Abstract
Engagement in mathematical problem-solving is an aspect of problem-solving that is often overlooked in our efforts to improve students’ problem-solving abilities. In this chapter, I look at these constructs through the lens of Csíkszentmihályi’s theory of flow. Studying the problem-solving habits of students within a problem-solving environment designed to induce flow, I look specifically at student behavior when there is an imbalance between students’ problem-solving skills and the challenge of the task at hand. Results indicate that students have higher than expected perseverance in the face of challenge, higher than expected tolerance in the face of the mundane, and use these as buffers while autonomously correcting the imbalance. Emerging from this research is an extension to Csíkszentmihályi’s theory of flow and support for the teaching methods emerging out of my earlier work on building thinking classrooms.
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Notes
- 1.
- 2.
I am not the first to do this. Schmidt et al. (1996) used flow as a framework for investigating mathematics and science teaching across six countries – France, Japan, Norway, Spain, Switzerland, and the United States – between 1991 and 1995.
- 3.
The second teacher in the prior research study (Liljedahl, 2016a) was also teaching according to this framework.
- 4.
Although the curricula tasks are simply questions from the textbook, I characterize them as problem-solving tasks because they are often new to the students, present something that is problematic for them, and often cause them to be stuck. However, as will be seen in the presentation of results, in some cases the tasks become rudimentary for the students.
- 5.
The term leveling originally comes from Schoenfled (1985) and refers to that moment when a teacher will go over the solution to a problem or exercise students have been working on. Leveling to the bottom specifies when that leveling is to occur.
- 6.
In the province where this research was conducted, these are the academic streams of mathematics laddering toward university-level calculus. Grade 11 students are typically 16 or 17 years old, and grade 12 students are typically 17 or 18 years old.
- 7.
In the province where this research was done, schools are either semestered or linear. Linear schools have students taking eight classes on a rotation schedule over the course of the whole year. Semestered schools have students taking the same four classes every day for the first half of the school year (first semester) and another four classes every day for the second half of the school year (second semester).
- 8.
Recall that Mikaela and Allison regularly worked together when given the opportunity.
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Liljedahl, P. (2018). On the Edges of Flow: Student Problem-Solving Behavior. In: Amado, N., Carreira, S., Jones, K. (eds) Broadening the Scope of Research on Mathematical Problem Solving. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-99861-9_22
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