“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.