DOI QR코드

DOI QR Code

How do one expert mathematics teacher in China implement deep teaching in problem-solving and problem-posing classroom: A case study

  • Yanhui Xu (Department of Mathematics, Wenzhou University)
  • 투고 : 2023.10.05
  • 심사 : 2024.01.30
  • 발행 : 2024.03.31

초록

In this paper, the author analyzed characteristics of deep mathematics learning in problem solving and problem-posing classroom teaching. Based on a simple wrong plane geometry problem, the author describes the classroom experience how one expert Chinese mathematics teacher guides students to modify geometry problems from solution to investigation, and guides the students to learn how to pose mathematics problems in inquiry-based deep learning classroom. This also demonstrates how expert mathematics teacher can effectively guide students to teach deep learning in regular classroom.

키워드

참고문헌

  1. Bransford, J. D, Brown, A. L, & Cocking, R. R. (2000/2004) (Expanded Edition). How people learn: Brain, mind, experience, and school. National Academic Press.
  2. Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Franklin Institute Press.
  3. Brown, S. I., & Walter, M. I. (1993). Problem posing in mathematics education. In I. Brown Stephen, & I. Walter Marion (Eds.), Problem posing: Reflection and applications (pp. 16-27). Lawrence Erlbaum Associates.
  4. Bruner, J. (1977). The process of education. Harvard University Press.
  5. Cuoco, Al. (2001). Mathematics for teaching. Notices of the American Mathematical Society, 48(2), 168-174.
  6. Da Ponte, J. P. (2007). Investigations and explorations in the mathematics classroom. ZDM-The International Journal on Mathematics Education, 39 (5-6), 419-430. https://doi.org/10.1007/s11858-007-0054-z
  7. Davis, P. J. (1985). What do I know? A study of mathematical self-awareness. The College Mathematics Journal, 16 (1), 22-41. https://doi.org/10.1080/07468342.1985.11972847
  8. English, L. D. (1996). Children's problem posing and problem solving preferences. In J. Mulligan, & M. Mitchelmore (Eds.), Research in early number learning (pp. 227-242). Australian Association of Mathematics Teachers.
  9. English, L. (1999). Reasoning by analogy: A fundamental process in children's mathematical learning. In L. V. Stiff, & F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12 (pp. 22-36). National Council of Teachers of Mathematics.
  10. Fullan, M., & Langworthy, M. (2014). A rich seam: How new pedagogies find deep learning. Pearson.
  11. Fullan, M., Quinn, J., & McEachen, J. (2018). Deep learning: Engage the world, change the world. SAGE.
  12. Hanna, G., & De Villiers, M. (Eds.). (2012). Proofs and proving in mathematics education. The 19th ICMI Study. Springer.
  13. Hashimoto, Y. (1987). Classroom practice of problem solving in Japanese elementary schools. In Becker, J., & Miwa, T. (Eds.), Proceedings of the U.S.-Japan seminar on mathematical problem solving (pp. 94-119). Southern Illinois University.
  14. Hattie, J., & Donoghue, G. (2016). Learning strategies: A synthesis and conceptual model. npj Science of Learning, 1, 16013. https://doi.org/10.1038/npjscilearn.2016.13
  15. Healy, C. C. (1993). Creating miracles: A story of student discovery. Key Curriculum Press.
  16. Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 65-97). Macmillan Publishing Co, Inc.
  17. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123-147). Lawrence Erlbaum Associates.
  18. Klamkin, M. S. (1986). Problem posing and mathematical creativity. Crux Mathematicorum, 12(10), 23-42.
  19. Kontorovicha, I., Koichua, B., Leikinb,R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. Journal of Mathematical Behavior, 31(1), 149-161. https://doi.org/10.1016/j.jmathb.2011.11.002
  20. Lavy, I., & Shriki, A. (2009). Small change-big difference. The Mathematics Enthusiast, 6(3), 395-410. https://doi.org/10.54870/1551-3440.1160
