Cognitive Psychology, Fifth Edition, Robert J. Sternberg Chapter 11 Chapter 11: Problem Solving and Creativity

Cognitive Psychology, Fifth Edition, Robert J. SternbergChapter 11

Chapter 11: Problem Solving and Creativity


Problem Solving A dealer in antique coins got an offer to buy

a beautiful bronze coin. The coin had an emperor’s head on one side and the date 544 B.C. on the other. The dealer examined the coin, but instead of buying it, he called the police. Why?In 544 B.C. Christ had not been born, so a coin from that time would not be marked "B.C." (before Christ).


Problem Solving

• Initial State– Current situation– Define the problem

• Goal State– Desired objective

• Obstacles– Choices made about limitations– Strategy choices– Limited resources


Problem Solving CycleIdentify Problem

Evaluate success

MonitorSolving

AllocateResources

Organize Info

Select Strategy

Define Problem


Sample Problem

• 15% of the people in Topeka have unlisted numbers. You select 200 names at random from the Topeka phone book. How many of these people will have unlisted numbers?– Did you say 30?

– The correct answer is zero


Sample Problem• A man wanted to enter an exclusive club but did not

know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six " and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said ,"ten" and the man replied, "five." But he was not let in.

• What should have he said?

– Three. The doorman lets in those who answer with the number of letters in the word the doorman says.


Problem Representation

• The importance of determining what information is relevant and what information is irrelevant is the process of problem representation– People pay attention to the wrong

information

– People need to focus on the right information


Strategy Formation

• Select a strategy to solve the problem– Analysis

• Breaking into sub goals• Study for exam sub goals

– Read textbook & class notes– Identify most relevant topics– Create study questions & answers on note cards– Learn all concepts on note cards– Test self with note cards– Recycle through learning and testing until

mastery is achieved


Strategy Formation

•Divergent thinking– Generate multiple solutions to problem

•Convergent thinking– Narrow down to best answer


Organization of Information

• Organize to aid solution– Symbols– Matrixes– Diagrams

Mango Peach Steak

Alex x 0 x

Jarod x x 0

Henry 0 x x

Let L = Lucy, S = Sean, 2L=3S, S=10


Problem Solving CycleIdentify Problem

Evaluate success

MonitorSolving

AllocateResources

Organize Info

Select Strategy

Define Problem


Types of Problems

• Well-structured problems– Clear path to the solution

• Math problems• Anagrams

• Ill-structured problems– Dimensions of problem are not specified

or easy to infer• Finding an apartment• Writing a book


Methods for Studying Problem Solving

• Error analysis or reaction time– Global measures of performance

• Verbal protocols– Participants speak their thoughts out loud while

solving problems– Strategies become evident in protocols

• Computer stimulation– Create models that can recreate human data


Newell and Simon (1972)

• Problem space – All possible actions that can be applied to a

problem

• Consists of states and operators– States represent the problem

• Initial-given information & prior knowledge

• Goal-desired outcome

– Operators transform one state to another state• Permitted or selected moves


Newell and Simon (1972)

• Use verbal protocol and reproduce using a production rule system to create a similar representation of the problem

• Created a General Problem Solver (GPS)


Strategies to Solve Problems

• Algorithms– Systematic procedure guaranteed to find

a solution

• Heuristics– Useful rule of thumb based on experience

– Efficient but does not guarantee a correct solution


Heuristics for Problem Solving

• Mean-ends analysis

• Working forward

• Working backward

• Generate and test


Means-End Analysis• Compare your current state with the goal

and choose an action to bring you closer to the goal

• Break a problem down into smaller sub goals – Win at Monopoly– You start by buying properties, continue to buy

until you get a set, buy houses, then buy hotels, wait for others to land on spaces, etc.

• May not work if sub goals cannot be identified


Working Forward

• Start at initial state and work to goal state– Math problems

– (2 + 6)/(4 x 1) = ?

– Complete the math inside parenthesis first, then divide the quantities to get to solution


Working Backward

• Figure out the last step needed to reach your goal, then the next-to-the-last step, and so on – You have lost your keys

– Try to remember the last time you used them and work backwards

• Work backwards from goal state


Generate and Test

• Trial and error strategy

• Create possibilities, test them and discard the ones that are incorrect – Your car will not start– Wait a moment and try again, may be flooded– Check to see if there is gas, if no success– Check to see if the battery is charged… etc.

• This may not be the most efficient strategy


Transformation Problem

• Hobbits & Orcs – Three hobbits and three orcs come to a

river and find a boat that holds two. If the Orcs ever outnumber the Hobbits on either bank, the Hobbits will be eaten.

