Obstacles to Problem Solving and How They Can Be Overcome Psychology 355: Cognitive Psychology Instructor: John Miyamoto 05/27 /2015: Lecture 09-3 This

Obstacles to Problem Solving

and How They Can Be Overcome

Psychology 355: Cognitive Psychology

Instructor: John Miyamoto

05/27/2015: Lecture 09-3

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Psych 355, Miyamoto, Spr '15 2

Outline

• Obstacles to successful problem solving

• Information processing approach to problem solving.

Example: The Tower of Hanoi

• Set & Functional Fixedness

• Insight Problems – Are they different cognitively from algorithmic

problems?

• Incubation Effects

Common Obstacles to Successful Problem Solving

Common Obstacles to Successful Problem Solving

Obstacle #1: A poor initial problem representation makes it difficult to solve a problem.

Remedy: Try changing the problem representation

Obstacle #2: People sometimes place a false constraint on the permissible ways to solve the problem.

Remedy: Examine the constraints – are you imposing a false constraint?


Circle Problem Mutilated Checkerboard Problem

Cheap Necklace Problem 9 Dot Problem

4Psych 355, Miyamoto, Spr '15

Time Permitting: An Example of a Real False Constraint – A Fishing Story

• Time permitting, give practical example of a false constraint.

Information Processing Approach to Algorithmic Problem Solving


Information Processing Approach to Problem Solving

Textbook calls this the "information processing approach to problem

solving" – Is this a good name for it?

PRO: "information processing approach to problem solving" - why it's a good nameo Alan Newell & Herbert Simon pioneered this approach to the study of problem solving.

They were also pioneers of the information processing approach to studying cognitive processes.

CON: "information processing approach to problem solving" - why it's a bad name.o Virtually all of modern cognitive psychology follows an information processing

approach. Even the Gestalt approach to problem solving is pursued within the information processing framework.

Better name: “Analysis of problem solving strategies”

Tower of Hanoi Problem



Same Slide with Emphasis Rectangles



The Tower of Hanoi Is a Problem with an Algorithmic Solution

Rules and Contraints

The Tower of Hanoi

• Tower of Hanoi is a problem with an algorithmic solution.

• There is a logically adequate strategy that will always solve this problem.

• The algorithm applies no matter how many disks are used in the problem.

• Next: Illustrate subgoal analysis (working backwards strategy)

Psych 355, Miyamoto, Spr '15 8Alternative Representation of the Tower of Hanoi


Alternative Representation of the Tower of Hanoi

|-ABC |-

|- |-

|- |-ABC

Initial State Goal State

Goal: Move the letters one at a time from the top pin to the bottom pin.

(A is "bigger" than B and B is "bigger" than C.)

Constraint: Later letters never precede earlier letters.

Show Diagrammatic Analysis – Working Backwards

Solving the Tower of Hanoi by Working Backwards

|-ABC |-|- |-|- |-ABCInitial State Goal State

..

.

Psych 355, Miyamoto, Spr '15 10Continue with this Diagram


|-ABC |- |-C|- |- |-|- |-ABC |-ABInitial State Goal State Subgoal 1

..

.



|-ABC |- |-C |-C|- |- |- |-B|- |-ABC |-AB |-AInitial State Goal State Subgoal 1 Subgoal 2

..

.




|-|-BC|-ASubgoal 3

..

.




|- |-A|-BC |-BC|-A |-Subgoal 3 Subgoal 4

..

.




|- |-A |-A|-BC |-BC |-B|-A |- |-CSubgoal 3 Subgoal 4 Subgoal 5

..

.




|- |-A |-A |-AB|-BC |-BC |-B |-|-A |- |-C |-CSubgoal 3 Subgoal 4 Subgoal 5 Subgoal 6

..

.

Psych 355, Miyamoto, Spr '15 16Depict the Solution to Tower of Hanoi By Using These Diagrams



|- |-A |-A |-AB|-BC |-BC |-B |-|-A |- |-C |-CSubgoal 3 Subgoal 4 Subgoal 5 Subgoal 6

Solution: Initial State Subgoal 6 Subgoal 5 Subgoal 4 Subgoal 3 Subgoal 2 Subgoal 1 Goal State

Above illustrates working backwards strategy.

Psych 355, Miyamoto, Spr '15 17Summary of Problem Solving Strategies


Strategies for Solving Algorithmic Problems

• Working backwards:

Start from the goal state.

Look for earlier states that transition to the goal state,

but are closer to the initial state.

• Working forwards:

Start from the initial state.

Work towards the goal state.

• Means-ends analysis: A strategy that focuses on generating

subgoals that bring the initial state and goal state closer together.

Why the Information Processing Approach is Important for Cog Psych

Why the (So-Called) Information Processing ApproachIs Important in Cognitive Psychology?

• It has lead to useful insights about problem solving.♦ Physics experts tend to use a working forwards strategy when solving problems

in introductory physics.

♦ Physics novices tend to use a working backwards strategy when solving problems in introductory physics.

• Information processing analysis has lead to much better understanding of the cognitive processes during problem solving.

