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DOI: 10.1177/0963721413484756
2013 22: 367Current Directions in Psychological Science
David H. Uttal, David I. Miller and Nora S. Newcombe
and Mathematics?
Exploring and Enhancing Spatial Thinking: Links to Achievement in Science, Technology, Engineering,
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Spatial thinking is essential to both human adaptation and
modern living. For instance, navigating in one’s environ-
ment is required of most living species, and tools such as
maps can help facilitate such reasoning for humans. Over
the past decade, researchers in psychology, education,
and a host of other disciplines have increasingly investi-
gated the role of spatial thinking in science, technology,
engineering, and mathematics (STEM) achievement. We
review this research briefly, finding that spatial thinking is
malleable and that inexpensive spatial interventions could
potentially make a large difference in STEM education.
Finally, we point out the research that remains to be done
to test experimentally whether spatial interventions will
indeed improve STEM achievement.
We define spatial thinking as the mental processes of
representing, analyzing, and drawing inferences from
spatial relations. These spatial relations could be relations
between objects (e.g., relations between landmarks in a
city) or relations within objects (e.g., the structure of the
DNA molecule). In addition, one could analyze spatial
relations as perceived and represented (e.g., seeing a
key structure on an engineering sketch) or, additionally,
imagine transforming spatial relations (e.g., mentally
rotating a three-dimensional [3-D] object) (Chatterjee,
2008; National Research Council, 2006).
The Role of Spatial Thinking in STEM
Learning and Achievement
Recent research indicates that spatial skills play a unique
role in predicting which students pursue STEM-related
careers. In a large nationally representative sample
(n ~ 400,000), Wai, Lubinski, and Benbow (2009) found
that spatial skills assessed in high school predicted which
students would enter a STEM career 11 years later. This
relation held even when controlling for verbal and math-
ematical cognitive skills. See Figure 1 for examples of the
spatial tests used in Wai et al. (2009).
What accounts for this predictive correlation? One
factor is probably that STEM fields directly call on these
484756CDPXXX10.1177/0963721413484756Uttal et al.Spatial Thinking and STEM
research-article2013
Corresponding Author:
David H. Uttal, 2029 Sheridan Rd., Evanston, IL 60208
E-mail: duttal@northwestern.edu
Exploring and Enhancing Spatial
Thinking: Links to Achievement in
Science, Technology, Engineering, and
Mathematics?
David H. Uttal1, David I. Miller1, and Nora S. Newcombe2
1Northwestern University and 2Temple University
Abstract
Although neglected in traditional education, spatial thinking plays a critical role in achievement in science, technology,
engineering, and mathematics (STEM) fields. We review this relationship and investigate the malleability of spatial
thinking. Can spatial thinking be improved with training, life experience, or educational interventions? Can improving
spatial thinking improve STEM achievement? Research indicates that the answer is “yes” to both questions. A recent
quantitative synthesis of 206 spatial training studies found an average training improvement of 0.47 standard deviations.
Training effects lasted for months in studies examining durability and transferred to tasks that differed at least moderately
from training tasks. A few studies indicate that spatial training can improve STEM learning, although more research
needs to be done on this issue. We argue that including spatial thinking in STEM curricula could substantially increase
the number of Americans with the requisite cognitive skills to enter STEM careers.
Keywords
spatial thinking, STEM education, cognitive training, transfer
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368 Uttal et al.
skills; that is, they require analyzing and imagining trans-
formations of spatial relations. For example, modern
chemistry depends on thinking about the functional role
of chemical spatial structures, ranging from relatively
simple molecules to complex proteins and polymers.
(See Kastens & Ishikawa, 2006, for a discussion of the
role of spatial thinking in geoscience.) Spatial skills may
also play a role in determining whether, and how well,
STEM learners and practitioners use external spatial rep-
resentations such as graphs, maps, or computer molecu-
lar models (Hegarty, 2010). In either case, given this
importance of spatial thinking in STEM fields, it is educa-
tionally important to determine which aspects of spatial
thinking can be improved and whether such improve-
ments can facilitate STEM learning.
