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Problem Solving

Xiaolin ZhouDepartment Psychology

Peking University Beijing, China

Http://cbcs.pku.edu.cn/

A prisoner was attempting to escape from a tower.

He found in his cell a rope which was half long enough to permit him to reach the ground safely.

He divided the rope in half and tied the two parts together and escaped.

How could he have done this?

What is a problem?

A problem occurs when we have a goal that we wish to attain and cannot immediately attain it. a problem consists of several basic components

an initial state (situation at the beginning of the problem)a goal state (the solution to the problem)a set of rules (or constraints) that must be followedand usually, a set of obstacles that must be overcome

Types of problemswell-defined problems: clear and structured; initial state, goal state, and constraints are all understood, and once you reach a solution, it’s easily assessed ill-defined problem: fuzzy and abstract; initial state goal state, and constraints are not well understood, and once a solution is reached, it is difficult to assess

Routine and Non-Routine Problemsproblems vary according to our familiarity with the procedures they involve

routine problem: one that can be solved by applying well-practiced procedures; tend to be more well-definednon-routine problem: one that can not be solved by applying well practiced procedures; tend to be less well-defined

Types of problemstransformation problems: solver is presented with the goal state and must find the proper strategies that will transform the initial state into the goal statearrangement problems: solver is presented with all the necessary elements to solve the problem and must figure out how the elements are to be arrangedinduction problems: solver is given a series of instancesand must figure out the rule that relates the instancesdeduction problems: solver is given premises and must determine whether a conclusion fits these premisesdivergent problems: solver must generate as many solutions as possible to a given problem

Problem Solving ResearchMethodological Challenges

because of its complexity, problem solving often occurs over a much longer time interval than many other cognitive processes

often, participants can only be presented with one problem within a reasonable time frame (prevents study of most everyday problems)

therefore, assessing problem solving in terms of accuracy rate provides a rather gross estimate of problem-solving proficiencymeasuring solution times provides some useful information, but doesn't account for the processing that occurs during problem-solving

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Methodologies and their ChallengesVerbal Protocols

reports generated by problem-solvers “thinking out loud” during solution

similar to introspective technique employed by the structuralists, but attempts to give a more dynamicview of cognitive processing as it occurs over a longer span of time

potentially serious limitations:not everyone has verbal ability to express well on what they’re thinkingno way to assess the accuracy of a verbal report; indeed, it may be that the most important processes cannot be verbalized at allthe mere act of thinking out loud may interfere with or change the nature of the thought processes being described

Approaches to Study of Problem Solving

Thorndike & Behaviorism: Problem Solving as Associative Learning (instrumental conditioning)Thorndike, in the late 1890s, used cats as subjects

placed in what was termed a “puzzle box;” ---- home-made enclosures that posed a problem for his feline subjects, who had to discover the trick to getting out

cats learned to escape due to the law of effect: if a response leads to a good outcome, the connection between the response and the situation in which it took place will be strengthenedif a response leads to a bad outcome, this connection will be weakened

• behaviorists believed problem solving is an essentially “mindless” process whereby learned responses automatically play themselves out

– a process of trial and error, reward and punishment

Kohler and Gestalt: Problem Solving as Insight

problem solving involves a restructuring or re-organization of problem elements that results in a sudden realization of the solutionthe sudden and successful restructuring of problem elements is termed insight, and became a major focus of the Gestalt approach

Kohler and Gestalt: Problem Solving as Insight

Kohler (1925) investigated problem solving in apesan ape was put in a pen with crates and something desirable (like a banana) suspended from the ceiling, just out of reachsolution was to use crates as steps to reach the bananaapes sat for a while as if they were pondering the problem, then all of a sudden would jump up, push the crates to the appropriate spot, stack them, and fetch their treat

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Contrasting Behaviorist and Gestalt Viewsbehaviorist approach

Appeal: precision and simplicity; many complex behaviors could be characterized as sets of simple responses that were based on a straightforward association mechanismDeficiency: limited in what they could explain via a simple S-R association mechanism; failed to explain more novel and creative behavior

gestalt approachAppeal: attempted to explain novel and creative behavior in terms of mental representationsDeficiency: imprecise and vague; never really provided satisfactory (i.e., testable) definitions for concepts like insight and restructuring of problem elements

Problem Solving as Information Processing

computer programs that mimic human solutions can be interpreted as models or theories of human problem solvingNewell, Simon: General Problem Solver

originated the conceptualization of problem solving as a step-by-step progression from an initial state to a goal statethey did so within the framework of a computer program termed the General Problem Solver (GPS), which they proposed as a general model of human problem-solving--one that could be applied to any problem

