10 Problemsolving NC

7/27/2019 10 Problemsolving NC

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PROBLEMSOLVING


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More Problems

You have 10 red socks and 20 brown socks inyour 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?


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Problem Solving

a s e nex e er n e o ow ng sequence

O T T F F S S


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Problem Solving

Initial State Current situation

Define the roblem

Goal State

Obstacles Choices made about limitations Strategy choices

Limited resources


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Problem Representation

relevant and what information is irrelevant is the

process o pro em represen a on People pay attention to the wrong information

People need to focus on the right information


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Sample Problem

know the password that was required. He waited by thedoor and listened. A club member knocked on the door

an t e oorman sa , twe ve. e mem er rep e , s x" and was let in. A second member came to the door andh rm n i " ix." Th m m r r li " hr " n

was let in. The man thought he had heard enough and

walked up to the door. The doorman said ,"ten" and theman rep e , ve. ut e was not et n.

What should have he said?


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The Problem-Solving Cycle

1. Problem Identification e ave to recogn ze t at we ave a goa or t at t esolution we had in mind does not work

2. Problem definition and representation h fin n r r n h r l m ll

enough to understand how to solve it


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3. Strategy Formation We have to plan a strategy for solving the problem

which may involve

Analysis breaking down the whole of a complexproblem into manageable elements

them into something useful

Diver ent thinkin ou tr to enerate a diverseassortment of possible alternative solutions to a problem

Convergent thinking you narrow down the multipleposs t es to converge on a s ng e, est answer


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Strategy Formation

Breaking into sub goals

Stud for exam sub oals

Read textbook & class notes Identify most relevant topics

reate stu y quest ons & answers on note car s

Learn all concepts on note cards

Test self with note cards Recycle through learning and testing until mastery is achieved


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Strategy Formation

Synthesis rgan ze to a so ut on

Symbols

Matrixes Diagrams

Mango Peach Steak

Alex x 0 x

Let L = Lucy, S = Sean,

2L=3S, S=10

Jarod x x 0

Henry 0 x x


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Strategy Formation

Divergent thinking Generate multiple solutions to problem

Convergent thinking w w w


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4. Organization of Information You have to organize the available information in a way

that enables you to implement the strategy

You organ ze t e n ormat on strateg ca y, n ng a t emost suitable representation

. esource ocat on

We have limited resources (time, money, equipment,space,

We have to decide how much we want to invest into the


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6. Monitoring It is necessary to monitor the process of solving the problem

to make sure that we are getting closer to the goal

compensate for possible flaws

. You need to evaluate your solution after you have finished

New roblems can be reco nized the roblem ma beredefined, new strategies may come to light, and newresources may become available


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Incubation Putting the problem aside for a while

Pr l m ill r n i l

The benefits of incubation can be enhanced in

Invest enough time in the problem initially

ow su c en me or ncu a on o perm ereorganization of information


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Types of Problems

Well-structured problems Clear path to the solution

Math roblems

Anagrams

-

Dimensions of problem are not specified or easy to

n er

Finding an apartment

Writing a book


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Well-Structured Problems Problems with clear paths to their solutions

Com uter simulations of well-defined roblems Problem space

The universe of all ossible actions that can be a lied to

solving a problem Algorithms

Sequences of operations that may be used recursively

(repeated over and over again)


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Well-Structured Problems Humans use heuristics

Informal intuitive s eculative strate ies thatsometimes lead to an effective solution and

sometimes do not

If we store in long-term memory several simple

problems, we can lessen the burden of our limited-


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Well-Structured Problems Heuristics

1. Means-ends anal sis Analyze the problem by viewing the end (the goal to be

sou ht and then tr to decrease the distance between the

current position in the problem space and the end goal inthat space

2. Working forward

Start at the beginning and try to solve the problem fromthe start to the finish


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Well-Structured Problems Heuristics

3. Workin backward The problem-solver starts at the end and tries to work

backward from there

4. Generate and test -

action, not necessarily in a systematic way, and then

notices in turn whether each course of action will work


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Ill-Structured Problems here is no clear, readily available path to

solution ill-structured problems do not have well-defined

problem spaces, and problem solvers have difficulty

constructing appropriate mental representations formodeling these problems and their solutions


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Ill-Structured Problems Insight

a distinctive and sometimes seemingly sudden understandingof a problem or of a strategy that aids in solving the problem

Often, an insight involves reconceptualizing a problem or astrategy or ts so ut on n a tota y new way

Insight can be involved in solving well-structured problems,-


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Gestalt View of Insi htInsight

Wertheimer Sudden rearrangement of elements creates insight

ro uc ve n ng goes eyon prev ous y earneassociations

Kohler

Animal Model of Insi ht


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Obstacles to Problem SolvinObstacles

Mental set

Functional fixedness

ncorrect or ncomp ete representat on o t e

problem Lack of domain knowledge

Ob l


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Obstacles

Mental Set

Seeing a problem in a particular way insteadof other plausible ways due to experience or

context

This usually causes you to adopt an ineffective

Make assumptions without realizing it

Difficult to approach the problem in a new way

Ob t l


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Obstacles

Functional Fixedness

An inabilit to assi n new functions and roles toelements of a problem

wo s r ng pro em

Dunckers candle problem

Ob t l


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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 theother

Materials:

Chairpiece of paper

pair of pliers

What is the Solution?

Obstacles


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Obstacles

Problem II

Box of thumb tacks

an e

Matches

ect ve: ount can e on wa to ma e g t

What is the Solution?

Obstacles


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Obstacles

rans er

Negative Transfer Solving prior problem makes it more difficult to solve

later roblem

Positive Transfer

Solving earlier problem helps to solve later problem

Obstacles


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Obstacles

Einstellung 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 cant be solved by 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


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Gick & Hol oak 1980Obstacles

Give participants one problem to read, with asolution

Then give them a second problem, which can be

solved using a similar solution

Obstacles


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Obstacles

Suppose you are a doctor faced with a patient who has a malignant tumor in his

stomach. It is impossible to operate on the patient, but unless the tumor is destroyedthe patient will die. There is a kind of ray that can be used to destroy the tumor. If

the rays reach the tumor all at once with sufficiently high intensity, the tumor will bedestroyed. Unfortunately, at this intensity the healthy tissue that the rays pass through

will also be destroyed. At lower intensities the rays are harmless to the healthy tissue,

but they will not affect the tumor either. What type of procedure might be used todestroy the tumor with rays without destroying the healthy tissue?

Obstacles


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Obstacles

Gick & Holyoak (1980)

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

roblem

A group previously given the analogous

A group given the General/Fortress problem and told

a s so u on wou e p n so v ng e ra a onproblem

Obstacles


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Gick & Holyoak (1980) Results

100

60

70

80

90

30

40

50

0

10

Obstacles


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Analo ies

Number of examples exposed to

Gick and Hol oak conducted a stud in which the dictator stor

wasjust one of three other storiesparticipants heard before radiationproblem

Whether schema for problem is activated

If the two roblems are se arated b a dela or if the arepresented in different contexts, almost none of the participantsuse the analogy


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10 Problemsolving NC