Toku does not need to turn every child into a competition mathematician. The useful connection is that competition problems make the value of flexible, non-scripted thinking especially visible.
The method is often not given
Creative mathematical reasoning research studies the difference between constructing a solution route and imitating one that has already been supplied.[1]
Flexibility helps when the obvious route is inefficient
Mental-set research shows why being locked into one procedure can interfere with recognising a better strategy.[2]
Novel problems draw on reasoning
Analogical and fluid reasoning are relevant to finding relationships and solving academic problems when familiar cues are limited.[3][4]
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المراجع
- Bert Jonsson, Carina Granberg & Johan Lithner (2020). Gaining mathematical understanding: the effects of creative mathematical reasoning and cognitive proficiency. Frontiers in Psychology.
- Marci S. DeCaro (2016). Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics. Memory & Cognition.
- Annie Brookman-Byrne et al. (2019). The unique contributions of verbal analogical reasoning and nonverbal matrix reasoning to science and maths problem-solving in adolescence. Mind, Brain, and Education.
- Caroline T. Green et al. (2017). Fluid reasoning predicts future mathematical performance among children and adolescents. Journal of Experimental Child Psychology.