Education of Primary School Mathematics (한국수학교육학회지시리즈C:초등수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Preservice Elementary Mathematics Teachers' Curricular Noticing: Focusing on the Lesson Planning for Rate

초등예비교사의 교육과정에 관한 노티싱: 비율 수업을 중심으로

  • Received : 2021.03.19
  • Accepted : 2021.04.21
  • Published : 2021.04.30
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Abstract

Curricular noticing is about how teachers understand the content and pedagogical opportunities inherent in curriculum materials. Since the enacted curriculum differs depending on which aspect of the curriculum material is paid attention to and how to interpret it, it is necessary to focus on Curricular Attending and Curricular Interpreting in Curricular Noticing for enhancing the teaching expertise of preservice teachers. First, this study categorized the objects that preservice elementary mathematics teachers attended when planning the lesson for rate. Second, in order to find out the reason for paying attention to those objects, it was analyzed what factors were related to interpret. By discussing the results, implications were drawn on how to use Curricular Noticing in preservice teacher education to enhance the pedagogical design competency of preservice elementary mathematics teachers.

교육과정에 관한 노티싱은 교사가 교육과정 자료에 내재된 내용과 교수학적 기회에 대해 어떻게 이해하는지에 관한 것이다. 교육과정에 관한 노티싱에서 교육과정 자료의 어떤 측면에 관심을 기울이고 그것에 관해 어떻게 해석하는지에 따라 교육과정의 실행 모습이 달라지기 때문에, 예비교사교육에서는 수업 전문성 신장을 위해 교육과정에 관한 노티싱의 과정 중 관심을 기울이고 해석하는 과정에 초점을 둘 필요가 있다. 이에 본 연구에서는 초등예비교사가 비율 수업을 설계하기 위하여 교육과정 자료를 활용할 때 관심을 기울이는 대상을 찾고, 그것에 관해 어떻게 해석하는지를 분석하였다. 이러한 분석결과에 따른 논의를 통해 초등예비교사의 수업 설계 역량 신장을 위해 예비교사교육에서 교육과정에 관한 노티싱을 활용하는 방안에 관한 시사점을 도출하였다.

Keywords

Acknowledgement

이 논문은 2020년 대한민국 교육부와 한국연구재단의 지원을 받아 수행된 연구임 (NRF-2020S1A5B5A17091256)