The Malleability of Spatial Thinking
To what extent does experience with spatial tasks
improve spatial thinking? Prior research on this question
has led to different conclusions. On one hand, some
researchers have claimed that spatial training is highly
effective. For example, Sorby (2009) found that a semes-
ter of a spatial training course improved spatial skills, and
gains exceeded 1 standard deviation or roughly +15 IQ
points. In contrast, other researchers have claimed that
training effects are small or nonsignificant and do not
transfer to other, nontrained tasks (Sims & Mayer, 2002).
We aimed to resolve these diverging conclusions by con-
ducting an exhaustive search of literature on spatial train-
ing (Uttal et al., 2013). We examined 2,545 relevant
Fig. 1. Examples of spatial tests used in Wai, Lubinski, and Benbow’s
(2009) longitudinal study. Students’ scores on these spatial tests in high
school predicted which students would enter a STEM career 11 years
later. Three-dimensional spatial visualization: Each problem in this
test has a drawing of a flat piece of metal at the left. At the right are
shown five objects, only one of which might be made by folding the
flat piece of metal along the dotted line. You are to pick out the one
of these five objects that shows just how the piece of flat metal will
look when it is folded at the dotted lines. When it is folded, no piece
of metal overlaps any other piece or is enclosed inside the object. Cor-
rect answer: A. Two-dimensional spatial visualization: In this test,
each problem has one drawing at the left and five similar drawings to
the right of it, but only one of the five drawings on the right exactly
matches the drawing at the left if you turn it around. The rest of the
drawings are backward even when they are turned around. For each
problem in this test, choose the one drawing that, when turned around
or rotated, is exactly like the basic drawing at the left. Correct answer:
A. Mechanical reasoning: This is a test of your ability to understand
mechanical ideas. You will have some diagrams or pictures with ques-
tions about them. For each problem, read the question, study the pic-
ture above it, and mark the letter of the answer on your answer sheet.
Correct answer: C. Abstract reasoning: Each item in this test consists
of a set of figures arranged in a pattern, formed according to certain
rules. In each problem, you are to decide which figure belongs where
the question mark is in the pattern. To do this, you have to figure out
the rule according to which the drawings change, going from row to
row, and the rule for the changes going from column to column. The
items have different kinds of patterns and different rules by which the
drawings change. The question mark in the lower right corner of each
box shows where a figure is missing in the pattern. You are to decide
which of the five figures under the pattern belongs where the question
mark is. Correct answer: D. Adapted from “Spatial ability for STEM
domains: Aligning over 50 years of cumulative psychological knowl-
edge solidifies its importance,” by J. Wai, D. Lubinski, & C. P. Benbow,
2009, Journal of Educational Psychology, 101, p. 822. Copyright © 2009
by the American Psychological Association. Adapted with permission.
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Spatial Thinking and STEM 369
articles reporting studies on spatial training and, on the
basis of systematic criteria, included 206 of them in our
analyses. For example, we excluded studies that did not
include behavioral measures, focused only on clinical
populations, or did not use a causally relevant design
(experimental, quasi-experimental, or before-after).
About half of the included studies (54%) were unpub-
lished. Using a technique known as meta-analysis, we
combined the quantitative results of the individual stud-
ies to arrive at overall conclusions regarding the benefits
of spatial training. We asked: How malleable are spatial
skills? How long does training last? Does training transfer
to other, nontrained tasks? Do some groups of people
(e.g., women vs. men) benefit more from training?
Spatial training was effective
The overall effect size of training was 0.47 standard devia-
tions or roughly +7 IQ points. This is considered a moder-
ate effect size and indicates that spatial skills are malleable.
Many different training methods (e.g., playing video
games, practicing spatial tests, or taking an engineering
graphics courses) improved spatial skills. Although we
found large variability in training effects across individual
studies, we found no overall difference across the three
training categories we coded (video game vs. spatial task
vs. course training). Hence, a variety of training methods
can substantially improve spatial skills.
Spatial training was durable
Although most studies (67%) measured spatial skills only
immediately after training, some studies measured spatial
skills weeks or months after training. In these longitudi-
nal studies, training effects persisted despite delays of up
to 4 months (e.g., Feng, Spence, & Pratt, 2007). Of course,
those researchers may have used particularly intensive
training because they knew that participants would be
tested after a long delay. Nevertheless, those studies
show that well-designed, intensive training can have last-
ing benefits.
