Memory and Memory and CognitionCognition

PSY 324PSY 324

Topic: Problem SolvingTopic: Problem Solving

Dr. Ellen CampanaDr. Ellen Campana

Arizona State UniversityArizona State University

OutlineOutline

The Gestalt Approach:The Gestalt Approach: Describe problem solving as involving Describe problem solving as involving

a process called a process called restructuringrestructuring.. The Information-processing The Information-processing

Approach:Approach: Describe problem solving as involving Describe problem solving as involving searchsearch..

Analogies:Analogies: A method that combines elements of A method that combines elements of

both restructuring and search.both restructuring and search. Experts and nonexperts:Experts and nonexperts: Creative thinking:Creative thinking:

Gestalt ApproachGestalt Approach

What Is a Problem?What Is a Problem? A problem occurs when there is an obstacle A problem occurs when there is an obstacle

between a present state and a goal, and it is not between a present state and a goal, and it is not immediately obvious how to get around the immediately obvious how to get around the obstacle (Lovett, 2002).obstacle (Lovett, 2002). Well-defined problemsWell-defined problems: usually have a correct answer : usually have a correct answer

and there are certain procedures that will lead to a and there are certain procedures that will lead to a solution.solution.

e.g. a math or physics probleme.g. a math or physics problem Ill-defined problems: Ill-defined problems: do not necessarily have one do not necessarily have one

“correct” answer and the path to the solution is often “correct” answer and the path to the solution is often unclear.unclear.

e.g. dealing with relationships or picking a careere.g. dealing with relationships or picking a career

Think of some problems you have solved or Think of some problems you have solved or are currently working on. are currently working on.

Gestalt ApproachGestalt Approach

How problems are represented in a How problems are represented in a person’s mind:person’s mind: How people represent a problem in How people represent a problem in

their mind?their mind? How solving a problem involves a How solving a problem involves a reorganizationreorganization or or restructuringrestructuring of this of this representation.representation.

Representing a Problem in Representing a Problem in the Mindthe Mind

The solution is obtained by first The solution is obtained by first perceiving the object and then perceiving the object and then representing it in a different way.representing it in a different way. Restructuring: the process of changing Restructuring: the process of changing

the problem’s representation.the problem’s representation.

Circle ProblemCircle Problem If the If the

length of length of the radius the radius is is rr, what , what is the is the length of length of line line xx??

Insight in Problem Insight in Problem SolvingSolving

Associate with restructuringAssociate with restructuring A sudden realization of a problem’s A sudden realization of a problem’s

solutionsolution Insight is reflected in the types of Insight is reflected in the types of

problems they posed.problems they posed. The solution involves discovering a The solution involves discovering a

crucial element that leads to solution crucial element that leads to solution of the problem (Dunbar, 1998).of the problem (Dunbar, 1998).

Metcalfe and Wiebe Metcalfe and Wiebe (1987)(1987)

Goal: to distinguish between insight Goal: to distinguish between insight problems and noninsight problems.problems and noninsight problems.

Starting point: there should be a basic Starting point: there should be a basic difference between how participants feel difference between how participants feel they are progressing toward a solution as they are progressing toward a solution as they are working on an insight problem, they are working on an insight problem, and how they feel as they are working on and how they feel as they are working on a noninsight problem.a noninsight problem.

Insight problems, noninsight problems, Insight problems, noninsight problems, and ‘warmth’ judgments every 15 secondsand ‘warmth’ judgments every 15 seconds

Insight ProblemInsight Problem

Triangle ProblemTriangle Problem How you can move three of the How you can move three of the

circles to get the triangle to circles to get the triangle to point to the bottom.point to the bottom. Chain ProblemChain Problem

To open a link costs 2 cents and To open a link costs 2 cents and to close a link costs 3 cents. to close a link costs 3 cents. How to join the pieces into a How to join the pieces into a single closed loop of chain with single closed loop of chain with 15 cents?15 cents?

Noninsight ProblemsNoninsight Problems

Algebra problemAlgebra problem Slove for Slove for xx: (1/5): (1/5)xx + 10 = 25 + 10 = 25 Factor 16Factor 16yy22 – 40 – 40 yzyz + 25 + 25 zz22

ResultsResults

Obstacles to Problems Obstacles to Problems SolvingSolving

Fixation: people’s tendency to focus Fixation: people’s tendency to focus on a specific characteristic of the on a specific characteristic of the problem that keeps them from problem that keeps them from arriving at a solution.arriving at a solution. Functional fixedness (Jansson & Simth, Functional fixedness (Jansson & Simth,

1991)1991) Candle Problem (Duncker, 1945)Candle Problem (Duncker, 1945) Two-string problem (Maier, 1931)Two-string problem (Maier, 1931)

Situationally produced mental setSituationally produced mental set Water-jug problem (Luchins, 1942)Water-jug problem (Luchins, 1942)

Candle ProblemCandle Problem

Some candles, matches in a matchbox, Some candles, matches in a matchbox, and some tacksand some tacks

To mount a candle on the corkboard so To mount a candle on the corkboard so it will burn without dripping wax on the it will burn without dripping wax on the floor.floor.