• How do you get them all to the other side?


Tower of Hanoi

Move all the discs from the left peg to the right one. Only one disc may be moved at a time. A disc can be placed either on an empty peg or on top of a larger disc. The goal is to move all the discs using the smallest number of moves possible.


Solution is the same as Forest Burners & Forest Lovers in text


Recognizing the Isomorphic

• Reed (1987) found that participants have difficulty recognizing that a past problem’s solution will help them to solve the current problem– Difficulty in recognizing crucial commonalities– Surface features of the problem distract

• Current research focuses on factors that help the transfer of solutions


Insight and Problem Solving• Insight is the apparent sudden solution to a

problem some time after the problem has been presented

• Metcalfe & Weibe (1987)– Participants were given either insight or

algebra problems to solve• Insight: A prisoner was attempting 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 this be?

• Algebra: (3x2 + 2x = 10)(3x) = ?


Metcalf & Wiebe (1987) Results

• Participants indicated how close they were to solution every 15 seconds

– 1 being very cold to 7 being very warm

• For insight problems–Sudden shift in warmth rating

• For algebra problems–A getting warmer pattern


Insight and Brain Activity

• Neural activity associated with insight

• fMRI studies found – Right hippocampus is active during

problem solving

– Another found spike in temporal lobe just before insight


Gestalt View of Insight

• Wertheimer– Sudden rearrangement of elements

creates “insight”

– Productive thinking goes beyond previously learned associations

• Kohler– Animal Model of Insight

– Sultan stacked boxes to get banana


Three-Process View

• Davis & Sternberg (1984)– Selective-encoding insights

• Sorting relevant from irrelevant

– Selective-comparison insights• Make connections to previously learned

information

– Selective-combination insights• Combine elements in a novel way


Insight

• Current Debate– Is insight a special process or just a

normal process in problem solving?


Schooler, Ohlsson & Brooks (1993)

• Proposed that solving insight problems rely on different mental structures than solving logical transformation problems – Logical, transformation problems were solved with

verbal systems, but insight problems were solved with nonverbal systems

• Participants were asked to solve a series of insight and logic problems – Half the participants were required to verbalize their

strategies as they tried to solve the problem– The control group did not verbalize as they solved the

problem


Schooler, Ohlsson & Brooks (1993) Results

0

10

20

30

40

50

60

70

80

90

Insight Logic

Verbal

Control


Obstacles to Problem Solving

• Mental set

• Functional fixedness

• Incorrect or incomplete representation of the problem

• Lack of domain knowledge


Mental Set

• Seeing a problem in a particular way instead of other plausible ways due to experience or context – May cause you to adopt an ineffective

strategy and prevents problem solving – May make assumptions without realizing

it – May find it hard to approach the problem

in a new way


Luchins (1942) Water Jar ProblemHow would you use 3 jars with the indicated capacities to measure out the desired amount of water?

Problem Jar A Jar B Jar C Desired

1 29 3 2 20

2 21 127 3 100

3 14 163 25 99

4 18 43 10 5

5 9 42 6 21

6 20 59 4 31

7 23 49 3 20

8 15 39 3 18

9 28 76 3 25


Bar Problem

• A man walked into a bar and asked for a drink. The man behind the bar pulled out a gun and shot the man. Why should that be so?

• Solution: The man behind the bar wasn’t a bartender. He was a robber.


Functional Fixedness

• An inability to assign new functions and roles to elements of a problem – Two string problem

– Duncker’s candle problem


Transfer

• Negative Transfer– Solving prior problem makes it more

difficult to solve later problem

• Positive Transfer– Solving earlier problem helps to solve

later problem

– Gick & Holyoak examine factors contributing to positive transfer


Gick & Holyoak (1980)

• Give participants one problem to read with a solution

• Give same participants a second problem which can be solved using a similar solution


Gick & Holyoak (1980)• Analogous General/Fortress problem

A dictator ruled a small country from a fortress. The fortress was situated in the middle of the country and many roads radiated outward from it, like spokes on a wheel. A great general vowed to capture the fortress and free the country from the dictator. The general knew that if his entire army could attack the fortress at once it could be captured. But a spy reported that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator needed to be able to move troops and workers about, however, any large force would detonate the mines. Not only would this blow up the road, but the dictator would destroy many villages in retaliation. A full-scale direct attack on the fortress therefore seemed impossible.



• Solution to general problemThe general, however, was undaunted. He divided his army up into small groups and dispatched each group to the head of a different road. When all was ready he gave the signal, and each group charged down a different road. All of the small groups passed safely over the mines, and the army then attacked the fortress in full strength. In this way the general was able to capture the fortress.


Ask Participants to Solve this Problem

• Radiation problemGiven a human being with an inoperable stomach tumor, and rays that destroy organic tissue at sufficient intensity, by what procedure can one free him of the tumor by these rays and at the same time avoid destroying the healthy tissue that surrounds it?



• 3 groups of participants – Control group that only tried to solve the

radiation problem

– A group previously given the analogous General/Fortress problem & solution

– A group given the General/Fortress problem and told that its solution would help in solving the radiation problem


Gick & Holyoak (1980) Results

01020

3040506070

8090100

Control Analogy Analogy & Hint


Factors Affecting Use of Analogies• Similarity• Number of examples exposed to

– Gick and Holyoak conducted a study in which the dictator story was just one of three other stories participants heard before radiation problem

– Only 20% got the problem correct

• Whether schema for problem is activated– If the two problems are separated by a delay or

if they are presented in different contexts, almost none of the participants use the analogy


Incubation

• Time away from a problem provides new insights or otherwise facilitates the problem solving process– Release from a problem solving set, or

functional fixedness

– Retrieval of new information by changing context

– Recovery from fatigue


Neuropsychology of Planning

• Frontal lobe active in problem solving

• Prefrontal cortex active in planning


Expertise

• Not a general ability

• Experts have extensive knowledge that is used to organize, represent, and interpret information

• Thus affecting their abilities to remember, reason, and solve problems


Chase & Simon (1973) & DeGroot (1965)

• Participants were chess masters and beginning chess players

• Studied a chess board that had the pieces randomly displayed or a chess board with pieces in the middle of a game.

• Beginners and experts had to recall as many pieces as they could


Experts vs. Beginners

Under what condition did the experts remember more?


Results

• Master chess players and beginning players recalled a similar number of pieces from the random board

• Master chess players remember significantly more chess pieces from the game board in play than did the beginning chess players


Beer Study

• Valentin, Chollet, Beal & Patris (2007)– Beer experts

• Two year beer training program in France

– Beer Novices• No prior training

– Tasted a series of 8 different beers


Beer Study

• Assessed memory of beers between experts and novices– Experts remembered more


Experts Differ From Novices

• Better schemas

• Well organized knowledge in specific domain

• Less time to set up problem

• Select more appropriate strategies

• Faster at solving problems

• Are more accurate


Innate Talent vs. Acquired Skill

• Clear that expertise requires acquired skill BUT some performance is not explainable by knowledge level alone


Creativity

• Process of creating something that is original and worthwhile


Creativity

• May refer to – The product

– The person\personality creating the product

– The process• Steps followed to create the product

– The environment

– A synthesis of all of the above


Psychometric View

• Emphasis is on the measure of the product a person creates—creativity test scores

• Guilford (1950)

• Torrance (1988)


The Process Approach

• Weisberg (1988)– Nothing innately special about people

– Hard work and dedication leads to creativity


Personality Approach

• Baron (1988)– Way of looking at things

• Amabile (1996)– Intrinsic motivation is important


Environment Approach

• Csikszentmihalyi (1996)– Must examine historical and social

context in which product is made

– When one achieves balance with context, one achieves flow

– Flow is the enjoyment we experience when we are engaged in mental and physical challenges that absorb us


A Synthesis

• Gardner (1993)– Examined case studies of creative people

• Albert Einstein (logical-mathematical),

• Pablo Picasso (spatial)

• T. S. Elliot (linguistic)

• Mohandas Gandhi (interpersonal)

– Most of these individuals had strengths in more than one intelligence (confluence), and had noticeable weaknesses in others

– Identified internal and external influences – First become a master; then creativity is possible


Sternberg, Kaufman, & Pretz (2002)

• Confluence of six main resources are necessary for creativity– intellectual abilities, knowledge, styles of thinking,

personality, motivation, and environment

• Three intellectual abilities are especially important:– Synthetic ability

• To see problems using novel perspectives and not be bound by conventional thinking

– Analytic ability • To recognize the importance of ideas and focus energy on those

worth pursuing– Practical-contextual

• To be able to convey and sell the importance of the ideas to others


Neuroscience of Creativity

• Prefrontal regions are active

• Brodmann’s area 39 is active


Sternberg’s Propulsion Model of Creative Contributions

• Replication• Redefinition• Forward Incrementation• Advance forward incrementation• Redirection• Reconstruction-redirection• Reinitiation• Integration

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Cognitive Psychology, Fifth Edition, Robert J. Sternberg Chapter 11 Chapter 11: Problem Solving and Creativity