Problem Modeling

This group of problems provides insufficient rules or information for the thinker to deduce the solution directly. As a result, the thinker must create a mental schema or model which simplifies the problem before solving it. For example, the thinker must start with a mental picture of a pond completely full of lilies (day 48) and then work backwards to understand that it will be half-full one day earlier. This sort of cognitive hinting is not present in the problem text but is the only way to solve this problem. Similarly, solving the widget problem using algebra is too intensive for many people; the most efficient way to solve this problem is for the thinker to picture a group of five machines each turning out a widget every five minutes, and then realizing that each of a hundred machines would still take five minutes to turn out a widget. Both these problems were very significant (p<0.01) in their correlation with academic performance, indicating that this sort of thinking is critical to success in learning computer programming.