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Fit the Mold of a Good Problem-Solver?

Too often we say someone is either good or bad in mathematics...but what does this mean? It is too vague.

The focus should be on the ability to use mathematical knowledge and skills to solve problems. So, the question now shifts...what are the characteristics of "good" problem-solvers in a mathematics context?

In her article in the 1980 NCTM Yearbook, Marilyn Suydam presented a list of characteristics that I have found quite useful (and true):

  1. Ability to understand mathematical concepts and terms
  2. Ability to note likenesses, differences, and analogies
  3. Ability to identify critical elements and to select correct procedures and data
  4. Ability to note irrelevant details
  5. Ability to estimate and analyze
  6. Ability to visualize and interpret quantitative or spatial facts and relationships
  7. Ability to generalize on the basis of a few examples
  8. Ability to switch methods easily
  9. Higher scores for self-esteem and confidence, with good relationships with others
  10. Lower scores for test anxiety
Again, a quality list, that gives us something to reflect on, shoot for, and perhaps even measure. But the list is missing some elements others have suggested as critical characteristics.

Thanks to Math Magician Bon Bishop and others, some additional characteristics are:

  • Enjoyment while solving problems
  • Reliance on their own judgment and decision-making abilities
  • Not afraid of being wrong or of making mistakes
  • Flexability and ability to see multiple solution paths for a problem
  • Ability to reflect on their thinking
  • Ability and willingness to work on enhancing their problem solving methods and tools
  • Ability to relate the underlying structure of a problem to other similar or previous problems
  • Willing to spend extended time thinking about the problem and possible solution routes
  • Self-motivated to extend a solved problem by posing new and related problems
  • So, what characteristics of good problem solvers do you think have been left off this list? Send me your ideas, as I am willing to expand this list.