General Problem Solver

GPS views problem-solving as an attempt to minimize the “distance” between an initial state and a goal state by breaking a problem down into a series of sub-goals. this sub-goal analysis is accomplished through the application of operators, which is to say, of problem-solving techniques

these techniques are applied to reduce the difference between the current state and the current sub-goal state or to reduce the difference between the initial state and the final goal state

problem space: solver’s mental representation of the initial state, the goal state, all possible intermediate (sub-goal) states, and the operators that can be applied to reach these sub-goals

Tower of London

Each position is a problem stateLinks are possible pathsOperators transform statesKey is to move efficiently to goal

Tower of London

Match start configuration to the goal configuration in the minimum number of moves

Constraints the three bins hold three balls, two balls and one ball, respectivelycan move only the top-most balls to a different bin

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The IDEAL Problem SolverIDEAL (Bransford and Stein, 1993): Hypothetical model of problem-solving stepsIdentify the problem: Recognize the signs that a problem existsDefine (represent) problem information in relevant ways: What is really nature of problem? What do we want out of it?Explore a variety of problem strategiesAct on the problem strategy you chooseLook back and evaluate whether the strategy was effective,If not, try something new (recycle through process)

Notice that this cycle may describe an individual thought process or a group or organizational dialogue.

Problem RepresentationTo solve a problem, it is imperative to correctly specify the problem space,

to correctly represent the aspects of the problem, one must correctly identify the initial state, as well as the operators that may be applied within the constraints of the problem failure to properly represent a problem can result in solutions being missed or overlooked

different problem statements may inadvertently lead to different problem representations

the ability to solve problems depends critically on the exact nature of the representation

Stereotype Threat Hinders Problem Representation

a woman's belief in the stereotype that men are better at math than women can interfere with her ability to devise a strategy to represent a mathematical problem and, consequently, her ability to solve it

Quinn and Spencer (2001)interested in why woman who have strong math skills underperform in comparison to their male peers

believed the answer might reside in the interactionbetween the cultural stereotype about women's math ability and the testing situationthis interaction creates stereotype threat

Stereotype Threat

stereotype threat occurs when a member of a negatively stereotyped group feels that the stereotype might be used to judge their behavior, resulting in a negative judgment that will propagate the stereotype

the anxiety created by this apprehension interferes with the ability to accurately represent the problem and performance suffers, not because of some inherent inferiority of women doing math, but because of a self-fulfilling prophecy driven by that stereotype

Quinn and Spencer (2001)had men and women solve math word problems or numeric/algebraic equivalents of the word problems

the mathematical knowledge necessary to answer these problems was equivalent in both conditions; however, the word problem condition required participants to transform the problem into its proper mathematical representation

resultsmen outperformed women on word problems only; on the simpler numeric/algebraic problems, men and women did not differwomen had the mathematical ability to solve the problem but ran into interference in conditions that required an involved the stage of problem representation

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Quinn and Spencer (2001)

Quinn & Spencer suspected interference was due to stereotype threatto test this suspicion, the researchers manipulated the level of stereotype threat in the situation

low-stereotype threat condition: told that the test had been shown to be gender-fair, yielding equivalent performance of men and womenhigh threat conditions: were not given this information

Results in the high-stereotype threat condition, men outperformed womenin the low-stereotype threat condition, there were no sex differences

Quinn and Spencer (2001)to determine if the deficits found were really due to difficulties in problem representation, participants in the second experiment were recorded while solving the problems (i.e., verbal protocol procedure)the number of problems in which participants could not determine a strategy (i.e., proper problem representation) to solve the problem (i.e., a “failure rate”) was assessed

in the high-threat stereotype condition, women had higher failure rate than men; in the low-threat condition, these failure rates were equivalent

when stereotype threat is reduced, women perform equally well as men quite possibly because an obstacle to successful problem representation has been removed

Rigidity in Representation

failure to represent a problem correctly may stymie a solution

Mental Set (mind set, habit pattern of the mind)the tendency to rely on habits and procedures used in the past

tends to exert its effect in the representation phase of problem solving, as past experience leads to inappropriate problem representationLuchins water jar problem is classic example of mental set:Given three water jars of different sizes, measure out a given amount:

Rigidity in Representation

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GoalCBAProblem

Rigidity in Representationfailure to represent a problem correctly may stymie a solution

Functional Fixednessthe tendency to view objects in a fixed sense (typical function of the object)

Duncker’s candle problem is a classic example of functional fixedness:given items depicted, how would you hang a candle on the wall so that it burns normally?