  21. Lavy, I., & Shriki, A. (2010). Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers' mathematical knowledge. Journal of Mathematical Behavior, 29(1), 11-24. https://doi.org/10.1016/j.jmathb.2009.12.002
  22. Leikin, R., & Grossman, D. (2013). Teachers modify geometry problems: from proof to investigation. Educational Studies in Mathematics, 82(3), 515-531. https://doi.org/10.1007/s10649-012-9460-4
  23. Li, Chunhui & Wen, Fengtong (2023). Promoting deep learning in mathematics education-Based on understanding by design theory. Academic Journal of Mathematical Sciences, 4(4), 57-61. https://doi.org/10.25236/AJMS.2023.040409
  24. Mackie, D. (2002). Using computer algebra to encourage a deep learning approach to calculus. In Deborah, H.H., & Constantinos, T. (Eds.), Proceedings from 2nd International Conference on the Teaching of Mathematics at the Undergraduate Level (pp. 1872-1880). Crete, Greece.
  25. Marton, F., & Saljo, R. (1976). On qualitative differences in learning: I-Outcome and process. British Journal of Educational Psychology, 46(1), 4-11. https://doi.org/10.1111/j.2044-8279.1976.tb02980.x
  26. Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. Addison Wesley Longman.
  27. Maxwell, J. (1992). Understanding and validity in qualitative research. Harvard Educational Review, 62(3), 279-301. https://doi.org/10.17763/haer.62.3.8323320856251826
  28. McPhail, G. (2021). The search for deep learning: A curriculum coherence model. Journal of Curriculum Studies, 53(4), 420-434. https://doi.org/10.1080/00220272.2020.1748231
  29. Ministry of Education of the People's Republic of China (2022). Mathematics curriculum standards for ordinary high schools. Beijing Normal University Press. (In Chinese)
  30. Ministry of Education of the People's Republic of China (2022). Mathematics curriculum standards for compulsory education. Beijing Normal University Press. (In Chinese)
  31. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Author.
  32. Parker, W., Mosborg, S., Bransford, J., Vye, N., Wilkerson, J., & Abbott, R. (2011). Rethinking high school coursework: Tackling the depth/breadth tension in the AP US government and politics course. Journal of Curriculum Studies, 43(4), 533-559. https://doi.org/10.1080/00220272.2011.584561
  33. Polya, G. (1957). How to solve it (2nd ed.). Doubleday.
  34. Polya, G. (1962). Mathematical discovery on understanding, learning, and teaching problem solving (Volume 2). John Wiley.
  35. Sawyer, R. K. (Eds.) (2014). The Cambridge handbook of the learning sciences. Cambridge University Press. https://doi.org/10.1017/CBO9781139519526
  36. Shriki, A. (2006). The area problem. Mathematical Spectrum, 38(1), 27-33.
  37. Shriki, A., & Lavy, I. (2004). Exploring mathematical patterns using dynamic geometry software. The Australian Mathematics Teacher, 60(3), 36-40.
  38. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
  39. Silver, E. A., & Cai, J. (2005). Assessing students' mathematical: problem posing. Teaching Children Mathematics, 12(3), 129-135. https://doi.org/10.5951/TCM.12.3.0129
  40. Silverman, F. L., Ken, W., and Donna, S. (1992). Student-generated story problems. Arithmetic Teacher, 39(8), 6-12. https://doi.org/10.5951/AT.39.8.0006
  41. Stein, M., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development (2nd ed.). NCTM.
  42. Whitin, D. (2004). Building a mathematical community through problem posing. In R, Rubenstein & G. W. Bright (Ed.), Perspectives on the teaching of mathematics (pp. 129-140). National Council of Teachers of Mathematics.
  43. Winch, C. (2017). Teachers' know-how: A philosophical investigation. Wiley Blackwell.
  44. Yerushalmy, M., Chazan, D., & Gordon, M. (1990). Mathematical problem posing: Implications for facilitating student inquiry in classrooms. Instructional Science, 19(3), 219-245. https://doi.org/10.1007/BF00120197