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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
Reason from base problem (previously solved) to target problem
INCORRECT
CORRECT
Only 20% solved it
Participants were more likely to solve the problem if they were given an analogy.
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.
Fortress ProblemRadiation Problem
Fortress Tumor
Mined RoadsSurrounding tissue
Attacking troopsRays varying in intensity
Small groups of troops
Converging on fortressWeak rays focused on tumor
Gick & Holyoak (1980)
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);
What do the results show?
“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.
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
ALIGN RELATIONS
BASED ON ALIGNED RELATIONS,
ALIGN OBJECTS
“the nucleus is like the sun”
Current temp.
Desired temp.
||50||60||70||80||
OR?
Kempton, ‘86
if you said “80”, what might your mental model be based on?
“there are two earths, one is flat, the other is a sphere out in space”
Nussbaum ‘79
Kaiser, McClosky & Profitt ‘86
?
OR
Kaiser, McClosky & Profitt ‘86
(The C-curve problem is the same but shows just the C part of the spiral)
What is the direction of this gear?
Suppose we swing this gear in this direction
Schwartz & Black, 1999
?
Suppose we swing this gear in this direction
Schwartz & Black, 1999
HINT:
?
Suppose we swing this gear in this direction
Schwartz & Black, 1999
Time A
Time B
Path Z
Path X
Path Y
From McCloskey, 1983
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