Inductive Reasoning
n
n
Structure of argument not sufficient
Must rely on content to aid in decisions
Reasoning by Analogy
n
Map current situation onto more familiar situation
n
Important in scientific discovery
n Understanding
n Understanding
of heart -- analogy to a pump
of gasses -- analogy to billiard balls
Extend known to unknown
n
n
Donnely & McDaniel (1993)
Collapsing stars spin faster and faster as the fold in on
themselves and their size decreases. This phenomenon of
spinning faster occurs because of a principle called
“conservation of angular momentum.”
n
What would happen to the rotation of a star if it
“expanded”?
n
Collapsing stars spin faster as their size shrinks. Stars are
thus like ice skaters, who pirouette faster as they pull in
their arms. Both stars and skater operate by a principle
called “conservation of angular momentum.”
1
Using Analogies
n
Must be able to find match to “familiar”
situation
n
How to find match?
n
n
relational / structural similarity
As opposed to featural similarity
Gentner’s Structure Mapping
Theory
n
n
SMT -- mapping from base to target domain
Series of steps
Must find correspondence between two domains
Focus on matching relations
n Focus on systematicity
n
n
n Systems
n
n
n
Find correspondence
Matching relations
n
n
n
Attracts
revolves
Higher order system?
n
n
of relations with higher order cause
Extend knowledge of base domain to target domain
Attraction causes
revolution
Transfer knowledge
n
Infer that attraction
causes revolution
2
Analogical Inferences
n
Powerful
n
n
n
Dangerous
n
n
n
n
Mapping may not be perfect
Lead to erroneous conclusions
Erroneous
conclusions:
Solar system:
n
n
Allow us to make inferences in a novel domain
Map known domain to novel domain
Increased mass causes
attraction
Atoms
n
Attraction not due to
increased mass of
nucleus
Structural Alignment
n
n
n
n
Markman & Gentner (1993)
Used when mapping one domain to another
Alignable differences
n
Matched elements in base and target domain
n
Sun ßà Nucleus
Nonalignable differences
n
n
n
n
No correspondence in other domain
Hotter than ßà ????
Also used in similarity judgments
Alignable differences more salient
n
More likely to be used in comparisons
3
How comparable are two pictures?
Commonalities and Differences
n
Commonalities
Commonalities and Differences
n
n
Commonalities
Alignable Differences
4
Commonalities and Differences
n
n
n
n
Commonalities
Alignable Differences
Nonalignable
Differences
Commonalities and
Alignable Differences
more salient in
comparisons
Gentner & Markman (1994)
n
Asked subjects to list one difference for 40 word
pairs
n
n
n
Half of the pairs – similar
Half of the pairs – dissimilar
Not enough time to do all
n
Do the easy ones first, then do the hard ones
Gentner & Markman (1994)
n
Similar Word Pairs
n
Dissimilar Word Pairs
n
Light bulb – Candle
n
Bowl – Dictionary
n
Magazine – Newspaper
Bowl – Mug
n
Bicycle – Refrigerator
Kite – Painting
Bicycle – Tricycle
Kite – Hang glider
n
n
n
Chair – Banana split
Magazine - Mug
n
Etc.
n
Etc.
n
11.38 pairs on average
n
5.88 pairs on average
n
n
n
5
Mental Models
n
Mental Model
n
n
Knowledge of a domain
May be:
n Simple
objects (e.g., water faucet)
n Complex
objects (e.g., solar system)
e.g., model of restaurant events)
n Events (Scripts -n Relations
(economy and Cadillac sales)
Web of beliefs surrounding concept
n Implicit “Theory”
n
n Example:
n
Understanding of blood pressure
Based on understanding of Heart, circulation, arteries, etc
Influence of mental models
n
Mental models guide behavior
n
n
n
Thermostat example in text
Study habits
Mental models affect reasoning ability
n
n
Novices -- incomplete -- poor reasoning ability
Experts -- (near) complete -- good reasoning ability
Reasoning
n
Can use mental models to aid in general reasoning
All of the artists are beekeepers
Some of the beekeepers are chemists
n Are some of the artists also chemists?
n
n
n
Imagine a set of people (artists, chemists, beekeepers)
n Little
n Test
world -- mental model
/ examine model -- what is necessarily true?
6
Knowledge and reasoning
n
Incomplete knowledge
n
Inaccurate mental model
n
Info about mental models being used
n
McCloskey (1983)
n Types
of errors
n People’s
mental models of object motion
McCloskey (1983)
McCloskey (1983) -- Results
n
n
n
Tube
n
47% straight
n
51% curved
Airplane
Broken string
n
53% straight
n
30% curved
7
McCloskey (1983)
n
Mental model -- Impetus Theory
Setting object in motion
Puts impetus or movement force into object
n Impetus slowly dissipates across time
n
n
n
“Naïve” Physics
n
n
Accepted theory of motion until 15th century
Replaced by Newton’s laws
Source of Mental Models
n
Based on knowledge
n
n
Increased knowledge
n
n
n
Experience with world
Better (but not perfect) mental models
Students in physics classes -- still misconceptions
Educational implications
n
n
Why faulty models arise
How to prevent / replace
8