The Pros of Rigiditythinking of things the same way is not always a bad thing

most situations in life require that we think conventionally, as opposed to non-conventionallyconventional, everyday thinking (because it tends to rely on processes that have become automatic), tends to be quicker and requires less conscious effort, allowing us to do other things at the same time

effective problem solving may require a balance between conventional and non-conventional thinking,

sticking with the “tried and trued” basics generally, but not mindlessly or absolutely; rather, flexibly, changeably, with a light touch

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Problem Solutionwithin the context of The General Problem Solver, problem solution amounts to traveling through the problem spacetwo approaches to traversing the problem space: algorithms and heuristics

Algorithmsa set of rules that can be applied systematically to solve certain sorts of problems; a mechanical, effective or step-by step procedurepowerful problem solving techniques

if applied correctly, an algorithm will always lead to the correct solution, if one exists requires explicit representation of initial state, ends state and all rules“Deep Blue”

Problem Solutioncomputers are well-suited to algorithmic problem solving because they are well-suited for what algorithms require: speed, power, and reliable applicationalgorithms are seldom, if ever, used to solve problems on a day-to-day basisfor human problem solvers, algorithms are often unfeasible. Why?

the exhaustive nature of algorithms makes them overly tedious and quite impractical – we just can’t check all possibilities

complex and ill-defined problems demand more flexible, dynamic approach

even some well-defined problems are not solvable algorithmically

Heuristicsgeneral strategies or rules of thumb that can be applied to various problems

given the strengths (flexibility) and limitations (computing power) of the human problem solver, the fact that most problems are ill-defined and have relatively large problem spaces, heuristic problem solving is much more effective

the strength of the heuristic approach is that the trip through problem space is faster; the solutions come more quicklyunlike algorithms, heuristics do not guarantee a correct solutionspecific heuristics exist for/within specific problem domains,

but there are a number of general purpose heuristics that can be applied to a wide array of problems.

Three general purpose heuristicsWorking Backward

focus on the goal state and work backwards in order to map out the steps that would get you thereaids problem solving by imposing constraints on what may be a difficult-to-define problem

Means-End Analysisinvolves breaking a problem down into smaller subgoals, where accomplishing each subgoal moves the solver closer to the final goal--the problem’s solutionthe solver systematically attempts to devise means to get to each of the subgoals’ ends

Three general purpose heuristics

Analogiesusing problems that have already been solved as aids for representing and solving the problem currently being facedproblem solvers are unlikely to use analogies to aid in problem solving, unless they are practically “hit over the head” with the connections between problemsstill analogies do spontaneously arise in thought.

Gick and Holyoak (1980)used the radiation problem created by Duncker to determine if providing an analogous problem might help solver’s succeed at finding a solution to itafter looking over a problem analogous to the radiation problem (the source problem) under the guise of a story comprehension task, participants were given Duncker’s radiation problem (the target problem)

some participants were only given the target problem 10% came up with the convergence solution

some participants were instructed to memorize the source problem and then tried to solve the target problem

in this condition 30% of participants came up with the convergence solutionup to 20% of participants “spontaneously” noticed the analogous relationship and used it

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Gick and Holyoak (1983)attempted to determine when analogical transfer occurs without explicit hintsgot solvers to notice and use analogies under three different conditions:

analogy-plus-general-principle condition: gave the analogous story, along with an extra passage that basically stated the underlying principle (or, in Gick and Holyoak’s terms, the underlying schema)analogy-plus-diagram-condition: gave the analogous story plus a diagram that sketched out the underlying principleanalogy-plus-another-analogous-problem condition: gave two analogous problems, had participants find a general schema themselves

Gick and Holyoak (1983)

resultsproviding a diagram or a statement of the general principle underlying the problem did not help subjects to spontaneouslyrecognize and use the analogywhen subjects read and related two analogous stories they were able to use the knowledge in another situation

in this condition, solvers were able to map the connections between the two different problems

Gick and Holyoak (1983)

resultsthis mapping process (determinant of whether an analogous problem is going to aid schema induction) is the defining feature of analogical reasoning,

in this context, a schema is the underlying principle that is shared by multiple problems

once this schema is formed, the problem solver can make use of it in solving analogous problems

Gick and Holyoak (1983)Steps necessary for analogies to succeed as problem solving techniques

noticing: the problem solver must notice that a relationship exists between the two problemsmapping: the solver must be able to map the key elements of the two problemsschema development: the solver must arrive at a general schema underlying the problems that will allow for the solution of the target problem

Gick and Holyoak (1983)much research shows that the first stage, where a relationship must be noticed, is a major culprit in failures of analogical problem solving

it’s basically a failure of memorythe source problem fails to cue memory retrieval of other problems that may be helpful; or semantic knowledge lacking.

a hint to specifically use the related problem (which serves as a retrieval cue) leads the solver to use the previous problem

in most everyday cases of problem solving, no one is there to whisper hints to other analogous problem

