Gestalt Problem Solving

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ways of conceptualizing what happens during insight: insight involves building a schema in 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 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 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 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 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 solver already knows how to solve). Gestalt theory informs educational programs aimed at teaching students how to represent problems.

teaching students how to represent problems.

Gestalt psychologists saw problem solving as the closure of a problem, achieved by the Gestalt psychologists saw problem solving as the closure of a problem, achieved by the represen

representation of the problem in tation of the problem in an appropriate way. A problem is an appropriate way. A problem is only a problem because it isonly a problem because it is incomplete; the solution makes it complete, and finding the solution closes the incomplete; the solution makes it complete, and finding the solution closes the incompleten

incompleteness. Closure is ess. Closure is accompanieaccompanied by d by the flash the flash of insight or of insight or aha! experience.aha! experience.

Gestalt psychologists typically studied problem solving by using verbal protocols. They were 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 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 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 problem and occurred when the participants restructured the problem. Insights occur when the participants are suddenly aware of the answer (the participants do not

participants are suddenly aware of the answer (the participants do not gradually work toward agradually work toward a solution; rather it appears in a

solution; rather it appears in a flash).flash).

Representation

P

P_{roblem solution involves mentally forming and reforming different representations of a}_{roblem solution involves mentally forming and reforming different representations of a}

problem until the right form is

problem until the right form is chosen. The ease with which the appropriate represenchosen. The ease with which the appropriate representation cantation can be found changes the difficulty of the problem. Difficult problems are those in which the be found changes the difficulty of the problem. Difficult problems are those in which the appropria

appropriate representation is not te representation is not apparent from the apparent from the initial description and must initial description and must be discoveredbe discovered by the solver.

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S S

_et

Gestalt psychologists argued that there are a number of possible negative effects of past 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 experience and reproductive thinking (using previous experience of problem solving to solve new ones) such as

new ones) such as problem solving problem solving set andset and functional fixedness. functional fixedness. PP_{roblem solving set occurs}_{roblem solving set occurs}

when participants learn to solve a series of problems in a specific manner. The solution then 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.

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 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 (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 though they are not helping you find a solution. Set can be reduced by giving objects nonsense names, or by intentionally trying to think

names, or by intentionally trying to think of novel uses of novel uses for objects.for objects.

II

_ncubation

P

P_{roblem solving has four stages:}_{roblem solving has four stages:}

a)

a) PP_{reparation ( when you discover the problem and think about it}_{reparation ( when you discover the problem and think about it unsuccessfully often for}_{unsuccessfully often for}

a long time) a long time) b)

b) IncubatioIncubation (when you give n (when you give up and do something else up and do something else for a while, for a while, perhapperhaps somethings something relaxing)

relaxing) c)

c) Illumination ( when the flash of Illumination ( when the flash of insight presents the solution to you)insight presents the solution to you) d)

d) Verification (when you check that your solution works, and perhaps refine it.Verification (when you check that your solution works, and perhaps refine it. In incubation stage, you are not trying to

In incubation stage, you are not trying to solve the problem and the sosolve the problem and the solution may appear in alution may appear in a flash of insight. Incubation may allow set to weaken, by giving time for obvious (but wrong) flash of insight. Incubation may allow set to weaken, by giving time for obvious (but wrong) ideas to fade; or it

ideas to fade; or it may give time may give time for unconscious processes to continue re-representinfor unconscious processes to continue re-representing theg the problem.

problem.

II

_nsight

There are two types of thinking that can be

There are two types of thinking that can be applied to solving applied to solving problems:problems: a)

a) ReproducReproductive thinking (using previous experience of problem solving to tive thinking (using previous experience of problem solving to solve new ones)solve new ones) b)

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While this approach can be useful, it can also lead to problems since people do not notice the 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

structure of the problem and may not see other simpler solutions.other simpler solutions. Insight experienc

Insight experience occurs due to a sudden release from e occurs due to a sudden release from set which is more likely to set which is more likely to happen afterhappen after incubation in a context different from the one i

incubation in a context different from the one in which the set n which the set was formed.was formed.