Adamson (1952)Adamson (1952)

Repeated Duncker’s Repeated Duncker’s exeprimentexepriment

Participants who were Participants who were presented with empty presented with empty boxes were twice as boxes were twice as likely to solve the likely to solve the problem as participants problem as participants who were presented who were presented with boxes that were with boxes that were used as containers.used as containers.

Two-string ProblemTwo-string Problem

Two separate Two separate strings that strings that were hanging were hanging from the ceilingfrom the ceiling

A chair and a A chair and a pair of plierspair of pliers

Water-jug ProblemWater-jug Problem Participants were Participants were

given three jugs of given three jugs of different capacities different capacities and were required to and were required to use these jugs to use these jugs to measure out a measure out a specific quantity of specific quantity of waterwater

B - A – 2C works for B - A – 2C works for all of the problemsall of the problems

Fewer steps A + C Fewer steps A + C for problem 7 and A- for problem 7 and A- C for problem 8C for problem 8

ResultsResults

Information Information Processing Processing ApproachApproach

Modern Research on Modern Research on Problem SolvingProblem Solving

Describe problem solving as a Describe problem solving as a search that occurs between the search that occurs between the posing of the problem and its posing of the problem and its solution.solution.

Design computer program to Design computer program to simulate human problem solving.simulate human problem solving.

Newell and Simon’s Newell and Simon’s ApproachApproach

Initial state: conditions at the beginning Initial state: conditions at the beginning of the problem.of the problem.

Goal state: the solution of the problem.Goal state: the solution of the problem. Operators: rules that specify which moves Operators: rules that specify which moves

are allowed and which are not.are allowed and which are not. Intermediate state: each step through Intermediate state: each step through

problem solving.problem solving. Problem space: initial state, goal state, Problem space: initial state, goal state,

and all the possible intermediate states and all the possible intermediate states for a particular problem.for a particular problem.

Tower of Hanoi ProblemTower of Hanoi Problem

Means-end AnalysisMeans-end Analysis

Primary goal: to reduce the Primary goal: to reduce the difference between the initial and difference between the initial and goal statesgoal states

Method: creating intermediate Method: creating intermediate states that are closer to the goal states that are closer to the goal (subgoals).(subgoals).

How a Problem Is StatedHow a Problem Is Stated

How a problem is stated can affect How a problem is stated can affect its difficulty.its difficulty. Acrobat ProblemAcrobat Problem Reverse Acrobat ProblemReverse Acrobat Problem

Acrobat ProblemAcrobat Problem

Kotovsky and Coworkers (1985)Kotovsky and Coworkers (1985)

Reverse Acrobat ProblemReverse Acrobat Problem Same as the acrobat problem, except rule 4 Same as the acrobat problem, except rule 4

was changed to state that a smaller acrobat was changed to state that a smaller acrobat could not stand on a larger one.could not stand on a larger one.

An average 9.51 minutes to solve instead of An average 9.51 minutes to solve instead of 5.63 minutes in acrobat problem.5.63 minutes in acrobat problem.

Reasons for the difficultyReasons for the difficulty A 400-pound acrobat standing on the shoulders A 400-pound acrobat standing on the shoulders

of a 40-pound acrobat is not consistent with our of a 40-pound acrobat is not consistent with our knowledge of the real world.knowledge of the real world.

Visualizing larger acrobats on top of smaller Visualizing larger acrobats on top of smaller ones would increase the load on the problem-ones would increase the load on the problem-solver’s memory.solver’s memory.

Mutilated –Checkerboard Mutilated –Checkerboard ProblemProblem

Kaplan and Simon (1990)Kaplan and Simon (1990) If we eliminate two corners of the If we eliminate two corners of the

checkerboard, can we now cover the checkerboard, can we now cover the remaining squares with 31 dominos?remaining squares with 31 dominos?

Mutilated –Checkerboard Mutilated –Checkerboard Problem (Cont.)Problem (Cont.)

blankblank colorcolor black and black and

pink pink bread and bread and

butterbutter

Mutilated –Checkerboard Mutilated –Checkerboard Problem (Cont.)Problem (Cont.)

Results: Results: The board that emphasized the difference The board that emphasized the difference

between adjoining squares was easier.between adjoining squares was easier. Participants in the bread-and-butter Participants in the bread-and-butter

group solved the problem twice as fast as group solved the problem twice as fast as those in the blank group and required those in the blank group and required fewer hintsfewer hints

Solving problem becomes easier when Solving problem becomes easier when information is provided that helps information is provided that helps point people toward the correct point people toward the correct representation of the problem.representation of the problem.

