Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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Examining Mathematics Teachers' Intentions regarding Formative Assessment

수학 수업 지도안에 나타난 교사가 설계하는 형성평가 분석

  • Received : 2021.11.18
  • Accepted : 2021.12.29
  • Published : 2021.12.31
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Abstract

The purpose of this study is to reveal what mathematics teachers focus on and how they assess students' thinking during lessons enacted. For this purpose, we googled and searched internet sites to collect formative assessment materials for the year 2014 to 2019. The formative assessment tasks data were analyzed according to the levels cognitive demand levels and tasks suggested in textbooks in terms of degrees to which how they are related. The data analysis suggested as follows: a) most of the formative assessment tasks were at the low-level, in particular, PNC level tasks that require applying particular procedures without connections to concepts and meaning underlying the procedures, b) the assessment tasks appeared to be very similar to the tasks suggested in the secondary mathematics textbooks, and c) it seemed that 3 types of formative assessment, observation notes, self-assessment, and peer-assessment were dominantly utilized during mathematics lessons and these different types of formative assessment were employed apparently to find out whether students participated actively in class and in group activity, not how they go through understanding or thinking processes.

수학교사가 수업 중에 형성평가를 통해서 강조하는 바가 무엇인지 그 내용과 형식을 알아본다. 각 시·도 교육청 혹은 학교 홈페이지를 통해서 최근 5년 동안에 작성된 총 93개의 수업에 해당하는 형성평가 자료를 수집하였고 형성평가의 내용과 유형이 어떠한지를 살펴보았다. 수업자료에 제시된 형성평가의 문항 총 307개의 문항을 교과서와 비교하였으며 인지적 노력수준은 어떠한지를 분석하였다. 자료를 분석한 결과, 교사가 수업에서 제시하는 형성평가 문항들의 대부분이 절차의 개념의 연결성 없이 공식이나 규칙, 알고리듬 등의 특정 절차를 적용해서 답을 구하는 수준에 해당하는 것으로 나타났다. 또한 대부분의 문항들이 교과서의 문제들과 유사한 형태이며 수식 등에서 숫자를 변형하거나 할 뿐 구조적으로 크게 다른 점은 드러나지 않았다. 형성평가를 어떻게 시행할 것인지 방법의 측면에서 3가지 유형 즉 관찰평가지, 자기평가지, 동료평가지 등으로 나타났다. 즉, 교사가 주로 자신이 학생을 관찰하기 위해 구성한 관찰평가지, 학생들이 스스로의 학습을 평가하도록 하는 자기평가지와 동료평가지 등을 활용하는 것으로 드러났다. 중요한 사실은 교사들은 학생들이 수학의 내용을 어떻게 이해하는지를 파악하기보다는 수업에서 학생들이 얼마나 적극적으로 참여했으며, 모둠활동 시 맡은 역할을 잘 수행했는지 등 수업 태도 등에 더 관심을 둔다는 점이었다.