Surface vs. Structural Featuressurface features: the specific elements of the problem

if problems share surface similarity, the elements of the problems look pretty similar

structural features: the underlying relationships between the surface features of the two problems

if two problems are structurally similar, they may look quite different on the surface, but have deep-rooted similarities in terms of relationships

People tend to not apply analogies unless surface similarities are apparent

structural similarity is not enough to cue a person’s memory regarding previous problems

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Needham and Begg (1991)

explain failures of analogical transfer through transfer-appropriate processingstudies of analogy often show mismatch of retrieval & encoding processing

at encoding, person encounters a problem and is asked to process it in some meaningful way, e.g. answering story comprehension questionsthese procedures don’t transfer very well to retrieval situations that require a solution-finding process (i.e., solving the target problem)

Needham and Begg (1991)two types of instructions:

memory-oriented instructions: told they would be reading some stories that they should try to remembersolution-finding instructions: told they should try to figure out why the solution to each of the story problems was correct

resultsthose who received solution-finding instructions with the source problems successfully solved more of the target problems than participants who received memory-oriented instructions (90% vs. 69%)

overall, the results indicate that people are likely to notice connections between problems and problem situations to the extent that they receive similar sorts of processing

Needham and Begg (1991)results

an interesting finding from this study was that, although most solution-finding processors were able to apply the source problems to target problems, most (80%) were not able to remember the solutions of the source problems

participants are preparing to solve problems, not memorize solutionsat retrieval if asked to solve problems, they do well because the encoding task was appropriate for the requirements of the retrieval taskhowever, if asked to recall the solutions, they do poorly because the solution finding encoding task is not appropriate for the requirements of a retrieval task

Blanchette & Dunbar (2000): An Ecological Critique

the seeming ineffectiveness of structural similarity for analogy use is deceiving;

some research suggests that it might be (at least in part) an artifact of the cognitive psychology laboratory

several studies of real-world reasoning indicate that the analogies people use are based on structural features, not surface ones

Blanchette & Dunbar (2000): An Ecological Critique

In this study, participants produced their own analogies to various target problems, and the characteristics of these generated analogies were evaluated

resultsresults indicated that these analogies shared structural similarity rather than surface similarity with the target problemindicating that people in everyday circumstances may actually be more sensitive to structural similarity than suggested by earlier research

Experts: Masters of Representation and Solution

expertise: exceptional knowledge/performance in a specific problem domain

for some time, it was commonly believed that the exceptional performance of an expert reflected some innate capacity or talentsince the advent of cognitive psychology, this view has given way to what might be termed an information-processing account of expertise:

expertise is an outgrowth of learning and repetition over the course of years that produces an extensive body of knowledge and an extremely well-learned set of skills

By one estimate, expertise involves approx. 10 years of continuous exposure to given domain, comprising thousands of hours of practice

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Three stages to skill learning

Cognitive stage (declarative knowledge)Memorizing the steps to do the skill

Associative state (procedural knowledge)Conversion of declarative knowledge into procedural knowledge (practice)Errors eliminated; connections strengthened

Autonomous stage (automaticity)Need few resources to do the skill

Expert performance

Developed through intensive deliberatepracticeEnhanced memory for information in domain (long-term working memory)

WM enhancement (Chase & Erricsson, 1982)Enhanced storage (associative network)

Domain specificGenerally does not apply across domains

Experts: Masters of Representation and Solution

to some extent, experts might be considered skilled memorizers; according to the skilled-memory theory, there are a number of fundamental differences between experts and novices

the semantic networks are much more richly elaborated in expertsexperts have quicker retrieval and more direct access to long-term memoryinformation is more easily encoded into long-term memory by experts, and the speed of this encoding improves with practicethese memory skills are usually specific to domain in which they were acquired

Expert Advantages

the core of problem solving is memory: long-term memory (storage of domain-related general knowledge & specific episodes) and working memory (with quick, efficient on-line processing of problem information)

DeGroot (1946/1978)investigated memory in chess players of varying skill levels by presenting brief glimpses of meaningful board positions, and then having them reconstruct the boards

recall differed as a function of expertise, with the best players recalling the boards almost perfectly

Chase and Simon (1973)replicated DeGroot’s findings, but included an encoding condition in which the chess pieces were randomly rearranged

to find out if the advantages enjoyed by experts was general (good working memory overall) or specific (exceptionally good for game configurations they’d seen before)

while expert chess players remembered game configurations better than novices, they demonstrated no superiority in memory for random board configurations

at first, this was explained by chunking in working memoryexperts could instantly recognize game board configurations based on their extensive knowledge and experience base

