Improving Students’
Spatial Thinking Skills
Carol Ormand, SERC, Carleton College
Based on research with
Cathy Manduca, SERC, Carleton College
Thomas Shipley, Temple University
Basil Tikoff, UW-Madison
What Research Tells Us
• Spatial skills cannot be measured and characterized with a
single test; a suite of tests is required
• Spatial thinking skills improve with practice
• There is a wide range of spatial thinking abilities, even
among geoscience majors in upper-level courses
• Although students can succeed in undergraduate geoscience
courses with weak spatial thinking skills, incorporating
spatial skills training is likely to have two benefits:
• Increasing the pool of potential geoscientists
• Improving gender equity in the geoscience workforce
What is Spatial Thinking?
• What are some of the tasks that you have your students do
that have a spatial component?
• What are some of the tasks that you do as a geoscientist
that have a spatial component?
• How can we help our
students progress from
where they are to where
you are?
Examples of Spatial Thinking
Student tasks:
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Interpret maps and aerial photos
Create physical geographic profiles
Interpret and correlate well logs
Draw a diagram of isotopic
composition of water in different
locations within a system
Making maps in GIS; 3D mapping;
drawing subsurface hydrology
Calculate the variation of properties in
space, statistically
Make a beach profile, interpret
sediment samples, compare to prior
years’ data
Develop computer models to solve
characteristic equations
Model 3D flow
Describe coastal upwelling (narrative)
Expert tasks:
• Reconstruct spatial cross-section from
time series from buoy and Gulf Stream
• Observe, interpret, and model what we see
in outcrops (sedimentary rocks)
• Analyze nutrients in water to interpret
inputs
• Contour maps – recognize errors in
computer-generated contouring
• Groundwater – surface water interactions
through time
• River scale flow modeling
• Using isotopes to reconstruct paleoclimate
• Reconstruct the subsurface from seismic
data
• Develop a GIS curriculum, including
teaching basic geographic concepts
• Organizing classroom to maximize
student interactions
Spatial thinking includes
(but is not limited to)…
• Mental rotation: imagining rotating an object
• In cognitive science research, mental rotation skills have served
as a proxy for all spatial thinking until quite recently. Data from
many different sources (including our studies) suggest this is
insufficient.
Spatial thinking includes
(but is not limited to)…
• Visualizing: imagining
a 3D object from a 2D
representation
• Perspective taking: imagining
looking at an object or scene
from a different direction
Spatial thinking includes
(but is not limited to)…
• Penetrative thinking:
imagining what a slice
thru an object would
look like
• Disembedding: attending to
one aspect of a complex scene
Spatial thinking includes
(but is not limited to)…
• Navigation
• Scaling
Spatial Thinking in Geoscience
• Spatial thinking appears to be essential in a number of
subdisciplines in the geosciences
• Faculty describe poor spatial skills as a barrier to success
• Spatial skills training in engineering has led to improved
class performance and retention in the major
Measuring Spatial Skills
• Mental rotation
Measuring Spatial Skills
• Penetrative thinking: imagining the shape of a slice through
an object
Measuring Spatial Skills
• Penetrative thinking: imagining a slice through an object,
including its interior
Measuring Spatial Skills
• Paper folding
• Disembedding *
* Disembedding: isolating and attending to one aspect of a complex display or scene
Measuring Spatial Skills
• Water level
Examples of the range of test
scores, geoscience students
Correlations between
spatial skills tests
Measured improvement, mental
rotation, one academic term
Our Conclusions
• There is a wide range of spatial thinking abilities, even
among geoscience majors in upper-level courses
• Spatial skills cannot be measured and characterized with a
single test; a suite of tests is required
• Spatial thinking skills improve with practice
So… what kind of training/practice would be most
effective?http://serc.carleton.edu/spatialworkbook/index.
html
What kinds of brief, weekly exercises
could you give your students?
Take a few minutes to brainstorm
a list of 10-minute exercises you
could have your students do to
practice the kinds of spatial
thinking that show up in your
courses.
Suggestions:
• Focus on what you want them to be able to do.
• Start simple, and build up to more difficult tasks over time.
• Demonstrate how to approach the exercises. Work an
example before having students tackle the first one.