Think-Aloud ProtocolThink-Aloud Protocol

Goal:Goal: To determine what information the person To determine what information the person

is attending to while solving a problem.is attending to while solving a problem. To reveal shifts in representation To reveal shifts in representation

ProcedureProcedure Talk aloud while you solve a problem (just Talk aloud while you solve a problem (just

verbalizing what you would normally think)verbalizing what you would normally think) Analysis of what was saidAnalysis of what was said

Russian Marriage ProblemRussian Marriage Problem

Russian Marriage Russian Marriage ProblemProblem

A “story” version of the mutilated A “story” version of the mutilated checkerboard problem that makes the checkerboard problem that makes the answer obviousanswer obvious 32 bachelors & 32 unmarried women32 bachelors & 32 unmarried women 2 of the men got into a fight and died2 of the men got into a fight and died Can matchmakers still arrange all the Can matchmakers still arrange all the

(hetero) marriages?(hetero) marriages? When people read this story first they can When people read this story first they can

easily solve the checkerboard problem if easily solve the checkerboard problem if they notice there is a connection…they notice there is a connection…

AnalogiesAnalogies

Analogical Problem Analogical Problem SolvingSolving

Often you can use the solution of one Often you can use the solution of one problem to guide the solution of another problem to guide the solution of another similar problemsimilar problem Russian Marriage Problem -> Checkerboard Russian Marriage Problem -> Checkerboard

ProblemProblem Analogical TransferAnalogical Transfer

People try to solve the Target ProblemPeople try to solve the Target Problem Some are presented with a Source Problem or Some are presented with a Source Problem or

Source Story that can help them solve the TargetSource Story that can help them solve the Target Russian Marriage (Source) -> Checkerboard Russian Marriage (Source) -> Checkerboard

(Target)(Target)

Steps of Analogical Steps of Analogical Problem SolvingProblem Solving

Noticing Noticing Seeing that there is a possible analogy Seeing that there is a possible analogy

between problemsbetween problems Most difficult, especially in the real worldMost difficult, especially in the real world

MappingMapping Connecting elements of the source Connecting elements of the source

problem to elements of the target problemproblem to elements of the target problem ApplyingApplying

Using the analogy to generate the solutionUsing the analogy to generate the solution

Improving Analogical Improving Analogical TransferTransfer

Two types of features (best when Two types of features (best when similar)similar) Structural FeaturesStructural Features Surface FeaturesSurface Features

Analogical EncodingAnalogical Encoding Strategy for training people to be able Strategy for training people to be able

to notice and apply analogies to notice and apply analogies Compare different source problems Compare different source problems

first, then solve Targetfirst, then solve Target

Analogical ParadoxAnalogical Paradox

Lab studies: People use surface Lab studies: People use surface featuresfeatures

Real World / In Vivo: People use Real World / In Vivo: People use structural featuresstructural features

Experts and Non-Experts and Non-expertsexperts

Differences Between Differences Between Novices and ExpertsNovices and Experts

Experts have more knowledge about their Experts have more knowledge about their fieldfield More analogies / strategies possibleMore analogies / strategies possible

Experts’ knowledge is organized differentlyExperts’ knowledge is organized differently Deep structural features Deep structural features physics problem examplephysics problem example

Experts spend more time analyzing Experts spend more time analyzing problemsproblems

BUT experts are only experts in their fieldBUT experts are only experts in their field

Creative Creative Problem-SolvingProblem-Solving

A StoryA Story

Physics exam question: Describe Physics exam question: Describe how the height of a building can be how the height of a building can be measured using a barometermeasured using a barometer

Teacher wanted an explanation Teacher wanted an explanation using principles in class using principles in class Compare barometric pressure at the top Compare barometric pressure at the top

of the building with barometric of the building with barometric pressure at the groundpressure at the ground

Equation to find the building’s heightEquation to find the building’s height

A StoryA Story

One student’s answersOne student’s answers Lower the barometer to the ground on a piece Lower the barometer to the ground on a piece

of string – length of string is height of buildingof string – length of string is height of building Put barometer in the sun and measure the Put barometer in the sun and measure the

length of its shadow and the length of the length of its shadow and the length of the building’s shadow, use proportions to find building’s shadow, use proportions to find building heightbuilding height

Give the building superintendent the barometer Give the building superintendent the barometer in exchange for info about building heightin exchange for info about building height

These are examples of These are examples of creativecreative answers answers

What is creativity?What is creativity?

