Cognitive psychologists have long focused in identifying how people identify approach the two major types of problems: well-defined and ill-defined. For the most part, scientists have come up with theories and models to explain in general terms how people elaborate steps to come up with solutions. However, there are some problems which cannot be defined and analyzed with a single model. These special kind of problems are called insight problems and usually require a bit of contemplation and creativity beyond that of regular ill-defined problems; thus they have presented a challenge for people to evaluate and measure. In this paper I will focus in one particular insight problem called the nine-dot-problem and review some of the experiments and theories that have been proposed to describe a path to its solution. But first I think it is important to become aware of what exactly distinguishes well-defined problems and ill-defined problems from one another.
Well-defined Problems vs. Ill-defined Problems
Well-defined problems are those that have clear, defined goals and can be met in a formal and set number of steps. An example of a well-defined problem would be a math equation such as 2(x) + 4 = 10. In order to understand how to solve said problem first we ought to know the meaning of the mathematical symbols and numbers, and define the goal, which in this case is to figure out the value of “x”. We have to know that “( )”; aside from their typical use in writing, tell us to enclose and multiply whatever numbers or symbols are between them with the numbers or symbols outside of them; as well as recognize that “+” means addition or more. We must also infer that since the whole equation has to equal to 10 after being multiplied by 2 and added 4, “x” cannot be larger than 4. Based on these rules and knowledge, we can develop certain steps to reach the conclusion. In this case we have to subtract 4 out of 10 which would leave us with 6, and then divide 6 by 2 which would give us a value of 3. Well-defined problems have a direct path to one clear solution, but unfortunately this kind of problems are not a common encounter in the real world and we more often come across ill-defined problems.
Ill-defined problems are those where goals and processes are not explicitly described. There might be an ideal goal, but there could be other alternative goals and different steps for each of them. There could also be constraints along the way which would require creativity, critical thinking, and the development of new strategies. An example of an ill-defined problem could be painting a beautiful picture. First of all, we are not told specifically what we are supposed to paint, how is supposed to be painted or even where it is supposed to be painted. Second, the final product could be anything we consider beautiful and the level of skill, creativity, and execution will differ greatly among individuals. Third, “beauty” is quite subjective, so what I might...