How analogical processing (and
spatial language) fosters spatial
learning
Dedre Gentner
Northwestern University
Benjamin Jee, Northwestern University
David Uttal, Northwestern University
Cathy Manduca, Carleton College
Thomas Shipley, Temple University
Brad Sageman, Northwestern University
Carol Ormand, Carleton College
1
Basil Tikoff, UW-Madison
Two lines of research
• Analogical processes support spatial
learning and cognition
• Spatial language supports spatial
learning and cognition
Overarching question: How do we
come to be fluent relational thinkers
2
http://www.spatialintelligence.org
Analogy as Structure-mapping
base
target
An analogy conveys that partly identical relational
structures hold between objects in different domains
Corresponding objects need not resemble each other
(though it’s easier if they do)
Gentner (1983, 1989); Falkenhainer, Forbus & Gentner (1989); Gentner & Markman (1997)
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http://www.spatialintelligence.org
Analogy highlights common relational structure and
fosters relational abstractions
e.g., A small force at a long distance from the fulcrum can
Balance a large force at a small distance from the fulcrum
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Gentner, 1983; Gentner & Markman, 1997; Gentner & Namy, 199; Gick & Holyoak, 1983
http://www.spatialintelligence.org
Progressive alignment from easily aligned to hard-to-align
is a good way to start early learning
Once understood, the
relational abstraction
can often be extended
to more dissimilar pairs via
Progressive alignment
(Kotovsky & Gentner, 1986;
Gentner, Anggoro & Klibanoff, in
5 press; Jee et al, in prep)
http://www.spatialintelligence.org
How analogy leads to spatial learning:
Detecting differences
Alignable
difference
Alignable difference : different elements that each occupy
the same role in the aligned structure:
e.g., “Motorcycles have two wheels, cars have four”
6
Gentner, 1983, 1989, 2003; Gentner & Markman,http://www.spatialintelligence.org
1997; Gick & Holyoak, 1983
Task: Name a difference between these two images
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Gentner & Sagi, 2006
http://www.spatialintelligence.org
Task: Name a difference between these two images
Nonalignable Difference
Alignable Difference
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Gentner & Sagi, 2006
http://www.spatialintelligence.org
Finding Fault: Using alignment to
supporting spatial learning
Alignable difference
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http://www.spatialintelligence.org
Progressive alignment of pairs
• 64 Psych 110 students
• 10 similar & 10 dissimilar pairs (No feedback on responses)
Similar first
Dissimilar first
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http://www.spatialintelligence.org
Comparison and learning
• Structural abstraction: Receiving multiple structurally-alignable
comparisons helps generalize the concept
• Progressive alignment: Transitioning from close (easy to align) pairs
to less similar pairs helps novice learners abstract a common
relation (Gentner, Loewenstein, & Hung, 2007)
Teaching students to recognize faults
• Alignable pairs showing fault/no-fault > same examples separately
• Order of pairs matters: Progressive alignment
High-similar (easy to align) pairs  low-similarity (hard to align) pairs
is better than the reverse order
11
http://www.spatialintelligence.org
Spatial Language helps children perform a spatial
mapping task (Loewenstein & Gentner, 2005)
“the
winner”
Hiding
Box
Finding
Box
For 6 trials (twice per location):
Baseline: “I’m putting it here”
(Noninformative Language)
Spatial Language: “I’m putting it on/in/under the box”
(Informative Language)
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Children are shown the correct answer on each trial
http://www.spatialintelligence.org
Loewenstein & Gentner, 2005
Spatial Mapping Task – Neutral Version
Search Trials
1.0
• Young (3 ½) children
benefit strongly from
relational language
• Older (4 year-olds)
perform well with or
without spatial language
Proportion Correct
Results
* On, In, Under
0.8
0.6
0.4
Baseline
0.2
0
3;8
4;1
N=20
N=20
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http://www.spatialintelligence.org
Cross-mapped Task
Neutral
1.0
Results
• 4 ½ & 5-year-olds
benefit strongly from
overt spatial language
Spatial Language
*
0.8
Proportion Correct
Pattern repeats at
older age:
• 4-year-olds fail
entirely
Cross-mapped
*
0.6
Baseline
0.4
0.2
0
3;8 yrs
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http://www.spatialintelligence.org
4;1 yrs
4;7 yrs
5;2 yrs
N=20
N=20
N=20
Thank you
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http://www.spatialintelligence.org
Ongoing Study in Chicago Children’s Museum
with Susan Levine, Sonica Dhillon, Jessica Saunders, Ashley Poltermann &
Tsivia Cohen
Does alignment foster acquisition of principles of stable
construction?
with Susan Levine, Sonica Dhillon, Jessica Saunders, &
Tsivia Cohen
Participants: Children 3-8 with families in Build-a-skyscraper activity
Key principle in engineering and architecture: Diagonal braces
confer stability
Vertical Brace
Diagonal
Brace
Horizontal Brace
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http://www.spatialintelligence.org
High
Alignability
Low
Alignability
“Which one do you think is
stronger?”
“OK, now see if you can
wiggle them”
The building with the
vertical piece bends.
The building with the
diagonal brace does not
bend.
