Gestalt Problem Solving

F1 Gestalt Problem Solving

Akram Faravani

The Gestalt theory of problem solving, described by Karl Duncker (1945) and Max Wertheimer(1959), holds that problem solving occurs with a flash of insight. Richard Mayer (1995) noted that insight occurs when a problem solver moves from a state of not knowing how to solve a problem to knowing how to solve a problem. During insight, problem solvers devise a way of representing the problem that enables solution. Gestalt psychologists offered several ways of conceptualizing what happens during insight: insight involves building a schema in which all the parts fit together, insight involves suddenly reorganizing the visual information so it fits together to solve the problem, insight involves restating a problems givens or problem goal in a new way that makes the problem easier to solve, insight involves removing mental blocks, and insight involves finding a problem analog (i.e., a similar problem that the problem solver already knows how to solve). Gestalt theory informs educational programs aimed at teaching students how to represent problems.

Gestalt psychologists saw problem solving as the closure of a problem, achieved by the representation representation of the problem in an appropriate way. A problem is only a problem because it is incomplete; the solution makes it complete, and finding the solution closes the incompleteness. incompleteness. Closure is accompanied accompanied by the flash of insight or aha! experience. Gestalt psychologists typically studied problem solving by using verbal protocols. They were more interested in the process of problem solving than the solution and verbal protocols are a way of studying the process. They believed that solutions came from an insight into the problem and occurred when the participants restructured the problem. Insights occur when the participants are suddenly aware of the answer (the participants do not gradually work toward a solution; rather it appears in a flash).

Representation Problem

solution involves mentally forming and reforming different representations of a

problem until the right form is chosen. The ease with which the appropriate representation representation can be found changes the difficulty of the problem. Difficult problems are those in which the appropriate appropriate representation is not apparent from the initial description and must be discovered by the solver. 1

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Set

Gestalt psychologists argued that there are a number of possible negative effects of past experience and reproductive thinking (using previous experience of problem solving to solve new ones) such as   problem solving set and  functional fixedness. Problem solving set occurs when participants learn to solve a series of problems in a specific manner. The solution then becomes a habit (or a mental set) which is used even if a simpler solution is possible. Set or fixity is a tendency to keep thinking about familiar uses of objects within a problem (functional set), or about familiar approaches to solving a problem (operational set), even though they are not helping you find a solution. Set can be reduced by giving objects nonsense names, or by intentionally trying to think of novel uses for objects. Incubation Problem

a)

solving has four stages:

Preparation

( when you discover the problem and think about it unsuccessfully often for

a long time) b) Incubation Incubation (when you give up and do something else for a while, perhaps perhaps something relaxing) c) Illumination ( when the flash of insight presents the solution to you) d) Verification (when you check that your solution works, and perhaps refine it. In incubation stage, you are not trying to solve the problem and the solution so lution may appear in a flash of insight. Incubation may allow set to weaken, by giving time for obvious (but wrong) ideas to fade; or it may give time for unconscious processes to continue re-representing re-representing the problem. Insight

There are two types of thinking that can be applied to solving problems: a) Reproductive Reproductive thinking (using previous experience of problem solving to solve new ones) b)

Productive thinking

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While this approach can be useful, it can also lead to problems since people do not notice the structure of the problem and may not see other simpler solutions. Insight experience experience occurs due to a sudden release from set which is more likely to happen after incubation in a context different from the one in i n which the set was formed. Thus, insight is equated with the moment of creative inspiration, and productive thinking is an insightful mode that allows novel associations to be made.

F2 Goals and States Problems

arise when people do not see immediately how to get from where they are (starting

state) to where they want to be. Therefore, every problem has a start state (or initial state) and this is the position you begin with. The goal state is the state you want to achieve. Something is only a problem if we do not know how to get from the start state to the goal state, since if we can immediately see how to achieve the goal state it is not a problem. For each problem, there are different types of processes or actions that enable us to get from one state to another; these are called operators. operators. State space includes every state of a problem. Problems are solved by finding a solution path that links the start space to the goal state.

Problems

that have

identical state spaces despite different descriptions (surface structure) are isomorphs of each other.

Operators and procedural knowledge The more familiar we are with the operators, the more procedural knowledge we have about them and the easier they are to apply.

Procedural

knowledge is knowing how to do an

operator, and if you have more procedural knowledge for some operators than others within a problem space, you may be more likely to construct a solution path that relies upon them than the others. This may limit your ability to find the best (or only) solution path. Problem

isomorphs can vary in the amount of procedural knowledge they allow us to use, and

so can vary in difficulty despite having the same state space.

Types of problems Problems

can differ in how well they are defined. When problems are well-defined (or (or well-

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Well-defined problems allow an algorithmic or step by step approach to problem solving, with all possible routes through the space being explored in a systematic way so that you never get lost, or repeat yourself, and when you have finished, you can be sure that you have found the shortest path. Ill-defined problems such as insight or real-world problems require heuristic approaches to problem solving. Where algorithms are guaranteed to produce the right answer, heuristics are not, but they are likely to be much faster to use and so more likely to result in a solution, if not the best solution. Heuristics may also be the best approach to problem solving when the problem space is very large, and so when an algorithmic would just tale too much time. Heuristics include forward and backward searching, generate-and-test generate-and-test and means-end analysis. Bounded

rationality

The ability to reason rationally is limited by our imperfect knowledge and our limited cognitive capacities. This means that we are unable to hold all of the relevant information in working memory, or we cannot combine all of this information using problem solving strategies within the time limits. This means that while we do attempt to reason in a rational manner, there are bounds placed upon our ability to do so, leading to errors and biases. Satisficing is a problem solving strategy which leads to an answer which is satisfactory and sufficient rather than optimal.

F3 Expertise Special Experts

knowledge can structure knowledge into chunks of schematic knowledge. This allows them to

encode the surface features of a problem faster than novices, and to build more complex representations. The better the representation, the faster the problem solving strategies can be applied and the quicker a solution can be found. Domain Specificity Expertise

is usually restricted to a particular area or domain. The schematic knowledge is

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that the expert may not be able to apply his knowledge, even though the problem is essentially the same.

Analogical reasoning Domain specificity does not mean that experts can never transfer their knowledge to new situations. Paradoxically, human experts are sometimes rapidly able to solve problems that they have never experienced before, in which they apparently have no expertise. This is because they are able to use analogical reasoning in which they recognize an abstract relationship between the novel problem and an old problem that they do know how to solve. Analogical reasoning, which is an aspect of human intelligence, involves noting similarities between the novel situation and a previously solved problem.

Creativity Creative individuals are experts who have built up a great deal of knowledge in their field through years of effort and application, and who are able to apply ordinary problem solving skills to their extraordinary knowledge. Creativity is an ability that we all have and is related to expertise. No one can be successfully creative on his own: they have to be in an environment which is both receptive to his ideas and stable enough to allow knowledge in a domain to accumulate.