♦ E.g., the role of the central executive in the Wisconsin Card Sorting Problem.

♦ E.g., the role of the central executive in strategic planning while working on the Tower of Hanoi.

• But the Gestalt approach is more applicable to everyday problems.

Psych 355, Miyamoto, Spr '15 19Set in Problem Solving


Set in Problem Solving

• Set refers to a person's implicit assumptions about how

to solve a problem.o Goldstein textbook calls it "mental set" (p. 340).

Set can be helpful or harmful to one's ability to solve a problem.

• Example: On the Cheap Necklace Problem, if you

wrongly assume that you have to open the links at the

ends of the chains, this is a harmful set.

Functional Fixedness - Definition

Functional Fixedness

• Functional fixedness: Tendency to assume that objects can only serve their typical functions.

• Functional fixedness is a particular kind of set.

Psych 355, Miyamoto, Spr '15 21Maier's Two String Problem

Example – Functional Fixedness

Maier's Two String Problem:

Goal = To tie two strings together that hang from the ceiling.

• The strings are too far apart to reach both at once.

• Two hints

• Class: Any proposed solutions?

Psych 355, Miyamoto, Spr '15 22Solution to Maier's Two String Problem

Example – Functional Fixedness

• Solution: Tie the pliers to onestring. Swing it like a pendulumso that you can reach it while holding the other string.

♦ 40% solve problem with no hint.

♦ 62% solve problem when experimenter "accidentally" brushes against a string, setting it in motion.

• Functional fixedness: In the "no hint" condition, subjects see only the typical function of the pliers, not its potential function as a weight on a pendulum.

Psych 355, Miyamoto, Spr '15 23Duncker's Candle Problem

Duncker's Candle Problem: Another Example of Functional Fixedness

• You have the materials shown above (subjects receive the actual materials).

• You are in a room with a corkboard for a wall.

• Your task is to mount a candle on the wall in such a fashion that the wax does not drip on the floor. How do you do it?

Psych 355, Miyamoto, Spr '15 24Solution to the Candle Problem

Solution to the Candle Problem

• Solution: Use the tacks to attach the matchbox to the wall. Mount the candle on the matchbox.

• Functional fixedness: Matchbox is seen only as a container of matches, not as a potential support for the candle.

• Adamson (1952): ♦ 80% of subjects solve the problem if the

matchbox is empty.♦ 40% of subjects solve the problem if matches are in the matchbox.

• Results support the functional fixedness hypothesis.When the matchbox is empty, it is easier to see that it can serve a different function from that of containing something.

Psych 355, Miyamoto, Spr '15 25Conclusions re Functional Fixedness


Conclusions: Functional Fixedness

• Set refers to assumptions that guide problem solving.o They are often unconscious assumptions.o Set is helpful when it leads the problem solver towards an efficient solution.

Having the right set makes problem solving faster and with fewer errors.o Set is unhelpful when it leads the problem solver towards an inefficient

solution or to a dead end (no solution).

• Functional fixedness is a particular type of set.

Functional fixedness is the assumption that objects can only serve

their typical functions.

• Functional fixedness can be interpreted as a false constraint,

i.e., the unstated constraint that objects can only be used with

their typical functions.

Are Insight Problems Really Different from Algorithmic Problems?

Are Insight Problems Really Different from Algorithmic Problems?

• Basic Question: People think that insight comes suddenly.Is this really true?

• Metcalfe & Wiebe (1987) Study titled “Premonitions of Insight”

• “Warmth” Rating – rate how close you are to a solution?♦ Algebra problems

♦ Insight problems

Psych 355, Miyamoto, Spr '15 27Reminder re Chain Problem (Cheap Necklace Problem)

Cheap Necklace Problem (a.k.a. Chain Problem)

Cheap Necklace Problem: Convert these 4 strands of chains into a single loop by opening and closing only 3 links. (Insight problem)

Psych 355, Miyamoto, Spr '15 28Solution to the Chain Problem


Solution to the Cheap Necklace Problem (a.k.a. the Chain Problem)

• Open all three links of one

strand.

• Use these open links to link

together the other three

strands.

Experimental Procedure of Metcalfe & Wiebe


Experimental Design of Metcalfe & Wiebe (1987)Premonitions of Insight

Metcalfe & Wiebe (1987) had subjects solve problems

while also rating their "warmth" towards finding a solution.

(Ratings measured every 15 seconds.)

Two types of problems:

Algebra problems (possess algorithmic solution)

Insight problems (require problem restructuring

or breaking false constraints)

• “Warmth Ratings" –

Every 15 seconds, rate how "cold" or "hot" you feel towards

solving the problem.

Results

Metcalfe & Wiebe (1987): Premonitions of Insight

• Graphs show “warmth” ratings as subject gets closer to a solution.

♦ “Time” is measured backwards from the time of solution, e.g., -15 means the rating was produced 15 seconds before the subject announced the problem solution.)

• For algebra problems, subjects feel as if they are getting warmer as they get closer to a solution.