Spatial training transferred
We defined transfer as improved performance on spatial
tasks not directly covered in training. Transfer tasks that
were very similar to the training tasks (e.g., mental rota-
tion with 3-D vs. 2-D figures) were coded as near trans-
fer, but substantially different transfer and training tasks
were coded as far transfer (Barnett & Ceci, 2002). The
effect sizes for overall improvement, near transfer, and far
transfer were remarkably similar. In other words, partici-
pants improved by approximately 0.5 standard deviations
on nontransfer, near-transfer, and far-transfer measures.
Of course, as in studies measuring durability, studies
measuring transfer may have deliberately used more
intensive training. Nevertheless, those studies still dem-
onstrate that well-designed training can yield improve-
ments that transfer. In summary, many different training
methods can yield effective, durable, and transferable
improvements in spatial skills.
The meta-analysis also sheds light on why prior
researchers have reached divergent conclusions regard-
ing training benefits. For example, variation in control
group tasks probably contributed to the variation in
results. Some control groups included tasks that were
likely to improve spatial skills, such as practicing spatial
tests, whereas other control groups completed only non-
spatial filler tasks, such as playing the card game solitaire.
We found that control group improvements were surpris-
ingly high, often exceeding 0.4 standard deviations. As
expected, control groups with spatial (vs. nonspatial)
filler tasks improved most, and variations in the type of
control groups and how much these groups improved
affected the overall effect of training. Thus, even the
improvement in control groups speaks to the malleability
of spatial thinking; taking spatial tests in itself served as a
form of spatial training. Even though control groups
sometimes improved, training groups still improved more
overall.
Our analyses also indicated that children and adults,
as well as women and men, responded equally to train-
ing. Although children (younger than 13 years) improved
slightly more than adolescents or adults, this difference
was not statistically significant. Further research compar-
ing children and adults in the same study is necessary to
determine whether this difference represents a real devel-
opmental difference in malleability. Likewise, although
women and men improved equally, further research with
more intensive training is necessary to determine whether
intensive training can narrow the male advantage often
found in some spatial skills (Terlecki, Newcombe, &
Little, 2008).
How Does Spatial Training Work?
Researchers have proposed numerous mechanisms to
explain the large training-related improvements in spatial
skills. We consider three candidate mechanisms here.
First, training may influence task-specific or process-
specific factors such as better encoding of test stimuli
(Sims & Mayer, 2002), more efficient transformational
processes (Kail & Park, 1992), or more adaptive strategies
(Stieff, 2007). Evidence exists for each factor. However,
Uttal et al.’s (2013) findings regarding transfer rule out an
account that is only test- or task-specific. For instance,
participants would not improve on a transfer spatial test
if they improved only in encoding test-specific stimuli.
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370 Uttal et al.
Hence, any model of improvement must account for
these process-based changes as well (Wright, Thompson,
Ganis, Newcombe, & Kosslyn, 2008).
These transfer effects have also led some researchers
to consider a second possible mechanism concerning
basic cognitive resources such as spatial attention or
memory. For instance, Feng et al. (2007) found that play-
ing an action video game improved participants’ ability to
simultaneously attend to multiple locations in a large
field of view. Other research finds that video-game play-
ers can more rapidly encode and process visual-spatial
information (Dye, Green, & Bavelier, 2009)—an ability
key to many spatial tasks. Improving working-memory or
attentional resources might allow for better encoding or
transformation of the represented information (see Chein
& Morrison, 2010).
A third, but more tentative, mechanism regards how
spatial training interacts with social-psychological vari-
ables. Social-psychological factors such as spatial anxiety
(Ramirez et al., 2012), confidence (Estes & Felker, 2011),
and gender stereotypes (Campbell & Collaer, 2009; Moè
& Pazzaglia, 2006) influence spatial performance. These
findings suggest that exposure to spatial activities may
make tasks in spatial tests more familiar and therefore
less threatening or anxiety provoking. Of course, none of
these candidate mechanisms is mutually exclusive, and
the truth may lie in some interaction between them.
Can Spatial Training Improve STEM
Learning?
The studies reviewed thus far indicate that spatial think-
ing is malleable and that some forms of training can
endure and transfer to other skills. However, the majority
of the studies reviewed thus far have focused only on
spatial outcomes. As we noted earlier, spatial thinking
may play a particularly important role in STEM fields.