More on Expert Advantages

Further research results indicate the expert advantage is not an exclusive function of workingmemory, because it doesn’t seem subject to many of the limits found in working memory

expert memory for chess positions was not diminished by delay, even with an interfering taskchess masters who quickly glimpsed at several game boards could process more chunks than a typical view of working memory would allow

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Ericsson and Kintsch (1995)Experts …..can bypass the limits of working memory by using the information in working memory to directly access LTM; in essence working memory serves as a retrieval cue for information in LTMuse general strategies that differ from those of novicestend to search problem space in a forward fashion, reasoning from givens toward the goal

novices, however, tend to think about the goal and reason backwards about the steps that will lead there

are much better at picking up on structural features of problems; whereas novices are more likely to focus on surface features;

so experts are more likely to recognize analogous problems or situations when faced with a new one (within their area of expertise)

Expertise and problem solving

ExpertiseMore knowledge in domain

chess - positions in memorylike the long distance runner, they rely on stored, chunkinglike runner, use deeper meaning to organizework forward when solving problems; “see” their way to the endrely heavily on pattern recognition and less on calculations; only calculate to verify intuition

NoviceLess domain knowledge

less use of chunking little reliance on stored info.use surface features to organizework backward when solving problemsrely more heavily on calculations

Expert Disadvantages: Costs of Expertise

chess novices were slightly better than experts at remembering the random chess piece configuration

intermediate effect: studies of medical expertise have revealed that those at an intermediate level of knowledge (e.g., residents in a teaching hospital) actually remember more information about specific patient cases than do experts (e.g., experienced physicians)

Voss, Vesonder, and Spilich (1980) found that baseball experts were worse than novices in recall of baseball-irrelevant details from a baseball storytaken together, these findings indicate that while experts may be able to encode important information by relating it to richly elaborated schemata, this can come at the expense of attention to (and subsequent retrieval of) detail information

Wiley (1998)

Wiley (1998) suggests that expertise itself may actually function as a type of mental set

to find out if expertise might prevent solvers from coming up with creative solutions to problems, due to the tendency to think of things in an automatic, expertise-driven fashion

Wiley (1998) employed the Remote Associates Test (RAT), in which solvers look at three apparently unrelated words and generate one word that ties the triplet together

the ability to make the connection between the three terms and come up with the remote associate is taken as a sign of creativity

Wiley (1998)tested experts and novices in baseball, presenting RAT items to them

on all trials, the first word (e.g., plate) formed a baseball phrase (home plate)the remote associate (home) was further supported by the second word (e.g., broken--broken home)however, the third word presented was the critical one:

on baseball-consistent trials, the third word presented (e.g., rest) was also consistent with the baseball interpretation of the remote associate (rest home)on baseball-misleading trials, the third word rendered the baseball-related term incorrect (e.g., plate, broken, shot--GLASS

Wiley (1998)

hypothesized that baseball experts were likely to start thinking baseball as soon as they saw the first word, resulting in their being stumped if the final word didn’t match the word they had generatedresults supported her hypothesisperformance of the experts was very poor if they were misled;

their ability to make creative connections was stifled by their tendency to think in terms of their area of expertise

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Insight and CreativityWallas (1926) proposed that the processes leading up to a creative breakthrough can be described in terms of four stages

Preparation: the solver gathers information and makes initial attempts at problem solution

this initial stage corresponds roughly to the problem representation phase of processing discussed earlier

Incubation: productive inactivity; occurs when initial attempts at solution are stymied

putting things aside awhile can help hereIllumination: after the incubation period, the problem solver arrives at an important realization or understanding

a solution to a problem has appeared suddenly, probably with a tangible “Aha!” feeling for the solver. This is classical insight.

Verification: problem solver assesses whether the solution will actually work

The Maier Two String Problem:How do you tie the strings together if you can’t reach them both at once?

Insightthe debate over the nature and existence of insight (as a special sudden, solution-finding experience) goes back to the debate between behaviorist and Gestalt views of problem solvingGestalt psychologists believed that the key to problem solution lay in a restructuring of the problem elements which, if successful, would lead to a sudden realization of the problem’s solution; this sudden realization is insightthe notion of insight is a controversial one;

many theorists believe that problem solving is an incremental process of getting closer and closer to a solution, rather than a sudden realization

another problem is that insight (until relatively recently) was never clearly defined or experimentally demonstrated

Insight vs. Non-insight Problemsmany researchers make a distinction between non-insight and insight problems

this distinction can be seen as loosely analogous to the earlierdistinction between ill-defined and well-defined problemsnon-insight problems are those that are likely solved through incremental, or “grind out the solution” processes; they require analytical, step-by-step processinginsight problems are those in which the solution appears suddenly

two of the key assumptions about insightful problem solving:1. it involves a mistaken assumption that, once removed, will clear

the way to successful solution2. that the solver is hit with the solution suddenly, and has what

might be termed an “AHA!!” experience

Insight as Removal of a Mistaken Assumption?Weisberg and Alba (1981)

employed an insight problem called the nine-dot problem--must connect all the dots with one continuous line

Insight as Removal of a Mistaken Assumption?