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“So which one was
stronger? Right! The one
with the brace was
stronger”
http://www.spatialintelligence.org
Ongoing Study in Chicago Children’s Museum
with Susan Levine, Sonica Dhillon, Jessica Saunders, Ashley Poltermann &
Tsivia Cohen
Post-test : Show me where you would put this to
make this building strong
Results:
High-alignment > Low-alignment
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http://www.spatialintelligence.org
Recognizing Faults
Fault = a fracture in a rock along which movement has occurred
19
http://www.spatialintelligence.org
Learning through examples
• Most introductory geology courses include instruction about faults &
other geological structures
• Students see multiple examples of faults
• Students vary in rate of learning
Sources: Wikipedia.org, USGS.gov
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http://www.spatialintelligence.org
Method: Transfer task & post-tests
14 single images, 7 fault and 7 no-fault
Is there a fault? If so, place 2 Xs on its location
X
X
X
X
Spatial ability tests: Mental rotation and water levels
Background experience questionnaire (10 questions)
• Key question: How many previous course in geology?
21
http://www.spatialintelligence.org
Results: Effects of condition
Does similar-first sequence lead to higher
performance in the initial phase?
No geo courses
At least 1 geo course
n=44
n=20
2
ns
1
0
Dissimilar-first
Similar-first
Initial Phase d-prime
Initial Phase d-prime
May depend on background experience
2
*
1
0
Dissimilar-first
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http://www.spatialintelligence.org
Similar-first
Results: Effects of condition
No geo courses
At least 1 geo course
n=44
n=20
Transfer task d-prime
Transfer task d-prime
Main effect of geo course experience in the transfer
task
2
1
0
Dissimilar-first
Similar-first
2
1
0
Dissimilar-first
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http://www.spatialintelligence.org
Similar-first
Results: Geoscience experience and spatial
ability
Are geoscience experience effects due to spatial ability?
• No significant difference on spatial ability measures between those with
geo experience and those without (no experience actually higher on
each measure)
What knowledge leads to higher performance?
• 17 participants asked to explain the information they used to find faults
in images, and how they know when they have found a fault
• 2 main types of information present in responses: use of
cracks/fractures, and use of movement/displacement of layers
Crack/Fracture
mentions
Movement/Displacement
mentions
Accuracy above mean
6
16
Accuracy below mean
14
7
24
http://www.spatialintelligence.org
Further directions
• More initial instruction that explicitly distinguishes faults from fractures
may be especially beneficial for novices
• e.g., diagrams, photos, or simulations of faults
Fracture, No fault
Fault
• Provide feedback during initial phase
• May enhance novice’s ability to profit from comparison
• Examine performance on new set of transfer items
• Examine eye movements to observe processing (search and
comparison) in more detail
25
http://www.spatialintelligence.org
How analogy leads to learning:
Detection of differences
Analogical comparisons make alignable
differences more salient
(Gentner & Markman, 1994; Markman & Gentner, 1993, 1996)
Example task: Find the
wrongly placed bone
(Kurtz & Gentner, in prep)
Target
26
http://www.spatialintelligence.org
Standard
Ongoing Study in Chicago Children’s Museum
with Susan Levine, Sonica Dhillon, Jessica Saunders, Ashley Poltermann &
Tsivia Cohen
Does alignment foster acquisition of principles of stable
construction?
with Susan Levine, Sonica Dhillon, Jessica Saunders, &
Tsivia Cohen
Participants: Children 3-8 with families in Build-a-skyscraper activity
Key principle in engineering and architecture: Diagonal braces
confer stability
Vertical Brace
Diagonal
Brace
Horizontal Brace
27
http://www.spatialintelligence.org
High
Alignability
Low
Alignability
“Which one do you think is
stronger?”
“OK, now see if you can
wiggle them”
The building with the
vertical piece bends.
The building with the
diagonal brace does not
bend.
28
“So which one was
stronger? Right! The one
with the brace was
stronger”
http://www.spatialintelligence.org
Method
Vertical Piece
Diagonal
Brace
Horizontal Piece
-- Pre-training
• Comparison: Diagonal brace vs. Horizontal/Vertical piece
• Conditions:
High-alignable
Low-alignable
Control (no pre-training)
-- Task: Child builds skyscraper
w/ family
-- Post-task: Questions
& assessment tasks
29
http://www.spatialintelligence.org
High
Alignability
“Which one do you think is
stronger?”
“OK, now see if you can
wiggle them”
The building with the
vertical piece bends.
The building with the
diagonal brace does not
bend.
30
“So which one was
stronger? Right! The one
with the brace was
stronger”
http://www.spatialintelligence.org
Results – Reaction time
RT (ms)
RT (ms)
“Different” Responses
Same-Diff (n=24)
Name-a-diff (n=20)
1. Same-Diff:
High Sim slower than
Low Sim (p<.01)
31
2. Name-a-Diff:
High Sim faster than
Low Sim (p<.01)
3. Same-Diff faster than Name-a-Diff
http://www.spatialintelligence.org
(p<.01)
Structure-Mapping Principles
Gentner, 1983, 1989

1. Structural Consistency
• 1-1 Correspondences
• Parallel Connectivity
a b
c
a’ b’ c’
BASE
TARGET
2. Systematicity
• Common Connected Systems of Relations
• Higher-Order Constraining Relations
3. Relational Focus
• Common Relations > Common Object Descriptions
Embodied in SME (the Structure-mapping Engine)
(Falkenhainer, Forbus & Gentner, 1989; Forbus, Gentner & Law, 1995)
Many of these principles now used in other models:
ACME, IAM, AMBR, SIAM, LISA, EMMA
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http://www.spatialintelligence.org
Structural alignment supports spatial learning
Structural
abstraction
Candidate
inference
• Highlights common spatial relational structure
• Supports abstraction of common spatial structure
• Invites new spatial inferences
33
Gentner, 1983, 1989, 2003; Gentner & Markman,http://www.spatialintelligence.org
1997; Gick & Holyoak, 1983