Abstract
It is agreed upon that a mathematical problem which is thought of as “difficult” but possibly accessible presents a challenge to the solver. We turn the conversation from a challenging task or problem to a challenging activity. We address in this chapter the challenge of convincing (oneself and others) of the correctness of an obtained solution. We use the framework of intellectual needs developed by Harel (Vital directions for mathematics education research. Springer, 2013) and analyse how an exercise of convincing satisfies several intellectual needs of problem solvers. We describe how people of different mathematics background (a mathematician, a teacher, a student) address a computational problem. We demonstrate how a challenge can be amplified by adding constraints to a presumably simple task and share our personal engagement with a generalised task.
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Notes
- 1.
Several versions are available, see for example, Burger (2007) or https://en.wikipedia.org/wiki/String_girdling_Earth
- 2.
One of the 17 teachers listed only 2 products, so we have 50 rather than the expected 51 products.
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Applebaum, M., Zazkis, R. (2023). Mathematical Challenge of Seeking Causality in Unexpected Results. In: Leikin, R. (eds) Mathematical Challenges For All . Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-18868-8_14
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