Difficult to defineDifficult to define Involves innovative thinking, Involves innovative thinking,

generating novel ideas, or making generating novel ideas, or making new connections between existing new connections between existing ideas to create something newideas to create something new

Involves Involves divergent thinkingdivergent thinking

Divergent vs. Convergent Divergent vs. Convergent ThinkingThinking

Divergent thinking Divergent thinking Open-endedOpen-ended Large number of potential “solutions” Large number of potential “solutions” No “correct” answerNo “correct” answer Associated with ill-defined problemsAssociated with ill-defined problems

Convergent thinkingConvergent thinking Finding a solution to a specific problemFinding a solution to a specific problem Thinking converges to the correct Thinking converges to the correct

solutionsolution Associated with well-defined problemsAssociated with well-defined problems

Fixation and CreativityFixation and Creativity

Earlier we talked about Gestalt Earlier we talked about Gestalt psychologists’ research on obstacles to psychologists’ research on obstacles to problem-solvingproblem-solving FixationFixation was one obstacle was one obstacle

Fixation can limit creativity in designFixation can limit creativity in design Example: Sony temporarily abandoned Example: Sony temporarily abandoned

work on CD because at the size of a record work on CD because at the size of a record it would produce 18 hours of music. it would produce 18 hours of music. Realized CDs could be smaller and then Realized CDs could be smaller and then resumed research.resumed research.

Jansson and Smith Jansson and Smith (1991)(1991)

Design students Design students Generate as many designs as possible in 45 Generate as many designs as possible in 45

minutesminutes Problem: Design an inexpensive, spill-Problem: Design an inexpensive, spill-

proof coffee cupproof coffee cup Do NOT include a mouthpiece or strawDo NOT include a mouthpiece or straw

Two groupsTwo groups Fixation group: got a picture of what NOT to Fixation group: got a picture of what NOT to

dodo Control group: no pictureControl group: no picture

Jansson and Smith Jansson and Smith (1991)(1991)

Results: Those who saw pictures of Results: Those who saw pictures of the design with the mouthpiece and the design with the mouthpiece and straw produced more designs with a straw produced more designs with a mouthpiece and straw mouthpiece and straw These were forbidden designsThese were forbidden designs Evidence of Evidence of design fixation design fixation

Factors Affecting Factors Affecting CreativityCreativity

What’s the point of Jansson and Smith What’s the point of Jansson and Smith (1991)?(1991)? Creative problem-solving affected by Creative problem-solving affected by

fixationfixation Similar to regular problem-solvingSimilar to regular problem-solving

Creative problem-solving is also similar Creative problem-solving is also similar to regular problem-solving because to regular problem-solving because analogy can be usedanalogy can be used George de Mestral – burrs / velcro (1955)George de Mestral – burrs / velcro (1955) Insight + 7 years of trial and errorInsight + 7 years of trial and error

Creative CognitionCreative Cognition Ronald Finke developed a technique for Ronald Finke developed a technique for

training people to think creatively (training people to think creatively (creative creative cognitioncognition)) Let’s try it!Let’s try it! You’ll need something to write with (and on)You’ll need something to write with (and on)

I’ve randomly selected three shapes – take I’ve randomly selected three shapes – take 1 minute to construct an object using the 1 minute to construct an object using the shapesshapes Don’t make it a familiar objectDon’t make it a familiar object Don’t worry about what it is used forDon’t worry about what it is used for You can vary size, position, orientation, material You can vary size, position, orientation, material Wires or tubes can be bentWires or tubes can be bent

Creative CognitionCreative Cognition

Creative CognitionCreative Cognition The next step is to interpret how these The next step is to interpret how these

objects could be usedobjects could be used I’ll give you a category and you’ll have 1 I’ll give you a category and you’ll have 1

minute to interpret your object as an item minute to interpret your object as an item in that categoryin that category

Decide what your object could be used for Decide what your object could be used for Decide how it would workDecide how it would work

CATEGORY: Tools and UtensilsCATEGORY: Tools and Utensils

You’ve just created a You’ve just created a preinventive preinventive formform

Creative CognitionCreative Cognition

People generated 360 preinventive People generated 360 preinventive formsforms 120 rated as being “practical”120 rated as being “practical” 65 rated as being “creative” AND 65 rated as being “creative” AND

“practical”“practical”

Creative CognitionCreative Cognition

The points of Finke, 1995The points of Finke, 1995 People generated creative solutions People generated creative solutions

even thougheven though They were not told to be creativeThey were not told to be creative They were not screened for creativityThey were not screened for creativity They were not trained in how to be creativeThey were not trained in how to be creative

Creative problem-solving similar to Creative problem-solving similar to regular problem-solvingregular problem-solving People were more likely to find creative People were more likely to find creative

uses for forms they generated uses for forms they generated Technique lessened fixation issuesTechnique lessened fixation issues

THE ENDTHE END

Don’t forget to read Don’t forget to read “Something to Consider”“Something to Consider”