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| Simple problem solving began to be studied intensively from the 1910s by a group of German psychologists known as the Gestaltists. The hallmarks of the Gestalt approach were the phenomenon of insight, and the view that the whole is greater than the sum of its parts. |
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| Insight has famously been labelled the ‘aha!' phenomenon, in that sudden restructuring or re-representings of a problem can sometimes lead to a solution. |
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| So-called ‘set' effects arise when learned or habitual ways of tackling a problem prevent the solver from identifying better and simpler methods, or when unwarranted assumptions are made. |
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| A block to effective problem solving known as ‘functional fixity' tends to be observed when an object has to be used in a new way. |
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| Problems that share the same underlying structure (i.e. have identical state–space diagrams) are said to be isomorphic. |
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| Internal problem representations |
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| Internal problem representations entail a processing and representational burden, because the information needed to solve the problem has to be encoded and maintained in some form. Internal rules then are rules that need to be memorized |
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| External problem representations |
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| External rules differ in that they are not stated explicitly in the problem instructions, but are implied or necessitated by the problem itself. |
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| Within the information-processing approach, problem solving is generally seen as a search process. |
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| Search may proceed in a forwards direction from the starting state by generating possible actions, evaluating the results of those actions and then choosing for further exploration those with best outcomes when assessed against the goal. |
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| Search may proceed backwards from the goal by using a problem reduction or means–ends approach. |
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| Problem reduction or means–ends approach |
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| Problem reduction or means–ends approach breaks down the overall goal into subgoals that should be easier to achieve. |
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| Ohlsson (1992) proposed that when working on a problem people generate possible actions or operators from long-term memory, which are cued by the problem representation. Applying the operators to the current problem state leads to a new problem state. |
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| When a state is reached in which no new useful operators can be retrieved, subjectively, we experience an impasse, a mental ‘blank'; we cannot think of anything new to try. |
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| Elaboration involves adding information to the problem representation by observing previously unnoticed features. For example, to use the matchbox tray in solving the ‘candle' problem (Duncker, 1945) the solver has to notice the possible use of the tray as a platform. |
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| Re-encoding involves changing the encoding rather than simply adding new information. For example, how could a man have legally married 20 women in one month in a country where polygamy is illegal and none of the women have died or been divorced? |
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| Constraint relaxation involves making the goal requirements less restrictive than initially assumed. For example, one source of difficulty in the 9-dot problem is the tendency to over-restrict the goal so that the four lines are kept within the square array of dots; removing (or relaxing) this constraint is necessary for a solution |
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| Analogical mapping and structural alignment |
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Definition
| According to 'structure mapping' theory, there is a process of analogical mapping whereby a structural alignment is established between the representations of the base and the target. That is to say, explicit correspondences are established between the represented elements and relationships in the two situations. As an example, consider the solar system analogy of the atom. |
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| Adversary problem solving |
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| Chess play is an example of adversarial problem solving, because the game of chess involves an opponent |
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| Non-Adversary problem solving |
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| Code breaking, de-bugging computer programs and medical diagnosis are examples of non adversarial problem domains |
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| Experts tend to use a working forwards strategy, beginning with information given in the problem statement and using that to derive a solution. |
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| Novices use a working backwards strategy (means–ends analysis), starting with the goal, or quantity to be solved, and then work backwards from that to the given information, until they are able to solve one part of the problem. Novices typically then retrace their steps, working forwards until the problem was solved. |
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| Metacognitive processes and strategies |
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| Metacognition can be defined as an appreciation of what one already knows, together with a correct apprehension of a learning task and what knowledge and skills it requires |
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