These fields require using external spatial representa-
tions (e.g., graphs, computer visualizations, etc.), and
there are spatial aspects to even simple STEM reasoning,
such as young children’s use of the number line
(Gunderson, Ramirez, Beilock, & Levine, 2012). Hence,
can spatial training improve STEM learning? Relatively
few training studies have directly addressed this ques-
tion, but those that have found encouraging results. For
instance, Sorby (2009) invited engineering undergradu-
ates who failed a spatial test to participate in a 3- to
4-month spatial training course that used sketching exer-
cises (see Fig. 2). Students who chose to take the course
had higher grades in several subsequent STEM courses.
Women who took the course were also more likely to
persevere in engineering rather than switch majors.
However, because students self-selected into the course,
these longitudinal differences might be explained by
other confounding factors. For instance, students who
choose to take the course may have started out with
higher levels of motivation or help-seeking attitudes.
Miller and Halpern (in press) extended this research in
two major ways: (a) using random assignment to control
for individual student differences, and (b) investigating
benefits among highly gifted STEM undergraduates (e.g.,
28% had perfect SAT Mathematics scores). Such under-
graduates are disproportionately more likely to become
STEM innovators. Compared with a randomized control
condition, Miller and Halpern found that 12 hours of
Sorby’s (2009) training improved grades in a challenging
calculus-based physics course by one-third of a letter
grade (approximately 0.4 standard deviation units). These
findings are particularly impressive because training chal-
lenged and benefitted those students who already had
high initial spatial skills. Gains in science learning were
evident up to 2.5 months after training, although they did
not last 8 to 10 months after training. In sum, the avail-
able evidence indicates that spatial instruction can
improve STEM learning in some instances (see also
Sanchez, 2012; Stransky, Wilcox, & Dubrowski, 2010).
Other Approaches to Using Spatial
Thinking in STEM Education?
The approaches described thus far focus mostly on train-
ing with abstract objects (e.g., Fig. 2) that are not particu-
larly connected to any specific STEM domain. One
important question is how these approaches could help
learners integrate spatial thinking with domain-specific
content knowledge. In this regard, it may be helpful to
develop spatial thinking in the specific educational
Fig. 2. Sample workbook problem from Sorby’s (2009) spatial train-
ing. On 2-D sketch paper, students are asked to mentally rotate the left
3-D object 90° around the indicated axis and then sketch the correct
rotation (shown in red) on the dot paper to the right. Sorby (2009)
and Miller and Halpern (in press) found that using such workbook
materials improved grades in subsequent STEM courses. Adapted from
“Introduction to 3-D spatial visualization: An active approach,” by
S. A. Sorby & A. F. Wysocki, 2003, Clifton Park, NY: Thomson-Delmar
Learning. Copyright © 2003 Thomson-Delmar Learning. Adapted with
permission.
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Spatial Thinking and STEM 371
contexts in which it used. For instance, in Kolvoord,
Charles, and Purcell’s (in press) Geospatial Semester, high
school students solved complex real-world problems by
using an interactive spatial visualization technology
known as geographic information systems (GIS). Practic-
ing scientists use GIS to solve geographic problems by
overlaying multiple layers of spatial information. For
instance, in the Geospatial Semester, one high school stu-
dent used GIS to decide how to relocate bears in the
Shenandoah National Park by simultaneously viewing
and considering mountains, food sources, and human
transportation routes. Systematic analyses of interview
data suggested that the course promoted spatial-based
approaches for solving other novel geography problems.
Other educational approaches that incorporate spatial
thinking include using sketching software to facilitate
learning of spatial concepts (Forbus, Usher, Lovett,
Lockwood, & Wetzel, 2011) or computer spatial visualiza-
tions to conduct virtual scientific experiments (Linn &
Eylon, 2011). These contextualized approaches may be
necessary for students to learn and apply the daily
practices of scientists and engineers. Training with
abstract objects may be effective only early in STEM
learning (Uttal & Cohen, 2012), and future research
should compare the merits of these different approaches.
Figure 3 indicates the potential payoff of investing in
such research. As shown, spatial training would approxi-
mately double the number of people with the level of
spatial skills associated with being an engineer. This
result indicates the need to develop evidence-based
materials for enhancing spatial thinking in both formal
and informal education.
