Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

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

DOI QR Code

An Analysis of Metacognition of Elementary Math Gifted Students in Mathematical Modeling Using the Task 'Floor Decorating'

'바닥 꾸미기' 과제를 이용한 수학적 모델링 과정에서 초등수학영재의 메타인지 분석

  • Received : 2023.05.17
  • Accepted : 2023.06.16
  • Published : 2023.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

Mathematical modeling can be described as a series of processes in which real-world problem situations are understood, interpreted using mathematical methods, and solved based on mathematical models. The effectiveness of mathematics instruction using mathematical modeling has been demonstrated through prior research. This study aims to explore insights for mathematical modeling instruction by analyzing the metacognitive characteristics shown in the mathematical modeling cycle, according to the mathematical thinking styles of elementary math gifted students. To achieve this, a mathematical thinking style assessment was conducted with 39 elementary math gifted students from University-affiliated Science Gifted Education Center, and based on the assessment results, they were classified into visual, analytical, and mixed groups. The metacognition manifested during the process of mathematical modeling for each group was analyzed. The analysis results revealed that metacognitive elements varied depending on the phases of modeling cycle and their mathematical thinking styles. Based on these findings, didactical implications for mathematical modeling instruction were derived.

수학적 모델링이란 실세계 문제 상황을 이해하고 이를 수학적인 방법으로 변환하여 수학적 모델을 토대로 실세계 문제 상황을 해결해나가는 일련의 과정이라고 할 수 있다. 선행연구를 통해 수학적 모델링을 활용한 수업의 학습 효과가 밝혀짐에 따라 우리나라에서도 효과적인 수학적 모델링 수업을 위한 다양한 연구가 이루어지고 있다. 본 연구는 초등수학영재의 수학적 사고 양식에 따라 수학적 모델링 과정에서 나타나는 메타인지적 특성을 분석함으로써 수학적 모델링 지도 과정에서의 시사점을 모색하는 것을 목적으로 한다. 이를 위해 S시 소재 대학부설과학영재교육원 초등수학 영재학생 39명을 대상으로 수학적 사고 양식 검사를 진행하여 검사 결과에 따라 시각적, 분석적, 혼합적 모둠으로 분류하고 각 사고 양식이 가장 뚜렷하게 드러나는 3개 모둠(총 12명)의 수학적 모델링 과정에서 나타나는 메타인지 특성을 분석하였다. 분석 결과, 모델링 단계와 모둠 특성에 따라 메타인지 요소가 다르게 나타나는 것을 확인하였으며, 이와 같은 분석 결과에 기초하여 수학적 모델링 지도 과정에서의 교수학적 시사점을 도출하였다.