Spatial Workbook Project:
focuses on penetrative thinking
• Builds on prior work:
• From geoscience education:
• Titus & Horsman’s exercises (JGE, 2009)
• Steve Reynolds’ computer visualizations
of landscapes and structures
• Visible geology tool
(http://app.visiblegeology.com/)
• Our studies thus far
Spatial Workbook Project
• Builds on prior work:
• From cognitive science:
• Progressive alignment
• Gesture
• From STEM education:
• Sorby workbook for engineers
Detailed look at instructional
“intervention” at UW-Madison
• Structural Geology class at the UW-Madison
• Test of 2011-2014 spatial thinking workbook concept
• Spring 2010: collect baseline data
• Pre- and post-tests of students’ penetrative thinking, mental rotation,
and disembedding skills
• Spring 2011:
• Same pre- and post-tests of penetrative thinking, mental rotation, and
disembedding skills
• Weekly penetrative thinking exercises at the beginning of lab
• Designed to take 10-15 minutes
• Variety of forms (pencil & paper, computer visualizations, play-doh)
• Geological and non-geological content
• All required students to sketch one or more cross-sections
Weekly Exercises: analog modeling
• Use play-doh to construct a model of
• An anticline
• Boudinage
• Lineation (for example, a stretched
pebble conglomerate)
• Slice through your model in several
different directions
• Sketch cross-sections parallel,
perpendicular, and oblique to the structural
grain
• How would your cross-sections be different
if the structure (or long axis of the strain
ellipsoid) was plunging?
Weekly Exercises: analog modeling
• Construct a model of a faulted fold, like the one illustrated
below, using play-doh. Slice the model
• Parallel to the fold hinge
• Perpendicular to the fold hinge, through the fault surface
• Sketch the resulting
cross-sections
• Investigate similar
structures:
• Faulted syncline
• Faulted plunging fold
Image by Titus and Horsman
Weekly Exercises:
computer visualizations
• Sketch a cross-section for the slicing
plane indicated, as viewed from the
right side of the block
• Sketch the 3 cross-sections of a human
foot indicated in the diagram below
A
C
B
Weekly Exercises: thought exercises
• Construct a structure contour
map for the top of the gray
unit, using 100m contour
intervals; describe the
orientation of this structure
and the structure contour
lines in words
• Sketch a cross-section from A-A’
Images & exercises by Titus and Horsman
Results: Penetrative Thinking
(ETS planes of reference)
Pre-test
Post-test
Gain
T-test
2010 (N=17)
8.6 (3.2)
10.1 (2.2)
1.5 (2.6)
0.03
2011 (N=16)
7.3 (2.5)
9.0 (3.1)
1.7 (2.2)
0.01
UW-Madison, Structure, Spring 2010
UW-Madison, Structure, Spring 2011
5
5
4
4
3
3
2
2
1
1
0
0
1
2
3
4
5
6
7
Pre-test
8
9
10
11
Post-test
12
13
14
15
1
2
3
4
5
6
7
Pre-test
8
9
10
11
Post-test
12
13
14
15
Results: Mental Rotation
(PVRT)
Pre-test
Post-test
Gain
T-test
2010
6.0 (2.1)
6.4 (1.9)
0.4 (2.0)
0.48
2011
4.9 (1.8)
6.2 (2.0)
1.3 (1.5)
0.00
UW-Madison, Structure, Spring 2010
UW-Madison, Structure, Spring 2011
6
6
5
5
4
4
3
3
2
2
1
1
0
0
1
2
3
4
5
Pre-test
6
7
Post-test
8
9
10
1
2
3
4
5
Pre-test
6
7
Post-test
8
9
10
Results: Disembedding
(ETS hidden figures)
Pre-test
Post-test
Gain
T-test
2010
8.0 (3.2)
9.3 (2.8)
1.3 (3.3)
0.12
2011
7.4 (3.0)
9.3 (3.7)
1.9 (2.8)
0.02
UW-Madison, Structure, Spring 2010
UW-Madison, Structure, Spring 2011
5
5
4
4
3
3
2
2
1
1
0
0
1
2
3
4
5
6
7
8
Pre-test
9
10
11
12
Post-test
13
14
15
16
1
2
3
4
5
6
7
8
Pre-test
9
10
11
12
Post-test
13
14
15
16
UW Structure Class Study Results
• Spring 2010:
• Students demonstrated a wide range of spatial thinking skills
• Students showed modest improvement (on average) on all 3
measures, with statistically significant improvement in
penetrative thinking
• Spring 2011:
• Students demonstrated a wide range of spatial thinking skills
• Students showed greater average gains on all 3 measures, and
all gains were statistically significant
Conclusions
• Spatial thinking skills improve with practice (even 10-15
minutes each week can make a difference)
• Interventions focused on strengthening penetrative thinking
may also help develop other aspects of spatial thinking
• Next year: testing progressive alignment and gesture
exercises. Stay tuned.
What kinds of brief, weekly exercises
could you give your students?