Weisberg and Alba (1981)the solution involves extending the lines beyond the boundary of the square defined by the nine dots the mental set of staying within this boundary is the primary block that prevents successful solutionaccording to the notion of insight, removing this mental set should produce an easy solutionbecause the inability to solve insight problems is the result of being blocked by one inappropriate assumption

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Weisberg and Alba (1981)to test this hypothesis they presented insight problems with or without hints

some were told they would have to break the imaginary boundary created by the dotssome were told the same thing along with the first or the first and second lines that needed to be drawna control group was simply told to solve the puzzle

resultssolvers who were told to go outside the boundary were only slightly more likely to solve the problemover 1/3 were unable to solve it even in the group given the first lineclearly, this does not fit the Gestalt prediction, which would predict that nearly everyone would solve it, once the offending assumption was removed Control

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Weisberg and Alba (1981)

The authors suggest the term insight offers little more than a description of what a person experiences in solving some problems

it doesn’t specify how a problem is being solvedin addition, the notion of insight is circular:

how do we know the problem was solved through insight?because it was solved suddenly, with an AHA! experience,

why was there a sudden solution, and an AHA experience?

because the problem was solved through insight

The “Aha!” Experience

insight problems are solved suddenly with a tangible feeling of discovery, usually described as an “AHA!”experiencewhat someone thinks about what they are thinking is metacognition

Metcalfe and Weibe (1987)presented participants with non-insight problems and insight problem--allowed 4 minutes for each problem, and within that interval, they performed two metacognitive tasks:

rate their “warmth” every 15 seconds by making a mark on a scaleasked to judge whether or not they would be able to solve each problem

Metcalfe and Weibe (1987)ratings of warmth: have subjects rate how close they are with regard to the solution of a problem >>“I think I am getting warmer” (closer to solution)insight problem: if it involves a sudden realization of the solution then solvers should have no idea if they’re close to a solution, and their warmth ratings should reflect this

they should report little warmth throughout the problem-solving interval, until a solution finally appears

non-insight problem: participants should realize they are getting closer to a solution, given the nature of a non-insight problem

Metcalfe and Weibe (1987)results

metacognition is better for noninsight than for insight problemsinsight problems: warmth ratings were incremental,increasing gradually throughout the solution interval

participants felt as if they were nearing a solution when they really were near a solution

non-insight problems: warmth ratings didn’t really increase at all throughout the solution interval, until the problem was solved

participants really had no idea if and when they were approaching a solution

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Metcalfe and Weibe (1987)results

the other metacognitive judgment paralleled the warmth ratings

non-insight problems: participants were decent judges of whether they would be able to solve the problemsinsight problems: participants were relatively poor judges of solution probability; they demonstrated overconfidence, underestimating how difficult the problems were

Metcalfe and Weibe (1987)conclusions

metacognitions about non-insight problems are accurate, and predictive of actual performancemetacognitions about insight problems tend to be unrelated to (or even negatively related to) the probability of eventual solutionpattern of warmth ratings during a solution can be used as an indicator of whether a problem involves insight, thereby avoiding the circularity problem in defining insight

objections to these conclusionsthere may be a subjective “Aha!” experience produced by some problems, but this does not necessarily mean that problems are solved suddenlya step-by-step processes may be involved, but the solver is unaware of them

Insight and Intuition

insight problems do seem unique phenomenologically, that is, in terms of the conscious experience that a problem solver has;

feels like an all-or-none process that occurs suddenlyExample - chess master, Kasparov, studied by Gobet & Simon (1996), playing 4 to 8 opponents simultaneously; unable to calculate; play did not decrease; used recognition memory

an alternative conceptualization is that insight problem-solving (like non-insight problem solving) is really more gradual, but the gradual progress is not open to conscious awareness

Bowers, Regehr, Balthazard, and Parker (1990)

these authors propose a two stage model of insight (they call it “intuition”)in stage one, the guiding stage, mnemonic networks relevant to the problem are activated, and this activation begins to spread

in essence, the problem solver is working on the problem unconsciously

in a second stage, the integrative stage, the buildup of activation reaches enough strength to break through into conscious awareness

this transition from stage one to stage two is insight

Bowers, Regehr, Balthazard, and Parker (1990)

used the dyads of triads task (RAT) - given 8-12 seconds to solve each triad

given two triads of words (e.g., notch/ flight/spin and clear/role/force)--for one of the triads, the words had a common associate; for the other one, no common associate existedif they couldn’t, they were asked to guess which of the two triads was coherent and to rate their confidence in this judgment