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References

  1. Kwon, H., & Kim, G. (2021). A comparative analysis of mathematical tasks in middle-school geometry of Korea and the US. Journal of Leaner-Centered Curriculum and Instruction, 21(3), 1531-1557. https://doi.org/10.22251/jlcci.2021.21.3.1531
  2. Kang, D., & Yeon, S. (2014). Elementary school teachers' perception and implementation of formative assessment. Journal of Leaner-Centered Curriculum and Instruction, 14(2), 27-43.
  3. Ministry of Education. (2015). National Mathematics Curriculum.
  4. Kwon, J., & Kim, G. (2013). An analysis of mathematical tasks in the middle school geometry. The Mathematical Education, 52(1), 111-128. https://doi.org/10.7468/MATHEDU.2013.52.1.111
  5. Kim, G., & Jeon, M. (2017b). Exploring how middle-school mathematics textbooks on functions provide students an opportunity-to-learn. School Mathematics 19(2), 289-317.
  6. Kim, G., & Jeon, M. (2017a). Exploring mathematics teachers' pedagogical design capacity: How mathematics teachers plan and design their mathematics lessons.. The Mathematical Education, 56(4), 365-385. https://doi.org/10.7468/MATHEDU.2017.56.4.365
  7. Kim, M., & Kim, G. (2013). The analysis of mathematical tasks in the high school mathematics. School Mathematics, 15(1), 37-59.
  8. Kim, M. (2013). Secondary mathematics teachers' use of mathematics textbooks and teacher's guide. School Mathematics, 15(3), 503-531.
  9. Kim, Y. (2017). Action research on math competencies-oriented assessment of integrated instruction. Journal of Elementary Mathematics Education in Korea, 21(1), 93-113.
  10. Kim, H. (2019). Effectiveness of mathematics education through the process-oriented evaluation-focusing on geometry and vector subjects. Journal of the Korean School Mathematics Society, 22(4), 369-393. https://doi.org/10.30807/ksms.2019.22.4.002
  11. Ryu, H., Lee, B., Yang, M., Choe, S., & Byun, H. (2012). Development of formative assessment program in geometry area for the first graders of middle school. Journal of the Korean School Mathematics Society, 15(1), 137-154.
  12. Park, J. (2018). Formative assessment and objectivity in assessment. Journal of Educational Evaluation, 31(3), 483-499.
  13. Seung, E., Nam, J., & Choi, B. (2000). The characteristics of formative assessment practiced in middle school science teaching from a constructivist perspective. Journal of the Korean Association for Research in Science Education, 20(3), 455-467.
  14. Lee, K., Kang, Y., Ko, E., Lee, D., Shin, B., Lee, H., & Kim, S. (2016). Exploration of the direction for the practice of process-focused assessment. Journal of Educational Research in Mathematics, 26(4), 819-834.
  15. Lee, B., Yang, M., Byun, H., & Ryu, H. (2011). Analysis on the effectiveness of applying CRESST formative assessment program to the 7th grade level-differentiated math classes. Communications of Mathematical Education, 25(2), 431-450. https://doi.org/10.7468/JKSMEE.2011.25.2.431
  16. Lee, S., & Kim, G. (2019). How middle-school mathematics textbooks of Korea and the US support to develop students' statistical reasoning. The Mathematical Education, 58(1), 139-160. https://doi.org/10.7468/MATHEDU.2019.58.1.139
  17. Choe, S., Hwang, H., & Ryu, H. (2010). Understanding and effectiveness of formative assessment program in CRESST focused on the algebra domain in the 8th grade. School Mathematics, 12(2), 193-217.
  18. Hong, C. J, & Kim, G. (2012). Functions in the middle school mathematics: The cognitive demand of the mathematical tasks. School Mathematics, 14(2), 213-232
  19. Baron, L. M. (2016). Formative assessment at work in the classroom. Mathematics Teacher, 110(1), 46-52. https://doi.org/10.5951/mathteacher.110.1.0046
  20. Brahier, D. J. (2009). Teaching secondary and middle school mathematics (3rd ed.). Boston: Pearson.
  21. Boston, M. D., & Wilhelm, A. G. (2015). Middle school mathematics instruction in instructionally focused urban districts. Urban Education, 1-33.
  22. Fennell, F., Kobett, B., & Wray, J. A. (2015). Classroom-based formative assessments: Guiding teaching and learning. In C. Suurtamm, & A. R. McDuffie (Eds.), Assessment to enhance teaching and learning (pp. 51-62). Reston, VA: National Council of Teachers of Mathematics.
  23. Henningsen, M., & Stein, 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
  24. Marynowski, R. (2015). Formative assessment strategies in the secondary mathematics classroom. In C. Suurtamm, & A. R. McDuffie (Eds.), Assessment to enhance teaching and learning (pp. 167-173). Reston, VA: National Council of Teachers of Mathematics.
  25. National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: Author.
  26. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  27. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
  28. National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Washington, DC: National Academy Press.
  29. Silver, E. A., & Smith, M. S. (2015). Integrating powerful practices: Formative assessment and cognitively demanding mathematics tasks. In C. Suurtamm, & A. R. McDuffie (Eds.), Assessment to enhance teaching and learning (pp.5-14). Reston, VA: National Council of Teachers of Mathematics.
  30. Steel, M., & Smith, M. S. (2018). The mathematical tasks framework and formative assessment. In Silver, E. A., & V. L. Mills(Eds.), A fresh look at formative assessment in mathematics teaching(pp. 103-125). Reston, VA: National Council of Teachers of Mathematics.
  31. Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction. Reston, VA: National Council of Teachers of Mathematics.