (2003). Nature and Development of Pedagogical Content Knowledge in Science Teaching. The Journal of The Korean Earth Science Society 24(4), 235-249.)
  8. 조지민.김수진.이상하.김미영.옥현진.임해미 (2011). 2011년 국제 학업성취도 평가 연구(PISS/TIMSS) : TIMSS 2011 본검사 시행보고서, 연구보고 RRE 2011-4-1. 한국교육과정평가원.(Cho, J. M., Kim, S. J., Lee, S. H., Kim, M. Y., Ok, H. J., & Lim, H. M. (2011). The 2011 International Academic Achievements Tests (PISS/TIMSS): An Administration Report of the 2011 TIMSS. Report, RRE 2011-4-1. Korea Institute for Curriculum and Education.)
  9. Ball, D. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21, 132-144. https://doi.org/10.2307/749140
  10. Ball, D. L., 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.
  11. 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
  12. 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
  13. Baroody, J., & Coslick, R. T. (1998). Fostering Children's Mathenatical Power: An Investigative Approach to K-8 Mathematics Instruction. Mahwha, NJ: Lawrence Erlbaum Associates.
  14. Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics 62, 211-230. https://doi.org/10.1007/s10649-006-7834-1
  15. Cobb, P., T. Wood, & E. Yackel(1993). Discourse mathematical thinking and classroom practice. In E. A. Forman, N. Minick, & C. A. Stone, (Eds.), Contexts for learning. New York: Oxford University Press.
  16. Cobb, P., T. Wood, T., Yackel E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M.(1991). Assessment of a Problem-Centered Second-Grade Mathematics Project. Journal for Research in Mathematics Education 22, 3-29. https://doi.org/10.2307/749551
  17. 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
  18. 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
  19. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers'understanding s of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
  20. McAllister, C., & Beaver, C. (2012). Identification of error types in preservice teachers' attempts to create fraction story problems for specified operations. School Science & Mathematics 112(2), 88-98. https://doi.org/10.1111/j.1949-8594.2011.00122.x
  21. National Mathematics Advisory Panel. (2008). Foun dations for success: The final report of the Natio nal Mathematics Advisory Panel. Washington, D C: U.S. Department of Education. Retrieved from http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf
  22. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Authur.
  23. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  24. 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
  25. Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review 57, 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
  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. 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 (pp. 95-113) . Reston, VA: NCTM.
  28. 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
  29. 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
  30. Vygotsky(1978). Mind in Society : The Development of Higher Psychological Processes. Cambridge: Harvard University Press
  31. 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 (pp. 129-140). Reston, VA: NCTM.

Cited by

  1. 초등학생들의 분수 나눗셈 문제해결 방법에 대한 예비교사들의 지식 분석 vol.23, pp.2, 2016, https://doi.org/10.30807/ksms.2020.23.2.002
  2. Analysis of Abduction in Mathematics Problem Posing and Solving vol.30, pp.0, 2020, https://doi.org/10.29275/jerm.2020.02.30.1.89