As I was preparing to hand in assignment 1, the annotated bibliography, I came across a study from Thailand by Firmansyah, Sunardi, Susanto, and Ambarwati (2018). Reading their introduction made a few things click for me across our MAE3 program in terms of the rigidity in student processing of particular mathematical procedures.
To sum up briefly in bullets:
- Student memorize procedure, and imitate how the teacher has solved problems without understanding.
- When presented with different questions, students don't know where to start.
- I've experienced this many many times especially in Workplace Math 10.
- “The ability to think critically and creatively plays an important role in modern society since it is capable to make people become more mentally flexible, open and easily adapt to various situations and problems.” (Firmansyah et al., 2019, p. 1)
- To stretch the students' understanding and allow them to gradually move from imitation to understanding underlying procedures, modifying the problem slightly and allowing students to apply what they have previously been able to challenge themselves with forces them to see baked-in patterns: What is similar? What is different?
- This is the foundation of Variation Theory, that we've previously read about from a paper by Askew (2011) in Week 3 of EDCP 550 (our second course).
- In addition, elementary and middle school students do this well through worksheets called Derived Facts like "If I know... then I know..." to establish connections between similar concepts/ideas. Here's a screenshot from the NCETM Five Big Ideas video that we discussed in Week 7 of EDCP 552 (course 4).
- This also relates to Thinking Mathematically by Mason et al. (1982) in terms of the students addressing problems with an Entry-Attack-Review sequence and the idea of problem-posing explained by English et al. (2005) in which students generating a similar but perhaps simplified problem on their own but with a twist to observe similarities and differences in the underlying concepts. This key skill is quite important for everyday life! (Both of these references were studied in EDCP 552 as well)
References
Askew, M. (2011). Variation theory. In Transforming primary mathematics (pp. 75–88). Routledge. https://doi.org/10.4324/9781315667256
English, L. D., Fox, J. L., & Watters, J. J. (2005). Problem Posing and Solving with Mathematical Modeling. Teaching Children Mathematics, 12(3), 156–163.
Firmansyah, F. F., Sunardi, E. Y., & Ambarwati, R. (2019). The
uniqueness of visual levels in resolving geometry of shape and space content
based on van hieles’s theory. Journal of Physics: Conference Series, 1211(1).
https://doi.org/DOI:10.1088/1742-6596/1211/1/012076
While I was working out how to recreate my art piece from the Bridges Conference, I also noticed how much I used the process described in Mason, Burton and Stacey so I appreciate this bonus connections post you have. When I got stuck I spent some time just noodling around with what I knew couldn't lead to solutions, but did in the end help me work out a path forward. It was very much that reflective/rest phase that Mason et al. talked about.
ReplyDeleteI know in my own practice, despite being aware of this, I quite often capitulate to all the outside pressures of time for "covering the curriculum", apathy of students (or I think more it is just being unaccustomed to challenge), and end up leaving my students in the memorize and imitate zone of understanding.
Thanks so much, Oliver and Kristie, for making these really important connections across your MAE3 program!
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