What makes solving math problems difficult? Diagnosis

“One of the most important factors [in deficient mathematical problem solving] is poor mental management:

  • Students did not pay attention to the winding path of their activities in solving a problem.
  • They often did not think to use heuristics they knew and could have applied.
  • They often perseverated in an approach that was not yielding progress rather than trying a new tack.
  • They often gave up without rummaging in their repertoire for another point of entry.
  • Amidst the trees, they lost sight of the forest.”

(I found this diagnosis in David Perkins’ book “Outsmarting IQ: The emerging science of learnable intelligence”. Perkins reports some of the findings of mathematician-psychologist Allan Schoenfeld (p. 87).)

One promising way of mastering these difficulties lies in combining two major approaches to problem solving:

  • heuristics in the tradition of George Polya’s “How to Solve It”, and
  • mapping techniques, like mind mapping (or concept mapping).

Here are more details.

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