Bowers, Regehr, Balthazard, and Parker (1990)

Predictionsfaced with triads, unconscious processes immediately begin to workevidence for solution is incrementally and unconsciously building up through spreading activation, which can serve as basis for an intuitionthis hunch should allow participants to succeed on the second task, picking which of the triads was coherent, even if they couldn’t come up with the solution

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Bowers, Regehr, Balthazard, and Parker (1990)

resultsable to guess which triad was coherent at a rate well above chance, even when they couldn’t come up with the solution

suggests that incremental processes outside conscious awareness work on the problem

since these processes are not open to the conscious awareness, accurate metacognitive judgments are not possible

may explain why warmth judgments were poor indicators of whether solvers were close to an answer--they were getting closer to the solution but they were not consciously aware of it

when solving problems, you may have the subjective experience that you arrived at the solution suddenly, when in reality you were (unconsciously) approaching that solution incrementally

Does Incubation Lead to Insight?

incubation: the idea that taking a break in problem solving leads to a quicker solution than does continuing effort

the break allows for the elements of the problem to be re-organized, or for unconscious processes to continue to work on the problemunconscious progress will not take place if conscious work on the problem continues

anecdotal evidence for incubation is strong but this evidence is viewed skeptically by scientists

still, the phenomenon has remained elusive for problem solving researchers, who for the most part fail to find incubation effects

Smith and Blankenship (1989)Smith (1995) suggests that incubation effects do occur, but onlyunder specific circumstances:

namely, when a problem is doable; when the solver is blocked in some way from the solutionthe incubation period allows the interfering information to be forgotten, clearing the way for a solution

Smith and Blankenship (1989)participants attempted to solve rebus problems (word puzzles in which pictures and words are used to indicate a common phrase)for some, a pair of misleading cue words was giventhey retested unsolved rebuses immediately or after varying periods of incubationafter attempting to solve the rebus again, they were asked to recall the cue word that went along with it originally

Smith and Blankenship (1989)results

longer break periods associated with higher probabilities of solutionmemory for the misleading cues provides a possible explanation;

memory for the misleading cues decreased as incubation time increasedas the misleading cue was forgotten, the problem became more solvable

Contextual view of incubation

contextual view of incubation:when problem solving is stymied, a solution will come more easily if there is a contextual change from the previous situation

staying in the same situation continually reinstates the circumstances in which the failure to find a solution was first encountered, increasing the likelihood that the failure will continuechanging environment prevents reinstatement, so success is more likely

Creativity

What is Creativity?experts on creativity generally agree that creative solutions have two components:

novelty: creative solutions are different from previous solutions, and usually unexpectedappropriateness: the solution must satisfy the constraints of the problem at hand; it must fulfill a need and be sensible and useful

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Creativity

Factors Associated with CreativitySimonton (2000) presents multidimensional perspective on creativity

cognition is involved, as creativity is the product of cognitive processescreativity is also influenced by a person’s personality and style of thinkingfollows a consistent pattern of developmentover a lifespanis (in part) a product of the intellectual and social environment in which a person works

Cognition and Creativity

Views concerning cognitive processing in creativityone view says creativity involves special processes and abilitiesthe other says creativity is product of normal cognitive processing

the creative cognition approach argues that creative thinking can be the result of either type of process, or both

although creativity requires a great deal of old knowledge, it requires that we do things in new waystoo much knowledge can hamper creativity but you have no chance of exhibiting creativity in a given area if you know nothing about it

Schank and Cleary (1995)

Schank and Cleary (1995) suggest that creativity involves the “intelligent misuse” of one’s knowledge

when faced with a situation where scripted knowledge doesn’t really fit, we have to find a way to make it fit, hence the phrase intelligent “misuse” of knowledgegiven knowledge is a critical component of creativity, creativity tends to be domain-specific

Individual Differences, Development, Social Factors

the relationship between intelligence and creativity depends on the particular view of intelligence to which one ascribes

according to traditional, unidimensional views of intelligence, a certain level of intelligence is necessary to exhibit creativity, but beyond this minimal threshold, there seems to be little relationship between the twomultidimensional views of intelligence proposeforms of creativity specific to the various types of intelligence

Individual Differences, Development, Social Factors

the relationship between personality and creativity has led to a fairly consistent profile of “the creative personality”:

creative individuals tend to exhibit independence, nonconformity, a wide set of interests, openness to new experiences, flexibility, and risk-takingcreativity is a constantly developing ability, rather than a static attribute that some lucky folks are born with

