George Bodner, Purdue University
Many people have tried to define problem solving. Perhaps the best definition was introduced by John Hayes in his book, The Complete Problem Solver (The Franklin Institute, 1980).
"Whenever there is a gap between where you are now and where you want to be, and you don't know how to find a way to cross that gap, you have a problem."
If you know what to do when you read a question, it is an exercise, not a problem. The difference between an exercise and a problem is best illustrated by the definition of problem solving introduced by Grayson Wheatley, a mathematics educator. He defined problem solving as "what you do, when you don't know what to do."
Purdue's Rules for Problem Solving: