cognitive psychology, sixth edition, robert j. sternberg chapter 11 chapter 11: problem-solving and...

Cognitive Psychology, Sixth Edition, Robert J. SternbergChapter 11

Chapter 11:Problem-Solving and

Creativity


Some Questions of Interest

• What are some key steps involved in solving problems?

• What are the differences between problems that have a clear path to a solution versus problems that do not?

• What are some of the obstacles and aids to problem-solving?

• How does expertise affect problem-solving?

• What is creativity, and how can it be fostered?


Problem-Solving Cycle


Problem Representation

• what information is relevant and what is irrelevant – 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 subgoals

• EX: Study for exam subgoals– Read textbook and class notes– Identify most relevant topics– Create study questions and 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 FormationDivergent thinking

– Generate multiple solutions to problem

Convergent thinking– Narrow down to best

answer


Organization of Information

Organize to aid solutionSymbolsMatrixesDiagrams

Mango Peach Steak

Alex x 0 x

Jarod x x 0

Henry 0 x x

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


Types of Problems

• Well-structured problems– Clear path to the solution

• Math problems• Anagrams


• 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?


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


Heuristic: 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 subgoals – EX: Win at Monopoly– 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 subgoals cannot be identified


Heuristic: Working Forward

• Start at initial state and work to goal state– EX: Math problems – (2 + 6)/(4 x 1) = ?– Complete the math inside parenthesis first,

then divide the quantities to get to solution


Heuristic: Working Backward

• Figure out the last step needed to reach your goal, then the next-to-the-last step, and so on – EX: You have lost your keys– Try to remember the last time you used

them and work backward

• Work backward from goal state


Heuristic: Generate and Test

• Trial-and-error strategy

• Create possibilities, test them, and discard the ones that are incorrect – EX: 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


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.


Types of Problems

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

easy to infer• Finding an apartment• Writing a book


Gestaltist View of Insight

Sudden rearrangement of elements creates “insight”

Apparent sudden solution to a problem some time after the problem has been presented


Insight: A prisoner was attempting escape from a tower. He found in his cell a rope that was almost long enough to permit him to reach the ground safely. He divided the rope in half and tied the two parts together and escaped. Algebra: (3x2 + 2x = 10)(3x) = ?

Participants indicated how close they were to solution every 15 seconds

1 being very cold to 7 being very warm

Non-Gestaltist View of Insight


Neuroscience and Insight

fMRI studies found– right hippocampus is active during problem-solving– another found spike in right anterior temporal lobe

just before insight– neural correlates measured before an individual

sees a problem can predict if insight will occur

• Prior to viewing of a problem, participants who had activation in the frontal lobes would later generate an insightful solution


Obstacles to Problem-Solving

• Mental set

• Functional fixedness

• Stereotypes


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


How 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


Functional Fixedness

• An inability to assign new functions and roles to elements of a 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 (1980) Results

01020

3040506070

8090

100

Control Analogy Analogy & Hint


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


Neuroscience and Planning during Problem-Solving

• Frontal lobe active in problem-solving

• Prefrontal cortex active in planning

• Greater bilateral prefrontal activation with incorrect than correct responses

• Both problem-solving and planning ability decline following traumatic brain injury


Intelligence and Problem-Solving

• Participants who score higher on traditional intelligence tests– take longer to encode the terms of the

problem (global planning)– are faster at forming and implementing

strategies for the details of the task (local 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


• Experts vs. beginners

• Under what condition did the experts remember more?

Chess Experts


Beer Experts??

– Beer experts • Two-year beer training

program in France

– Beer novices• No prior training

– Tasted a series of 8 different beers


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


Computer “experts”?

• The Turing test– What questions would you ask?


Creativity

• Process of creating something that is original and worthwhile


Test of creativity


Improving creativity?

• What is a product or service that needs to be improved?– select 10 common nouns at random

from the dictionary

– task is to figure out ways to change and improve the product/service

– use the 10 stimulus words to stimulate thinking.


Theories of creativity

• Psychometric view– Emphasis is on the measure of the product a

person creates—creativity test scores

• The process approach– Nothing innately special about people– Hard work and dedication leads to creativity

• Personality approach– Way of looking at things– 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

Examined case studies of creative peopleAlbert Einstein (logical-mathematical) Pablo Picasso (spatial) T.S. Elliot (linguistic)Mohandas Gandhi (interpersonal)

•Most had strengths in more than one intelligence and weaknesses in others

•First become a master; then creativity is possible


What is necessary for creativity?

Synthetic abilityTo 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-contextualTo 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

cognitive psychology, sixth edition, robert j. sternberg chapter 11 chapter 11: problem-solving and...

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