Chapter 11 Problem Solving and Creativity University of Utah Joel Cooper

Chapter

11 Problem Solving and Creativity

University of Utah

Joel Cooper

Changes to the syllabus

Next Week Chapters 12 and 13 No supplementary readings

Following week, Lecture on parapsychology Reading from “why people believe

weird things” to be posted online.

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).

More Problems

What is the next letter in the following sequence?

O T T F F S S

1 2 3 4 5 6 7

More Problems

You have 10 red socks and 20 brown socks in your bureau drawer. If you reach into it in the dark, how many socks must you take out to be sure of having a pair that matches?

Problem Solving

Initial State Current situation Define the problem

Goal State Desired objective

Obstacles Choices made about limitations Strategy choices Limited resources

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

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.

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 Select a strategy to solve the problem

Synthesis 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

Strategy Formation

Divergent thinking (Analysis) Generate multiple solutions to problem

Convergent thinking (Synthesis) Narrow down to best answer

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 simulation Create models that can recreate human data

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

Heuristics for Problem Solving Mean-ends analysis Working forward Working backward Generate and test

Each box is labeled incorrectly. You may select one fruit from one box. How can you label each box correctly?

Apples

Oranges Apples&

Oranges

Step 1 A or OStep 2 A&O or A

Step 3 A&O or O

Working Forward

Start at initial state and work to goal state Math problems (2 + 6)/(4 * 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


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

Recognizing the Isomorphic

From variants of the Hobbit/Orc problem, 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

On the insight problem there is a sudden shift in warmth rating

On the algebra problem there is a consistent getting warmer pattern

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

Insight

Insight

Current Debate Is insight a special process or just a

normal process in problem solving?

Schooler, Ohlsson & Brooks (1993)

Logic, Insight ≠ Structures Participants solved insight and logic

problems Half participants verbalized strategies The control group did not verbalize as they

solved the problem

Insight

Schooler, Ohlsson & Brooks (1993) Results

0

10

20

30

40

50

60

70

80

90

Insight Logic

Verbal

Control

Insight

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

Insight

Obstacles to Problem Solving

Mental set Functional fixedness Incorrect or incomplete representation

of the problem Lack of domain knowledge

Obstacles

Mental Set

Seeing a problem in a particular way instead of other plausible ways due to experience or context This usually causes you to adopt an

ineffective strategy and can prevent problem solving

Make assumptions without realizing it

Difficult to approach the problem in a new way

Obstacles

Two flagpoles, 150’ high. A 150’ rope suspended from each end reaches 75’ from the ground. How far apart are the flagpoles?

?

75’

150’

Mental Set?

Functional Fixedness

An inability to assign new functions and roles to elements of a problem Two string problem Duncker’s candle problem

Obstacles

Problem I

Two strings are suspended from the ceiling

Goal: Tie the strings together Problem: Too far apart to hold one and reach

for the other Materials:

Chair piece of paper pair of pliers

What is the Solution?

Obstacles

Problem II

Materials: Box of thumb tacks Candle Matches

Objective: Mount candle on wall to make light

What is the Solution?

Obstacles

Functional Fixedness?

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

Obstacles

Water JugsObstacles

Jug A Jug B Jug C Goal 21 127 3

100 14 163 25 99 18 43 10 5 9 42 6 21 20 59 4 31 23 49 3 20 14 36 8 6 28 76 3 25

Einstellung phenomena and (or) Negative Transfer

Tendency to solve problems in a particular way when a different approach might have been more productive

Problems 1-5: B-2C-A Problems 6-8: A-C Problem 8 can’t be solved B-2C-A 80% who see all 8 problems use B-2C-A 1% of controls use B-2C-A 64% fail to solve #8 vs. 5% of controls

Obstacles

Gick & Holyoak (1980)

Give participants one problem to read, with a solution

Then give them a second problem, which can be solved using a similar solution

Obstacles

Gick & Holyoak (1980)

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

Obstacles

Gick & Holyoak (1980) Results

01020

3040506070

8090

100

Control Analogy Analogy & Hint

Obstacles

Transfer Recap

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

Obstacles

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

Obstacles

Expertise

Not a general ability Have an extensive knowledge that

they use to organize, represent, and interpret information in their environment

This affects their abilities to remember, reason, and solve problems

Expertise

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

Expertise

Experts vs. Beginners

Under what condition did the experts remember more?

Expertise

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

Expertise

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

Expertise

Creativity

Process of creating something that is original and worthwhile

Multiple views which emphasize The product The person\personality creating the product The creative process; the steps that the

creative person followed to create the product

The creative environment A synthesis of all of the above

Boost your creativity for inspiring ideas and innovationAre you seeking inspiration for a project?Do you want help 'thinking outside of the box'?Do you need to get over a creative block?

True creativity seems to happen by itself because it is a product of the unconscious mind, that 'back part' of the mind that incubates ideas until they are ready for the light of day.

Hypnosis can help you take your conscious fingers out of the creativity process and leave your unconscious mind to come up with the sorts of ideas, solutions and innovations that it is so good at.

Creativity is such a great advantage in all sorts of situations: •for humor in social situations•for innovation in business•for art, music and writing•for originality in public speakingGet the Creativity Booster today, sit back, relax, and watch the ideas come flooding in.

Psychometric View

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

Guilford (1950) Torrance (1988)

Creativity

Breaking Functional Fixedness

Coat hanger creativity test

You have 2 minutes, write down all possible uses for a coat hanger.

Think outside the box

STOP

START

Creativity

The Process Approach

Weisberg (1988) Nothing

innately special about people

Hard work and dedication leads to creativity

Creativity

Personality Approach

Baron (1988) Way of looking at things

Amabile (1996) Intrinsic motivation is important

Creativity

Environment

Csikszentmihalyi (1996) Historical and social context critical Contextual balance begets “flow” Flow = enjoyment when absorbed

Creativity

A Synthesis

Gardner (1993) Examined case studies of creative people Strengths and weakness’ internal and external First became a master, then creative works

cameth forth

Creativity

Sternberg, Kaufman, & Pretz (2002)

Creativity is not a monolithic ability 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

Creativity

How to Improve Your Problem Solving

Follow a systematic plan Draw inferences Develop sub-goals Work backwards Search for contradictions

How to Improve Your Problem Solving

Search for relations among problems Reformulate problems Represent problems graphically Define boundary conditions

Documents

Chapter 11 Problem Solving and Creativity University of Utah Joel Cooper