To realize these goals, the National Science Foundation
founded the large-scale Spatial Intelligence and Learning
Center (SILC). SILC is an interdisciplinary collaboration
among several universities (Temple University, University
of Chicago, Northwestern University, University of Penn-
sylvania), involving researchers from psychology, educa-
tion, geology, neuroscience, medicine, engineering, and
several other fields. While advancing basic theory on
spatial thinking, SILC catalyzes new research that gives
both formal and informal educators the tools they
Fig. 3. The distribution of spatial skills before (dotted line) and after (solid line) spatial training. The
shaded parts of the distributions illustrate the possible consequences of training on the percentage
of individuals with spatial skills similar to those of engineers. Improving spatial skills by 0.40 stan-
dard deviations (the most conservative estimate of training improvements in the meta-analysis by Uttal
et al., 2013) would approximately double the number of people with spatial skills exceeding those
of an average engineering college graduate. Data from Wai, Lubinski, and Benbow (2009) and Wai,
Lubinski, Benbow, & Steiger (2010). Reprinted from “The malleability of spatial skills: A meta-analysis
of training studies,” D. H. Uttal, N. G. Meadow, E. Tipton, L. L. Hand, A. R. Alden, C. Warren, & N. S.
Newcomb, 2013, Psychological Bulletin, 139, p. 369. Copyright © 2013 American Psychological Associa-
tion. Reprinted with permission.
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372 Uttal et al.
need to enhance spatial thinking across the curriculum.
SILC’s Web site (http://www.spatiallearning.org) contains
resources for researchers and educators, including testing
instruments, research papers, electronic mailing lists, and
conference information relevant to spatial thinking. The
websites TeachSpatial (http://www.teachspatial.org) and
Web-based Science Inquiry Environment (http://wise
.berkeley.edu) also contains many excellent educational
resources.
Conclusions
The research reviewed in this article demonstrates spatial
thinking’s malleability and its importance in STEM educa-
tion. Improving spatial thinking can help provide the
skills necessary to succeed in STEM fields, yet a specific
focus on spatial thinking has been lacking in almost all
educational programs. Future research is needed to spec-
ify which methods of training will lead to the greatest
STEM-related improvements. Like any cognitive skill, spa-
tial thinking can improve if nurtured and supported.
Considerable effort has been made toward investigating
how to enhance relevant cognitive skills for math, read-
ing, and many other disciplines. Now is the time to add
spatial skills to this list.
Recommended Reading
Miller, D. I., & Halpern, D. F. (in press). (See References). A
randomized, longitudinal spatial training study investigat-
ing transfer to STEM outcomes among highly gifted STEM
undergraduates.
National Research Council. (2006). (See References). In-depth
recommendations for incorporating spatial thinking in K-12
education, written by a panel of experts in education, psy-
chology, geography, and geoscience.
Newcombe, N. S. (2010). Picture this: Increasing math and sci-
ence learning by improving spatial thinking. American
Educator, 34, 29–43. A concise summary of literature and
recommendations for incorporating spatial thinking in
STEM education, with a particular focus on earlier grades
in elementary school.
Uttal, D. H., & Cohen, C. A. (2012). (See References). A litera-
ture review of correlational studies investigating the rela-
tionship between spatial skills and STEM outcomes.
Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R.,
Warren, C., & Newcombe, N. S. (2013). (See References). A
systematic, quantitative review of 206 spatial training stud-
ies conducted within the past 25 years.
Acknowledgements
We thank David B. Wilson, Larry Hedges, Loren M. Marulis, and
Spyros Konstantopoulos for their help in designing and analyz-
ing the meta-analysis. We also thank Greg Ericksson and Kate
O’Doherty for assistance in coding and Kseniya Povod and Kate
Bailey for assistance with references and proofreading.
Declaration of Conflicting Interests
The authors declared that they had no conflicts of interest with
respect to their authorship or the publication of this article.
Funding
This work was supported by the Spatial Intelligence and
Learning Center (National Science Foundation Grants SBE-
0541957 and SBE-1041707), the Institute for Education Sciences
(U.S. Department of Education Grant R305H020088), and a
National Science Foundation Graduate Research Fellowship
(Grant DGE-0824162 awarded to D. I. Miller).
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