References

  1. Kang, H. I., & Choi Eun Ah(2015). Teacher knowledge necessary to address student erros and difficulties about ratio and rate. School Mathematics, 17(4), 613-632.
  2. Ministry of Education (2015). Mathematics curriculum. Ministry of Education Notice 2015-74 [supplement 8].
  3. Ministry of Education (2018). National plans for diversification of textbooks and free publication system, Retrieved from https://www.moe.go.kr/boardCnts/view.do?boardID=295&lev=0&statusYN=W&s=moe&m=020401&opType=N&boardSeq=76393 (2021.03.15.)
  4. Ministry of Education (2019a). Korean national elementary mathematics 6-1. Seoul: Visang Education.
  5. Ministry of Education (2019b). Korean national elementary mathematics activity book 6-1. Seoul: Visang Education.
  6. Ministry of Education (2019c). Korean national elementary mathematics 6-1 teachers' guide. Seoul: Visang Education.
  7. Ku, N. Y., & Lee, K. H. (2020b). A study on middle school teachers' geometric unit curriculum material use A case of teacher community. School Mathematics, 22(2), 251-275. https://doi.org/10.29275/sm.2020.06.22.2.251
  8. Ku, N. Y., Tak, B. J., Choi, I. Y., & Kang, H. Y. (2019). An analysis of preservice mathematics teachers' reading of curriculum materials: Focused on conditional probability. The Mathematical Education, 58(3), 347-365. https://doi.org/10.7468/MATHEDU.2019.58.3.347
  9. Park, S. Y., & Lee, K. H. (2018). The comparison and analysis of models on ratio and rate in elementary mathematics textbooks: Centering on multiplicative perspectives on proportional relationships and the structure of proportion situations. Education of Primary School Mathematics, 21(2), 237-260. https://doi.org/10.7468/JKSMEC.2018.21.2.237
  10. Park, S. A., & Oh, Y. Y. (2017). An analysis of teachers' pedagogical content knowledge about teaching ratio and rate. Journal of Elementary Mathematics Education in Korea, 21(1), 215-241.
  11. Park, H. O., & Park, M. G. (2012). An analysis on the epistemological obstacles of elementary students in the learning of ratio and rate. Education of Primary School Mathematics, 15(2), 159-170. https://doi.org/10.7468/JKSMEC.2012.15.2.159
  12. Park, H. J., & Jeong, E. S. (2010). A comparative analysis on units about ratio and rate between Korean mathematics textbook and MIC textbook. Journal of Elementary Mathematics Education in Korea, 14(3), 769-788.
  13. Sang, K. A., Kim, K. H., Park, S. W., Jeon, S. K., Park, M. M., & Lee, J. W. (2020). The Trends in International Mathematics and Science Study (TIMSS): Finding form TIMSS 2019 for Korea. Chungbuk: Korea Institute for Curriculum and Evaluation.
  14. Seo, E. M., Pang, J. S., & Lee, J. Y. (2017). An analysis of lessons to teach proportional reasoning with visual models-Focused on ratio table, double number line, and double tape diagram. Journal of Educational Research in Mathematics, 27(4), 791-810.
  15. Yoo, H. J., Cho, Y. M., Na, G. S., Go, E. S., Go, J. H., & Lee,.D. H. (2019). Elementary Mathematics Textbook Research and Guidance. Gyeonggi: Dongmyeongsa.
  16. Yim, J. H., & Lee, H. S. (2015). Visual representations for improving proportional reasoning in solving word problems. Journal of Educational Research in Mathematics, 25(2), 189-206.
  17. Chang, H. W., Lim, M. I., Yu, M. G., Park, H. M., Kim, J. S., & Lee, H. Y. (2017). A comparative analysis of ratio and rate in elementary mathematics textbook. Journal of Elementary Mathematics Education in Korea, 21(1), 135-160.
  18. Chang, H. W., Lim, M. I., Yu, M. G., Park, H. M., Kim, J. S., & Lee, H. Y. (2018). The application of double number line in elementary school mathematics education. School Mathematics, 20(1), 227-249. https://doi.org/10.29275/sm.2018.03.20.1.227
  19. Chong, Y. O. (2015). Teaching proportional reasoning in elementary school mathematics. Journal of Educational Research in Mathematics, 25(1), 21-58.
  20. Jeong, E. S. (2003). An educational analysis on ratio concept. Journal of Educational Research in Mathematics, 13(3), 247-265.
  21. Choi, J. S. (2019). Reflection on Korea mathematics curriculum through analyzing TIMSS 2015 'Number' Domain. Journal of Learner-Centered Curriculum and Instruction, 19(11), 1211-1233.
  22. Amador, J. M., Males, L. M., Earnest, D., & Dietiker, L. (2017). Curricular noticing: Theory on and practice of teachers' curricular use. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 427-443). Cham, Switzerland: Springer.
  23. 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), 6-14. https://doi.org/10.2307/1177151
  24. Beckmann, S., & Izsak, A. (2015). Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Journal for Research in Mathematics Education, 46(1), 17-38. https://doi.org/10.5951/jresematheduc.46.1.0017
  25. Brown, M. (2009). Toward a theory of curriculum design and use: Understanding the teacher-tool relationship. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 17-37). New York, NY: Routledge.
  26. Choppin, J. (2011). Learned adaptations: teachers' understanding and use of curriculum resources. Journal of Mathematics Teacher Education, 14(5), 331-353. https://doi.org/10.1007/s10857-011-9170-3
  27. Choy, B. H., & Dindyal, J. (2021). Productive teacher noticing and affordances of typical problems. ZDM, 1-18.
