Human beings are fundamentally goal-directed, guided by a constant need to reduce differences between our current state of being and some goal state. Given that a ‘problem’ can be defined as any situation in which one’s current state differs from a goal state, problem solving can thus be considered a central task of human existence and of the human mind.
Problems can be divided into two general classes: well-defined and ill-defined. With a well-defined problem, the correct formulation is given. That is, the problem is
presented with the expectation that the current state, the goal state and the ‘operators’ – the resources available to get from one state to the other – will be sufficiently obvious to allow steady progress towards the goal. If progress cannot be made, this will be due to a lack of relevant knowledge or skill, rather than to some inadequacy in the problem formulation.
Unfortunately, most problems in life look nothing like this. Instead, they are ill-defined: uncertainty is inherent not only in whether the goal will be reached, but in how best to conceive of the current state, the goal state, and the operators. The task at hand in such cases entails developing a problem formulation that transforms the ill-defined problem into a well-defined one that can be tackled. The major obstacle to generating such problem formulations involves determining which aspects of the situation are relevant. Unfortunately, the amount of information available in any situation is vast relative to our limited capacities to process it, and in many cases no objective criteria can be specified to determine which aspects are relevant to a given goal.
While researchers have paid considerable attention to understanding how people go about solving well-defined problems, much less attention has been given to the particular skills required for tackling ill-defined problems. We believe that three particular cognitive skills help people deal with these problems, and in this article we will argue that these skills can be defined by examining a particular type of ill-defined problem: the insight problem.
The role of insight in ill-defined problems
Ill-defined problems quickly become apparent when the way in which one is approaching a goal proves inadequate and when all other readily-conceived strategies (the aforementioned ‘available operators’) prove inadequate. An impasse is reached, and to continue moving forward, the thinker must restructure the problem formulation: the way in which the problem’s starting state, goal state and/or operators are conceived must be changed in some way. The term ‘insight’ typically indicates the moment when a new, more effective formulation suddenly appears in one’s mind, enabling one to view the given situation in a new light.
The formal insight problems used in research studies actually possess multiple possible problem formulations, the one that is most often selected by people on first encounter turns out to be incorrect, leading to an impasse. As such, insight problems require significant restructuring by the thinker if a solution is to be reached.
Consider the following: an unemployed woman who did not have her driver’s license with her failed to stop at a railroad crossing, then ignored a one-way traffic sign and traveled three blocks in the wrong direction down the one-way street. All this was observed by a nearby police officer, who was on duty, yet made no effort to arrest the woman. Why?
Solution: She was not driving; she was walking. If you didn’t figure this out on the first try, don’t feel bad – only 59 per cent of people did so in a laboratory study.
While relatively few studies of individual differences in insight have thus far been reported, two patterns are nonetheless emerging: first, performance on well-defined problems – including those that make up standard IQ tests – is positively associated with performance on insight problems. That is, people who are more intelligent in the standard sense also tend to be more insightful; and second, insight is associated with a set of interrelated abilities that involve using loose or remote associations, analogies and pattern recognition.
The fact that insight problem solving appears to be associated with standard analytic problem solving and IQ indicates that it may involve some of the same processes; however, we believe that it also requires some additional processes that are not shared with standard problem solving and IQ. We recently set out to determine which distinct abilities are required for dealing with ill-defined problems.
The cognitive abilities involved in insight
Our consideration of the differences between well and ill-defined problems and of the difficulty of generating effective problem formulations led us to develop a model featuring three types of cognitive ability that contribute to restructuring and insight.
Operating within a particular problem formulation requires the efficient logical application of available operators, bearing in mind relevant constraints; this is equivalent to solving well-defined problems. On the other hand, operating without a specific problem formulation – in other words, attempting to generate a novel formulation – requires the ability to access a wide range of associated or analogous information and to recognize relevant patterns. Cognitive abilities characteristic of the former mode appear linear, logical, and analytical – and highly similar, if not identical, to standard intelligence or IQ. The cognitive abilities characteristic of the latter mode, by contrast, appear more loosely associative, non-linear and holistic.
These two distinct types of ability map reasonably well onto psychologist J. P. Guilford’s classic distinction between convergent and divergent thinking.