Thus, insight is equated with the moment of creative inspiration, and productive thinking is an Thus, insight is equated with the moment of creative inspiration, and productive thinking is an insightful mode that allows novel associations to be

insightful mode that allows novel associations to be made.made.

F2 Goals and States

P

P_{roblems arise when people do not see immediately how to get from where they are (starting}_{roblems 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

state) to where they want to be. Therefore, every problem has a start statestart state (or initial state) and(or initial state) and this is the

this is the position you begin with. Theposition you begin with. The goal stategoal state is the state you is the state you want to achieve. Something iswant 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 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 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; are different types of processes or actions that enable us to get from one state to another; these are called

these are called operatorsoperators. State space includes every state of a problem.. State space includes every state of a problem. PP_{roblems are solved}_{roblems are solved}

by finding a solution path that links the start space to the goal state.

by finding a solution path that links the start space to the goal state. PP_{roblems that have}_{roblems that have}

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

other.

Operators and procedural knowledge

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

them and the easier they are to apply. PP_{rocedural knowledge is knowing how to do an}_{rocedural knowledge is knowing how to do an}

operator, and if you have

operator, and if you have more procedural knowledge for some operators than others within amore 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 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.

the others. This may limit your ability to find the best (or only) solution path.

P

P_{roblem isomorphs can vary in the amount of procedural knowledge they allow us to use, and}_{roblem isomorphs can vary in the amount of procedural knowledge they allow us to use, and}

so can vary in

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

Types of problems

P

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well-Well-defined problems allow an algorithmic or step by step approach to problem solving, with 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 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 lost, or repeat yourself, and when you have finished, you can be sure that you have found the shortest path.

shortest path.

Ill-defined problems such as insight or real-world problems require heuristic approaches to 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 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 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 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. problem space is very large, and so when an algorithmic would just tale too much time. Heuristics include forward and

Heuristics include forward and backward searching, generate-andbackward searching, generate-and-test and means-end -test and means-end analysis.analysis.

B

_{ounded rationality}

The ability to reason rationally is limited by our imperfect knowledge and our limited cognitive 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 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 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 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 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 solving strategy which leads to an answer which is satisfactory and sufficient rather than optimal.

optimal.

F3 Expertise

S

_{pecial knowledge}

E

E_{xperts can structure knowledge into chunks of schematic knowledge. This allows them to}_{xperts 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 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 representations. The better the representation, the faster the problem solving strategies can be applied and the quicker a solution can be

applied and the quicker a solution can be foundfound

..

D

_omain

SS

_pecificity

E

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that the expert may not be able to

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

the same.

Analogical reasoning

Domain specificity does not mean that experts can never transfer their knowledge to new Domain specificity does not mean that experts can never transfer their knowledge to new situations.

situations. PP_{aradoxically, human experts are sometimes rapidly able to solve problems that}_{aradoxically, human experts are sometimes rapidly able to solve problems that}

they have never experienced before, in which they apparently have no expertise. This is 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 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. 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 Analogical reasoning, which is an aspect of human intelligence, involves noting similarities between the novel situation and a

between the novel situation and a previously solved problem.previously solved problem.

Creativity

Creative individuals are experts who have built up a

Creative individuals are experts who have built up a great deal of knowledge in their fieldgreat deal of knowledge in their field through years of effort and application, and who are

through years of effort and application, and who are able to apply ordinary problem solvingable to apply ordinary problem solving skills to their extraordinary knowledge. Creativity is an ability that we all

skills to their extraordinary knowledge. Creativity is an ability that we all have and is related tohave and is related to expertise. No one can be successfully creative on his own: they have to

expertise. No one can be successfully creative on his own: they have to be in an environmentbe in an environment which is both receptive to his

which is both receptive to his ideas and stable enough to allow ideas and stable enough to allow knowledge in a domain toknowledge in a domain to accumulate.