  28. Choy, B. H., Thomas, M. O., & Yoon, C. (2017). The FOCUS framework: characterising productive noticing during lesson planning, delivery and review. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 445-466). Cham, Switzerland: Springer.
  29. Creswell, J. W. (2007). Qualitative inquiry & research design: choosing among five approaches (2nd ed.). 조흥식, 정선욱, 김진숙, 권지성 역 (2010). 질적 연구방법론-다섯 가지 접근. 서울: 학지사.
  30. Dietiker, L., Males, L. M., Amador, J. M., & Earnest, D. (2018). Research Commentary: Curricular Noticing: A Framework to Describe Teachers' Interactions With Curriculum Materials. Journal for Research in Mathematics Education, 49(5), 521-532. https://doi.org/10.5951/jresematheduc.49.5.0521
  31. Earnest, D. & Amador, J. M. (2019). Lesson planimation: prospective elementary teachers' interactions with mathematics curricula. Journal of Mathematics Teacher Education, 22(1), 37-68. https://doi.org/10.1007/s10857-017-9374-2
  32. Grossman, P., & Thompson, C. (2004). Curriculum Materials: Scaffolds for New Teacher Learning? A Research Report. Document R-04-1. Center for the study of teaching and policy.
  33. Ivars, P., Fernandez, C., Llinares, S., & Choy, B. H. (2018). Enhancing noticing: using a hypothetical learning trajectory to improve pre-service primary teachers' professional discourse. Eurasia Journal of Mathematics, Science and Technology Education, 14(11), em1599.
  34. Jacobs, V. R., Lamb, L. L. C., & Phillip, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
  35. Lamon, S. J. (1999). Teaching fractions and ratios for understanding : Essential context knowledge and instructional strategies for teachers. Lawrence Erlbaum Associates, Inc.
  36. Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. Lester (Ed), Second handbook of research on mathematics teaching and learning (pp. 629-666). Reston, VA: National Council of Teachers of Mathematics.
  37. Land, T. J., Tyminski, A. M., & Drake, C. (2015). Examining pre-service elementary mathematics teachers' reading of educative curriculum materials. Teaching and Teacher Education, 51, 16-26. https://doi.org/10.1016/j.tate.2015.05.009
  38. Lloyd, G. M. (2009). School mathematics curriculum materials for teachers' learning: future elementary teachers' interactions with curriculum materials in a mathematics course in the United States. ZDM, 41, 763-775. https://doi.org/10.1007/s11858-009-0206-4
  39. Lobato, J., Ellis, A. B., Charles, R. I., & Zbiek, R. M. (2010). Developing essential understanding of ratios, proportions, and proportional reasoning. 박정숙, 강현영, 고은성, 이동환 역 (2016). 비, 비례, 비례추론의 필수 이해. 서울: 교우사.
  40. Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. 권오남 외 역 (2015). 수학 과제의 설계와 활용. 서울: 경문사.
  41. NCTM (2000). Principles and standards for school mathematics. 류희찬 외 역 (2007). 학교수학을 위한 원리와 규준. 서울: 경문사.
  42. Remillard, J. T. (2000). Can curriculum materials support teachers' learning? Two fourth grade teachers' use of a new mathematics text. The Elementary School Journal, 100(4), 331-350. https://doi.org/10.1086/499645
  43. Remillard, J. T. (2005). Examining key concepts in research on teachers' use of mathematics curricula. Review of Educational Research, 75(2), 211-246. https://doi.org/10.3102/00346543075002211
  44. Remillard, J. T. (2013). Examining resources and re-sourcing as insights into teaching. ZDM, 45(7), 925-927. https://doi.org/10.1007/s11858-013-0549-8
  45. Roth-McDuffie, A., Choppin, J., Drake, C., & Davis, J. (2018). Middle school mathematics teachers' orientations and noticing of features of mathematics curriculum materials. International Journal of Educational Research, 92, 173-187. https://doi.org/10.1016/j.ijer.2018.09.019
  46. Roth-McDuffie, A., & Mather, M. (2009). Middle school mathematics teachers' use of curricular reasoning in a collaborative professional development project. In J. T., Remillar, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 302-320). New York, NY: Routledge.
  47. Sherin, M. G., & Drake, C. (2009). Curriculum strategy framework: Investigating patterns in teachers' use of a reform based elementary mathematics curriculum. Journal of Curriculum Studies, 41(4), 467-500. https://doi.org/10.1080/00220270802696115
  48. Shield, M., & Dole, S. (2013). Assessing the potential of mathematics textbooks to promote deep learning. Educational studies in mathematics, 82(2), 183-199. https://doi.org/10.1007/s10649-012-9415-9
  49. Streefland, L. (1985). Search for the Roots of Ratio: Some Thoughts on the Long Term Learning Process (Towards... A Theory): Part II: The Outline of the Long Term Learning Process. Educational Studies in Mathematics, 16(1), 75-94. https://doi.org/10.1007/BF00354884
  50. Tyminski, A. M., Simpson, A. J., Land, T. J., Drake, C., & Dede, E. (2020). Prospective elementary mathematics teachers' noticing of childrens' mathematics: a focus on extending moves. Journal of Mathematics Teacher Education, 1-29.
  51. Warshauer, H., Starkey, C., Herrera, C. A., & Smith, S. (2019). Developing prospective teachers' noticing and notions of productive struggle with video analysis in a mathematics content course. Journal of Mathematcis Teacher Education, 1-33.
  52. Webb, D. C., Boswinkel, N., & Dekker, T. (2008). Beneath the tip of the iceberg: Using representations to support student understanding. Mathematics Teaching in the Middle School, 14(2), 110-113 https://doi.org/10.5951/mtms.14.2.0110