Can Twitter help? Has anybody ever seen convincing experimental research on the effects of exercising math problems of the PISA Math type: transfer to realistic / real world contexts. Implicit assumption seems to be that exercise strengthens the brain muscles of math thinking.
Contrast the work of George Polya ‘How to solve it’. With Polya building problem solving power depends on building problem solving knowledge, in a systematic way by doing math problems. KNOWLEDGE. More or less like building expertise in chess. Polya is not about ‘model building’.
Allen Newell studied math with Polya. In information theory (Newell & Simon) problem solving is possible only if one has mastered the ‘productions’ necessary to obtain a solution for the problem at hand. In other words: the necessary MATH KNOWLEDGE must already be available.
A simple model in my 1998, in Dutch: benwilbrink.nl/publicaties/98… Esp. the section ‘Relevante literatuur sinds 1998’ [English titles]
Ocean’s of precious instruction and exercise time get lost in trying to develop mathematical muscle strength by solving problems situated in real world contexts. That thinking muscles do not exist was demonstrated already more than a century ago by Edward L. Thorndike.
An examination, it is in Dutch but the illustrations already tell the story. www2.cito.nl/vo/ex2018/GT-0…
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