One of the most tedious and taxing aspects of problem solving is identifying the problem as it requires one to consider the problem through multiple lenses and perspectives without being attached to one particular solution to early on in the task For example consider the following problem: Becka baked a chocolate cake in her oven for twenty five minutes.
How long would it take her to bake three chocolate cakes?
An example of a well-defined problem is an algebraic problem (ex: 2x - 29 = 7) where one must find the value of x.
Another example may be converting the weight of the turkey from kilograms to pounds.
In addition these teachers offered significantly more solutions to problems posed in both ill-defined and well-defined problems.
Therefore it is implicated that successful problem solving is associated with the time spent finding the correct problem and the consideration of multiple solutions.In both instances these represent well-defined problems as there is one correct solution and a clearly defined way of finding that solution.In contrast, ill-defined problems represent those we may face in our daily lives, the goals are unclear and they have information that is conflicting, incomplete or inconclusive .Research also supports the importance of taking one's time to clearly identifying the problem before proceeding to other stages.In support of this argument, Getzel and Csikszentmihalyi found that artist students that spend more time identifying the problem when producing their art were rated as having more creative and original pieces than artists who spent less time at this stage.This chapter on problem solving will first differentiate between well-defined and ill-defined problems, then explain uses of conceptualizing and visually representing problems within the context of problem solving and finally we will discuss how mental set may impede successful problem solving.Problems can be categorized into two types: ill-defined or well-defined to the problem at hand.These findings highlight the benefits of problem-based learning on understanding and defining problems in science.Given the positive effects of defining problems this education approach may also be applied to our next sub-topic of conceptualizing problems.Most people would jump to the conclusion to multiply twenty five by three, however if we place all three cakes in the oven at a time we find it would take the same time to bake three cakes as it would take to bake one.This example highlights the need to properly conceptualize the problem and look at it from different viewpoints, before rushing to solutions.