Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

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

DOI QR Code

Analysis of the productive struggles experienced by sixth-grade students in mathematical problem-solving

초등학교 6학년 학생들이 수학적 문제해결에서 경험하는 생산적 어려움 분석

  • Kil, Yeabin (Seoul Shinhyun Elementary School) ;
  • Chang, Hyewon (Seoul National University of Education)
  • 길예빈 (서울신현초등학교) ;
  • 장혜원 (서울교육대학교)
  • Received : 2024.05.14
  • Accepted : 2024.08.06
  • Published : 2024.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

This study analyzed the productive struggles experienced by the sixth-grade elementary school students when productively overcoming the struggles they encountered during mathematical problem-solving. By analyzing their processes of solving multi-strategic and open-ended problems, productive struggles were categorized according to two steps of problem-solving. Additionally, we examined the factors that support students in overcoming these struggles, distinguishing between individual, peer, and teacher influences. The study identifies four types of productive struggles during the problem-understanding step and six during the plan devising and carrying-out step. In the problem-understanding step, the most prevalent type involved overcoming difficulties to grasp the elements and conditions of the problem, while in the plan devising and carrying-out step, persistence in problem-solving was the most common. The factors supporting productive struggles were ranked in order of influence: individual, peer, and teacher support. Teacher support played a significant role during the problem-understanding step, whereas individual and peer supports were more influential during the plan devising and carrying-out step. Based on these findings, the study offers some didactical implications for understanding the characteristics of productive struggles and strategies for effectively supporting students through the problem-solving process.

본 연구는 초등학교 6학년 학생들이 수학 문제를 해결하며 겪은 어려움을 생산적으로 극복한 사례, 즉 수학적 문제해결 시 초등학교 6학년 학생들이 경험한 생산적 어려움을 분석하였다. 다전략, 개방형 문제를 해결하는 과정을 분석하여 생산적 어려움을 문제해결 단계별로 유형화하였다. 또한 어려움을 생산적으로 극복할 수 있도록 지원하는 요인을 개인, 동료 학생, 교사로 구분하여 특징을 알아보았다. 생산적 어려움 유형은 문제 이해 단계에서 4가지, 해결계획 수립 및 실행 단계에서 6가지로 구분할 수 있었다. 문제 이해 단계에서는 어려움을 극복하며 문제의 요소와 조건을 이해한 유형이 가장 많았으며, 해결계획 수립 및 실행 단계에서는 끈기 있게 문제해결을 시도한 유형이 가장 많았다. 생산적 어려움의 지원 요인은 개인, 동료 학생, 교사 순으로 나타났다. 그중 문제 이해 단계에서는 교사, 해결계획 수립 및 실행 단계에서는 개인과 동료 학생 요인이 생산적 어려움 지원에 많은 영향을 주었다. 연구 결과를 바탕으로 문제해결 과정에서 생산적 어려움의 특징 및 지원 방안과 관련된 교수학적 시사점을 도출하였다.

Keywords

References

  1. Ko, C. (2015). The effects of mathematical modeling activities on mathematical problem solving abilities and mathematical dispositions for the fifth graders [Master's thesis, Seoul National University of Education]. 
  2. Ministry of Education (2022). Mathematics curriculum. Proclamation of the Ministry of Education #2022-33[Annex8]. Author. 
  3. Kil, Y. (2024). Analysis of the productive struggle by the 6th grade students in mathematical problem solving [Master's thesis, Seoul National University of Education]. 
  4. Kim, S. (2018). A case study on reflection and practice of an elementary school teacher in the process of planning, executing and criticizing a lesson on division with decimals. Education of Primary School Mathematics, 21(3), 309-327. http://doi.org/10.7468/jksmec.2018.21.3.309 
  5. Kim, S. (2020). The effects of mathematical problem solving with multiple strategies on the mathematical creativity and attitudes of students [Master's thesis, Seoul National University of Education]. 
  6. Kim, S., & Kim, S (2018). The international research trends of mathematical education by language network analysis method - Based on the titles of 2017 international conference -. School Mathematics, 20(4), 591-608. http://doi.org/10.29275/sm.2018.12.20.4.591 
  7. Kim, S. (2019). A study on productive struggle in mathematics problem solving. Journal of the Korean School Mathematics, 22(3), 329-350. http://doi.org/10.30807/ksms.2019.22.3.008 
  8. Kim, Y. (2017). The study of the gifted students education about doing mathematical task with the face plot. Journal of the Korean School Mathematics, 20(4), 369-385. http://doi.org/10.30807/ksms.2017.20.4.002 
  9. Kim, E. (2010). An analysis on the responses and the behavioral characteristics between mathematically promising students and normal students in solving open-ended mathematical problems [Master's thesis, Seoul National University of Education].
  10. Shin, H., Kim, T., Kim, L., Jeong, N,. Choi, H., ... Hwang, H. (2023). Mathematics 6-1. Visang. 
  11. Son, T., & Hwang, S. (2021). Analysis of the research trends of domestic elementary mathematics education using topic modeling. Journal of Elementary Mathematics Education in Korea, 25(1), 61-80. 
  12. Woo, S. (2016). A comparative analysis on preference of representation types used in elementary mathematics problem solving process [Master's thesis, Seoul National University of Education]. 
  13. Chang, H. (2009). Study on problem solving in elementary school mathematics through comparative analysis. The Journal of Education Research in Mathematics, 19(2), 207-231. 
  14. Jeong, E. (2015). Reconsideration of teaching mathematics problem solving in elementary school. Journal of Elementary Mathematics Education in Korea, 19(2), 123-141.
  15. Aljarrah, A., & Towers, J. (2021). Productive struggle leading to collective mathematical creativity. In D. Olanoff, K. Johnson, & S.M. Spitzer (Eds.), Proceedings of the forty-third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1172-1181). Philadelphia, PA.
  16. Baker, K., Jessup, N. A., Jacobs, V. R., Empson, S. B., & Case, J. (2020). Productive struggle in action. Mathematics Teacher: Learning and Teaching PK-12, 113(5), 361-367. https://doi.org/10.5951/MTLT.2019.006
  17. Botelho, A. F., Varatharaj, A., Inwegen, E. G. V., & Heffernan, N. T. (2019). Refusing to try: Characterizing early stopout on student assignments. In Proceedings of the 9th International Learning Analytics & Knowledge (LAK19) (pp. 391-400). Association for Computing Machinery, Inc.
  18. Caprioara, D. (2015). Problem solving-purpose and means of learning mathematics in school. The Proceedings of 6th World Conference on educational Sciences, 191, 1859-1864. https://doi.org/10.1016/j.sbspro.2015.04.332
  19. Cirillo, M., & Jennifer, M. (2018). Using classroom discourse as a tool for formative assessment. In A. Edward & L. Valerie (Eds.), A fresh look at formative assessment (pp. 21-40). NCTM.
  20. Common Core State Standards Initiative[CCSSI] (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers. Retrieved on May 11, 2024 from https://www.thecorestandards.org/wp-content/uploads/Math_Standards1.pdf
  21. DiNapoli, J. (2018). Supporting secondary students' perseverance for solving challenging mathematics tasks [Doctoral dissertation, University of Delaware].
  22. Granberg, C. (2016). Discovering and addressing errors during mathematics problem-solving: A productive struggle?. Journal of Mathematical Behavior, 42, 33-48. https://doi.org/10.1016/j.jmathb.2016.02.002
  23. Jonsson, B., Norqvist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, 36, 20-32. https://doi.org/10.1016/j.jmathb.2014.08.003
  24. Kapur, M. (2014). Productive failure in learning math. Cognitive Science, 38(5), 1008-1022. https://doi.org/10.1111/cogs.12107
  25. National Council of Teachers of Mathematics (1980). An agenda for action: Recommendations for school mathematics of the 1980s. Author.
  26. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Author.
  27. National Council of Teachers of Mathematics (2014). Principles to actions: Ensuring mathematical success for all. Author.
  28. O'Dell, J. R. (2018). The interplay of frustration and joy: Elementary students' productive struggle when engaged in unsolved problems. In T. E. Hodges, & G. J., Roy, & A. M., Tyminski (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 938-945). Greenville, SC: University of South Carolina & Clemson University.
  29. O'Dell, J., & Frauenholtz, T. (2020). Elementary students and their self-identified emotions as they engaged in mathematical problem solving. In A. I. Sacristan, J. C. Cortes-Zavala, & P. M. Ruiz-Arias (Eds.), Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1360-1368). Cinvestav, Mexico.
  30. Smith, M. S., & Stein, M. K. (1998). Reflections on practice: Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344-350.
  31. Valerio, J. (2021). Tracing take-up across practice-based professional development and collaborative lesson design. In D. Olanoff, K. Johnson, & S. M. Spitzer (Eds.), Proceedings of the forty-third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 633-641). Philadelphia, PA.
  32. Van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of Learning Disabilities, 40(6), 540-553.
  33. VanLehn, K., Burkhardt, H., Cheema, S., Kang, S., Pead, D., Schoenfeld, A., & Wetzel, J. (2021). Can an orchestration system increase collaborative, productive struggle in teaching-by-eliciting classrooms?. Interactive Learning Environments, 29(6), 987-1005. https://doi.org/10.1080/10494820.2019.1616567
  34. Warshauer, H. K. (2011). The role of productive struggle in teaching and learning middle school mathematics [Doctoral dissertation, The University of Texas at Austin].
  35. Young, J. R., Bevan, D., & Sanders, M. (2024). How productive is the productive struggle? Lessons learned from a scoping review. International Journal of Education in Mathematics, Science and Technology, 12(2), 470-495. https://doi.org/10.46328/ijemst.3364
  36. Zeybek, Z. (2016). Productive struggle in a geometry class. International Journal of Research in Education and Science, 2(2), 396-415.