• For insight problems, subjects do not feel as if they are getting warmer. The solution comes suddenly and without warning.

Psych 355, Miyamoto, Spr '15 31Same Graph on Right – Discuss these Results

Very slight premonition of

insight

Metcalfe & Wiebe (1987): Premonitions of Insight

• Subjectively, we feel like the solution to an insight problem comes “out of the blue.”

♦ This result supports the idea that solutions to insight problems depend on a sudden unanticipatedrestructuring of the problem representation.

♦ I.e., it documents the occurrence of sudden insight. The "aha" experience is a real cognitive experience.

• This result supports the idea that insight problems are different from algorithmic problems

Psych 355, Miyamoto, Spr '15 32Incubation Effects


Incubation Effects

• Incubation effect – discovery of problem solution after a period

during which one does not think about the problem.

Temporal pattern of an incubation effect.

• Problem solver initially works hard but unsuccessfully on a

problem.

• Problem solver spends some time doing something completely

different.

• When the problem solver returns to working on the original

problem, she suddenly finds a solution.

Above is the subjective impression that is reported by many problem

solvers. Is it real, or some kind of illusion?Incubation Effects on the Cheap Necklace Problem – Silveira's (1971) Study

Exp Group 2

85% solve the Circle Problem

Exp Group 1


Study of Incubation Effects on the Cheap Necklace Problem (Silveira, 1971)


Control Group:

• Worked on problem for 30 minutes.

Exp Group 1:

• Work on problem for 15 minutes. • Perform other activities for 30 minutes. • Return to problem for 15 minutes.

Exp Group 2:

• Work on problem for 15 minutes. • Perform other activities for 4 hours. • Return to problem for 15 minutes.

Conclusions re Incubation & Cheap Necklace Problem

Control Group



Conclusions re Incubation Effects on the Cheap Necklace Problem (Silveira, 1971)

• Conclusion 1: Incubation can be very beneficial.

• Conclusion 2: Protocol analysis suggested that people don't solve the problem unconsciously while thinking about something else. o After incubation period, subjects returned to the problem at the same stage

at which they had stopped, but they make more progress from that stage.

• Why do incubation effects occur?Why is it helpful to stop working on a problem for awhile?

Why is Incubation Helpful?


Why Is Incubation Helpful for Problem Solving?

• One benefit of incubation comes from forgetting inappropriate

strategies or problem representations, i.e., a break down of an

unhelpful set. o Incubation weakens adverse priming of ineffective problem strategies.

• Another benefit comes from consolidation of the memory

of problem structure (analogous to the effects of massed

versus spaced practice on recall from LTM).

• Another benefit comes from sleep and dreaming

(not yet known why this benefit occurs).

• Another benefit of incubation: Exposure to helpful hints

(next slide)

Exposure to Helpful Hints – Kaplan's Study


Exposure to Helpful Hints Can Help to Solve a Problem

• Kaplan (1989) dissertation experiment.

• Subjects were given a list of insight problems.

Sample Problem: On this hill there was a green house. And inside

the green house there was a white house. And inside the white

house, there was a red house. And inside the red house there were a

lot of little blacks and whites sitting there.

What place is this?

• Subjects worked on the problems over many days. Subjects were

given pagers, and a small microphone and tape recorder.

Periodically, subjects were beeped – they had to describe their

progress on the problems.

Effect of Helpful Hints


Exposure to Helpful Hints Can Help to Solve a Problem

Sample Problem: On this hill there was a green house. And inside the green house there was a white house. And inside the white house, there was a red house. And inside the red house there were a lot of little blacks and whites sitting there. What place is this?

• Every so often, Kaplan would put up a hint

for a problem in the form of graffitti.

For example, something like this image

was posted in the men’s bathroom in the

psychology department.

• Finding: Subjects would suddenly discover solutions to

problems shortly after the posting of hints without being

aware that they had been given a hint.

Summary re Incubation Effects


Summary re Incubation Effects

• Incubation effect – discovery of problem solution after spending

time thinking about something else.

• Incubation can be beneficial. o One benefit of incubation comes from forgetting of inappropriate strategies or

problem representations, i.e., a break down of an unhelpful set. o Another benefit of incubation: Exposure to helpful hints – even

accidental hints provided by daily experience.o Other benefits of incubation:

Consolidation of problem structure. Sleep and dreaming contributes to problem solving.

Summary – Obstacles to Problem Solving - END


Summary: Obstacles to Problem Solving

• Misleading or uninformative problem representation. Recommendation: Look for alternative problem representations.

• Adopting unnecessary assumptions (false constraints).Recommendation: Check your assumptions. Are they really necessary?

• Inappropriate Set: Recommendation: If you are stuck on a problem, look for alternative strategies.

General Advice:

• Incubation can be helpful.

Recommendation: Get away from the problem, then return to it.

• Sleep on it (problems can be solved after sleeping on it).

END

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Obstacles to Problem Solving and How They Can Be Overcome Psychology 355: Cognitive Psychology Instructor: John Miyamoto 05/27 /2015: Lecture 09-3 This