Insight Problem Solving and the Nine-Dot Problem

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...

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...and diminish their distance between their present state and a mental sub-goal state, and apply a criterion against which to compare their progress (MacGregor et al., 2001). If a criterion is one step closer to the sub-goal or seems promising enough to reach the solution, then it is often applied and repeated. If not, the criterion will be discarded and new operators shall be taken into consideration. MacGregor et al. (2001) also came up a model comprised of two stages, to suggest plausible operators that people apply when faced with the nine-dot problem. Stage 1 comprises the selection of “optimal moves,” such as tracing lines in strategic places to cancel out the most number of dots. However, since Stage 1 alone does not incite a person to draw outside the boundaries, Stage 2 comes into play to allow people to consider a larger working area and new strategies.
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