Individual Differences, Development, Social Factors

creativity is not always the product of a comfortable environment, but may arise better when challenges are confronted

in fact, a person’s potential to exhibit creativity seems dependent on having had a diverse set of life experiences, which then enhance an individual’s ability to take fresh perspectives

creativity is the product of interpersonal, disciplinary, and sociocultural environments

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Individual Differences, Development, Social Factors

creativity is sensitive to a number of interpersonal factors:being evaluated by others can decrease creativitythe popular notion of brainstorming refers to the supposed creative benefit of generating ideas in groups

unfortunately, evidence fails to support a relationship between brainstorming and creativity; still, the technique enjoys great popularity in corporate settings

creativity is partially dependent on the socioculturalmilieu in which one’s work is conducted

cultural diversity enhances creativity; a civilization’s creativity tends to thrive when it opens itself up to alien influences through immigration or foreign study

Creativity and the Right Hemisphere

Recent evidence suggests the right hemisphere plays the more important role in creativity

Bowden and Beeman (1998)began with assumption that insight problems involve more creative thought than non-insight problemsused the Remote Associates Test (RAT)

combined the logic of priming with the RAT to investigate the relative roles of the left and right hemispheres in making these creative connectionsif the solution of an insight problem is associated, to a greater degree, with right-hemisphere activation, thensolution-related concepts should show more priming when presented to the right hemisphere than when they’re presented to the left hemisphere

Bowden and Beeman (1998)participants were presented with a word triad for 15 seconds

on all trials, the disappearance of the word triad was followed by the presentation of the solution word or a non-solution word (a word that did not relate the three words together), which they were to pronounce as quickly as possible

critical to note here is exactly where the fourth word was presented

sometimes it was presented left of fixation (i.e., to the right hemisphere), sometimes right of fixation (i.e., to the left hemisphere)if the right hemisphere is more involved in creative problem solving, then pronunciation times should reveal more priming (i.e., faster pronunciation times for solution than non-solution words) when presented to the right hemisphere

Bowden and Beeman (1998)because the increased activation of the right hemisphere when solving (or attempting to solve) a problem should translate into an enhanced ability to say the solution word relative to the non-solution word

resultssolved problem condition: a priming effect for both solved and unsolved problems but the effect was greater for words presented to the right hemisphere

indicates that the activation of the solution word was greater in the right hemisphere; this greater activation led to greater priming in pronunciation

Bowden and Beeman (1998)unsolved problems condition: a priming effect was found only for words presented to the right hemisphere (the small priming effect in the left hemisphere was not significantly greater than 0)

when a solution has not yet been consciously reached, the right hemi-sphere “knows what’s coming,” is sped up in naming the solution wordthe left hemisphere doesn’t know what’s coming, and is not sped up

Bowden and Beeman (1998)

Prim

ing

Scor

es (R

T, in

ms)

Is T

his

the

Solu

tion?

(RT,

in m

s)

Solved Problems

Unsolved Problems

0

120

40

80

940

1000

Unsolved Problems

(a) (b)

920 920

Solved Problems

800

1050

850

900

1000

950

Right hemisphere

Left hemisphere

Right hemisphere

Left hemisphere

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Bowden and Beeman (1998)in a follow-up study, Bowden and Beeman used exactly the same procedure, but changed the required response

after presentation of the fourth word participants had to make asimple yes/no response, “yes” if the word was the solution word or “no” if it wasn’t

resultssolved problems--there was no difference between the right and left hemispheres; the solution had already been figured out so saying “yes” or “no” was trivially easy for either hemisphereunsolved problems--the right hemisphere was faster than the left hemisphere, indicating that only the right hemisphere was “aware”of the solution

Taken together, the results indicate that activation of the right hemisphere is more strongly associated (relative to the left) with the (perhaps creative) processes involved in solving insight problems

Reading List罗劲. 顿悟的大脑机制. 心理学报，2004, 36：219-234Mai XQ, Luo J, Wu JH, et al."Aha!" effects in a guessing riddle task: An event-related potential studyHUMAN BRAIN MAPPING 22 (4): 261-270 AUG 2004 Luo J, Niki KFunction of hippocampus in "insight" of problem solvingHIPPOCAMPUS 13 (3): 316-323 2003 Cognitive flexibility across the sleep–wake cycle: REM-sleep enhancement of anagram problem solving Cognitive Brain Research Volume: 14, Issue: 3, November, 2002, pp. 317-324 Walker, Matthew P.; Liston, Conor; Hobson, J. Allan; Stickgold, Robert