Analogical reasoning
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Analogical Reasoning. Types of reasoning. Content free reasoning: Deductive reasoning Reasoning by similarity Inductive reasoning Analogical reasoning: analogical transfer: solving problem in one domain based on solution in another domain

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Analogical Reasoning

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Analogical reasoning

Analogical Reasoning


Types of reasoning

Types of reasoning

  • Content free reasoning:

    • Deductive reasoning

  • Reasoning by similarity

    • Inductive reasoning

    • Analogical reasoning:

      • analogical transfer: solving problem in one domain based on solution in another domain

      • Analogical inference: generalizing properties/relations from one domain to another


Analogical transfer

Analogical transfer

Reason from base problem (previously solved) to target problem

  • Recognition: identify a potential analog

  • Abstraction: abstract general principle from base problem

  • Mapping: apply principle to target


Radiation problem

Radiation Problem

  • Problem

    • Patient has an abdominal tumor (in center of body)

    • Radiation will kill tumor

    • But rays strong enough to kill tumor will also destroy healthy tissue that rays pass through on way to tumor

  • Solution?


Solution

Solution

INCORRECT

CORRECT


Gick holyoak 1980

Gick & Holyoak (1980)

Only 20% solved it

Participants were more likely to solve the problem if they were given an analogy.


Fortress problem

Fortress Problem

  • Army general wants to attack a fortress in center of forest.

  • Many roads lead to fortress like spokes of a wagon wheel.

  • All the roads have land mines that are triggered by heavy traffic.

  • If entire army travels down a road, land mines will go off.

  • Solution?


Solution1

Solution

The general sends small groups of soldiers down each of the roads, co-ordinating their movements so that they all arrive at the fortress at the same time.


Structural similarities

Structural Similarities

Fortress ProblemRadiation Problem

Fortress Tumor

Mined RoadsSurrounding tissue

Attacking troopsRays varying in intensity

Small groups of troops

Converging on fortressWeak rays focused on tumor


Recognition process

Recognition Process

  • Radiation problem hard problem:

    • Preceded by Fortress problem, 20% solved it

    • If given hint that problems are related, 92% solved it

  • Subjects do not produce corresponding solutions with any great frequency unless given a hint

  • These results demonstrate the difficulty of recognizing the relevance of one problem and its solution to another

Gick & Holyoak (1980)


Transfer aspects of fortress problem to radiation problem

Transfer aspects of fortress problemto radiation problem

  • Fortress problem was given with three different solutions:

    • Dispersion: the general’s army approaching the fort from several roads at once.

    • Tunnel: a general digging a tunnel to the fort

    • Open-route: a general attacking the fort via a supply route


Problem solutions

Problem Solutions

Solutions to the Radiation problem fell into three main categories:

The DISPERSION solution, in which small doses of radiation

are aimed at the tumor from different directions so that the

radiation accumulates and destroys the tumorous tissue;

The TUNNEL solution, in which an incision is made which leaves

the tumor in place but which allows direct delivery of

radiation.

The OPEN-ROUTE solution, in which radiation is delivered to

the tumor through the esophagus (tube leading from the throat to

the stomach);


Distribution of solutions

Distribution (%) of Solutions

What do the results show?


Abstraction process

Abstraction Process

  • Does performance improve if principle of base problem is stated? No

  • Showing diagrams helps? No

  • Showing multiple problems with related solutions helps? Yes


Analogical inference

Analogical Inference

“An atom is like the solar system”

TARGETBASE

Knowledge about the base domain can be used to reason about the target domain. Structure mapping theory is a theory for how this could work.


Structure mapping theory dedre gentner 83 89

Structure Mapping Theory(Dedre Gentner, ’83, ’89)

Theory on how to interpret an analogy

1) set up correspondences

2) focus on matches of relations, not attributes

3) focus on higher-order relations

4) extend knowledge about target by mapping relations from source to target


Analogical reasoning

ALIGN RELATIONS


Analogical reasoning

BASED ON ALIGNED RELATIONS,

ALIGN OBJECTS

“the nucleus is like the sun”


Mental models

Mental Models

  • Knowledge structure used to understand how objects and physical processes work

  • Sometimes, mental models are based on poor analogies and can lead to incorrect predictons

  • Example: thermostats. How to heat up a room quickly?

Current temp.

Desired temp.

||50||60||70||80||

OR?

Kempton, ‘86


Analogical reasoning

if you said “80”, what might your mental model be based on?


Children s mental models

Children’s Mental Models

“there are two earths, one is flat, the other is a sphere out in space”

  • Children were told facts:

    • Columbus sailed around the earth

    • Shown space photographs

  • What is their Conception of earth given these facts?

Nussbaum ‘79


Intuitive physics

Intuitive Physics

Kaiser, McClosky & Profitt ‘86

  • Intuitive physics is based on naive mental models of physical processes

  • The diagram shows a curved tube, lying flat on a table. A ball is shot into the opening and out the other end. What is the ball’s path after it shoots out the tube?

?

OR


Results

Kaiser, McClosky & Profitt ‘86

Results

(The C-curve problem is the same but shows just the C part of the spiral)


Explanation by kaiser et al

Explanation by Kaiser et al.

  • Grade school children start constructing theories of motion

  • Theories of persistence of motion: “an object persists in the way it is moving, unless there is friction”. E.g., bouncing ball continues to bounce

  • Theory is wrongly applied to spiral problem: overgeneralization


Intuitive physics with a set of gears

Intuitive Physics with a set of gears

What is the direction of this gear?

Suppose we swing this gear in this direction

Schwartz & Black, 1999


Analogical reasoning

?

Suppose we swing this gear in this direction

Schwartz & Black, 1999


Analogical reasoning

HINT:

?

Suppose we swing this gear in this direction

Schwartz & Black, 1999


Analogical reasoning

Time A

Time B

Path Z

Path X

Path Y

From McCloskey, 1983


Analogical reasoning

Mental models might be initially be based on perceptual simulations (e.g., turning the gears in your mind)

After training, these models might shift to more abstract rules to solve problems


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