Keywords

References

  1. Ministry of Education (2022). Mathematics curriculum 2022-33 [Book 8]. Ministry of Education. 
  2. Ministry of Education (2023). The fifth master plan for promotion of gifted education. Ministry of Education. 
  3. Ko, C., & Oh, Y. (2015). The effects of mathematical modeling activities on mathematical problem solving and mathematical dispositions. Journal of Elementary Mathematics Education in Korea, 19(3), 347-370. 
  4. Kim. M., Hong, J., & Kim, E. (2009). Exploration of teaching method through analysis of cases of mathematical modeling in elementary mathematics. The Mathematical Education, 48(4), 365-385. 
  5. Kim, S. (1992). A study on metacognition in mathematics education. Journal of the Korea Society of Educational Studies in Mathematics, 2(2), 95-104. 
  6. Kim, Y., & Kim, S. (1996). A study on the concept of metacognition in mathematics education. Journal of Educational Research in Mathematics, 6(1), 111-123. 
  7. Do, J. (2018). Aspects of meta-affect in collaborative mathematical problem-solving processes [Doctorial dissertation, Seoul National University of Education]. 
  8. Park, K., et al. (2015). A Study on the development of the 2015 revised mathematics curriculum draft II. BD1512005. 
  9. Park, J. (2017). Fostering mathematical creativity by mathematical modeling. Journal of Educational Research in Mathematics, 27(1), 69-88. 
  10. Sin, S., & Ryu, S. (2014). The relationship between mathematically gifted elementary students' math creative problem solving ability and metacognition. Education of Primary School Mathematics, 17(2), 95-111.  https://doi.org/10.7468/JKSMEC.2014.17.2.95
  11. Shin, E., Shin, S., & Song, S. (2007). A Study on the cases of mathematically gifted elementary students' metacognitive thinking. Journal of Educational Research in Mathematics, 17(3), 201-220. 
  12. Shin, E., & Lee, C. (2004). An analysis of metacognition on the middle school students' modeling activity. The Journal of Educational Research in Mathematics, 14(4), 403-419. 
  13. An, I., & Oh, Y. (2018). An analysis of mathematical modeling process and mathematical reasoning ability by group organization method. Journal of Elementary Mathematics Education in Korea, 22(4), 497-515. 
  14. Lee, C., & Yi, A. (2012). An analysis of the middle school students' modelling process. Journal of Research in Curriculum & Instruction, 16(3), 815-838.  https://doi.org/10.24231/RICI.2012.16.3.815
  15. Chang, H., Kim, E., Choi, H., & Kang, Y. (2018). Teaching & learning analysis of mathematical modeling in 6th grade elementary school class using 'amount of milk'. School Mathematics, 20(4), 547-572.  https://doi.org/10.29275/sm.2018.12.20.4.547
  16. Jung, H., & Lee, K. (2021). Promoting in-service teacher's mathematical modeling teaching competencies by implementing and modifying mathematical modeling tasks. Journal of Educational Research in Mathematics, 31(1), 35-62.  https://doi.org/10.29275/jerm.2021.02.31.1.35
  17. Choi, J. (2017). Prospective teachers' perception of mathematical modeling in elementary class. Journal of Educational Research in Mathematics, 27(2), 313-328. 
  18. Choi, H. (2022). A case study of lesson design based on mathematical modeling of pre-service mathematics teachers. Communication of Mathematics Education, 36(1), 59-72. 
  19. Han, S., & Song, S. (2011). A case study on the metacognition of mathematically gifted elementary students in problem-solving process. Journal of Elementary Mathematics Education in Korea 15(2), 437-461. 
  20. Hwang, H. & Kim, S. (2019). A study on the meaning of reflection and meta-cognition in mathematics education. Communication of Mathematics Education, 33(1), 35-45.
  21. Artzt, A. F., & Thomas, E. A. (1997). Mathematical problem solving in small groups: Exploring the interplay of student's metacognitive behaviors, perception, and ability level. Journal of Mathematical Behavior, 16(1), 63-74.
  22. Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. A. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA14. pp.15-30. Springer.
  23. Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of Mathematical Modelling and Application, 1(1), 45-58.
  24. Borrromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners' modelling behaviour. Journal fur Mathematikdidaktik, 31(1), 99-118. https://doi.org/10.1007/s13138-010-0009-8
  25. Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer. 장혜원, 김은혜, 최혜령, 강윤지 (역, 2020). 수학적 모델링, 어떻게 가르칠까?. 경문사.
  26. Brown, A. N. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, motivation and understanding, pp.65-116. Lawrence Erlbaum Associates.
  27. Chan, E. C. M. (2010). Tracing primary 6 students' model development within the mathematical modelling process. Journal of Mathematical Modelling and Application, 1(3), 40-57.
  28. Common Core State Standards Initiative (CCSSI: 2010). Common core state standards for mathematics. 6-8.
  29. Flavell, J. H. (1979). Metacognition and cognitive monitoring : A new area of cognitive developmental inquiry. American Psychologist, 34, 906-911. https://doi.org/10.1037/0003-066X.34.10.906
  30. Hirsch, C. R., & McDuffie, A. R. (2016). Annual perspectives in mathematics education 2016: Mathematical modeling and modeling mathematics. National Council of Teachers of Mathematics.
  31. Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr, (Eds.). Beyond constructivism: A models and modeling perspective on mathematics teaching, learning and problem solving, Hillsdale, Lawrence Erlbaum Associates.
  32. National Council of Teachers of Mathematics (NCTM: 1996). Mathematical modeling in the secondary school curriculum (3rd ed.). NCTM.
  33. OECD (2013). PISA 2012 Assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. OECD Publishing. http://dx.doi.org/10.1787/9789264190511-en.
  34. Redmond, T., Brown, R., & Sheehy, J. (2013). Exploring the relationship between mathematical modelling and classroom discourse. In G. A. Stillman, et al. (Eds.), Teaching mathematical modelling: Connecting to research and practice. Springer.
  35. Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
  36. Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In Schoenfeld, A. H. (ed.), Cognitive Science of Mathematics Education (pp.189-215). Lawrence Erlbaum Associates.
  37. Shahbari, J. A. (2020). Mathematical thinking styles and the features of modeling process. Scientia in Educatione, 11(1), 59-68. https://doi.org/10.14712/18047106.1579
  38. Sokolowski, A. (2015). The effects of mathematical modelling on students' achievement-meta-analysis of research, IAFOR Journal of Education, 3(1), 93-114. https://doi.org/10.22492/ije.3.1.06