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The Lay of the Land
The Baltic International Yearbook of
Cognition, Logic and Communication
December 2015
pages 1-57
Volume 10: Perspectives on Spatial Cognition
DOI: http://dx.doi.org/10.4148/1944-3676.1099
NORA NEWCOMBE
Temple University∗
STEVEN M. WEISBERG
University of Pennsylvania∗
KINNARI ATIT
Temple University
MATTHEW E. JACOVINA
Arizona State University
CAROL J. ORMAND
Carleton College
THOMAS F. SHIPLEY
Temple University
SENSING
T HE LAY OF THE LAND:
AND R EPRESENTING T OPOGRAPHY
ABSTRACT: Navigating, and studying spatial navigation, is difficult enough in two dimensions when maps and terrains are flat.
Here we consider the capacity for human spatial navigation on
sloped terrains, and how sloping terrain is depicted in 2D map
representations, called topographic maps. First, we discuss research on how simple slopes are encoded and used for reorientation, and to learn spatial configurations. Next, we describe how
slope is represented in topographic maps, and present an assessment (the Topographic Map Assessment), which can be administered to measure topographic map comprehension. Finally, we
describe several approaches our lab has taken with the aim of improving topographic map comprehension, including gesture and
analogy. The current research reveals a rich and complex picture
of topographic map understanding, which likely involves perceptual expertise, strong spatial skills, and inferential logic.
There are many ways to navigate the spatial world. In the past
decade, we have come to rely on technology to find our destinations,
using computers and smart phones to provide step-by-step instructions
on the best route, display an overall map, or tell us which way is north
(if we choose to ask that question). But humans did not evolve in the
technological world, although they eventually created it. Our ancestors
used many cues for wayfinding. Some of these systems were part of a
common evolutionary heritage, shared with other mammals and also
with birds, insects and even with reptiles and amphibians, as would be
expected given the importance of successful navigation for survival. But
humans’ abilities for abstract and symbolic reasoning also supported
our species in the invention of complex and culturally communicated
systems (Gladwin 1970; Hutchins 1995; Huth 2013), and increasingly,
technological tools. Thus, for humans, understanding navigation entails both understanding shared cross-species capacities for navigation,
and the uniquely human symbolic additions that augment those capacities.
Modern cross-species research on navigation has generally concentrated on two navigation systems, often called the egocentric and allocentric systems (for reviews, see Jacobs & Menzel 2014; Wiener et al.
2011). These systems are distinct, but they can combine and supplement each other in various ways (e.g., Zhao & Warren 2015). Egocentric systems involve our bodily senses and body-centered encoding
of spatial location, e.g., the window is behind me. Egocentric coding
is useful for wayfinding only if it is updated by information about our
movement through space, both in terms of direction (e.g., we know
that the window that was behind us is now to our left, after we turn 90
degrees), and distance (e.g., we know that the window is now much
further behind us after we walk 100 paces forward). When egocentric
systems are updated in this way, they are often called inertial navigation
systems, or dead reckoning. Allocentric coding does not depend on the
body, but rather uses external landmarks, such as distinctive buildings
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Nora Newcombe et al.
or mountains in the distance. These landmarks are most helpful when
they are large (and hence visible), distinctive (and hence recognizable),
and, crucially, stable (or else they will be misleading). Landmarks may
be related to each other to form a frame of reference. A particularly
interesting kind of allocentric framework is provided by the geometric
shape of enclosures (for review, see Cheng et al. 2013). This tradition
of navigation research has led to many interesting discoveries and a
rapidly growing body of knowledge.
Productive as this research agenda has been, however, the dichotomy between egocentric and allocentric systems over-simplifies the
problem of navigation. For instance, research on these two systems
generally ignores things such as the positions of the sun and the stars,
the direction of the prevailing winds, and the ocean currents, information that can be used not only by human navigators lacking access to
GPS but also by many non-human species, such as migrating birds and
foraging bees. The traditional dichotomy also neglects the usefulness
of gradient cues (Jacobs & Schenk 2003). Gradient cues include scent
(Wallraff 2004), sound (King & Parsons 1999), and luminance (Petie
et al. 2011). For these cues, the intensity of the stimulus is greatest at
the source, and decreases logarithmically as the source becomes more
distal (e.g., the smell of doughnuts gets less intense as you move away
from the bakery). Such cues tell us about direction (we can follow our
nose to the bakery, or away from it). These cues also tell us about distance, through processing of the intensity’s rate of change over time
(the bakery must be very close when the smell of sugar is becoming
rapidly more intense).
The topic of this article is terrain slope, another important, yet relatively under-studied, gradient cue that can be perceived and used for
spatial orientation by birds and by other mammals. In addition, humans have invented ways to measure slope precisely, to measure the
associated but distinct concept of elevation, and to organize, integrate
and transmit these measurements using symbolic means, notably topographic maps. However, interpreting such maps is not straightforward,
and we consider how learning to interpret them can best be supported
and how the user’s level of expertise can be assessed.
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The Lay of the Land
1. ENCODING SLOPE AND TERRAIN
Slope is a gradient cue that differs from light, smell or sound. One point
of contrast is that it is multi-modal rather than unimodal, perceivable
by the kinesthetic sense (angle of the joints/muscular exertion), by the
vestibular sense (sense of balance), and by the visual system (angles
formed when a sloped terrain intersects a vertical plane). Multi-modal
input might be surmised to make slope a particularly accessible navigational cue. However, slope information turns out to be equally accessible for spatial search when presented unimodally, so the fact of multimodality does not seem to provide a significant advantage (Weisberg
et al. 2014). A second point of contrast is that slope does not consistently vary as a function of distance in the natural environment as do
gradient cues such as smell (e.g., a mountain can be steepest at its base,
midpoint, and/or apex). This fact may make slope more challenging to
use for navigation, because sensing slope does not provide information about distance or precise location. Furthermore, use of slope in
wayfinding is also complicated by the fact that most terrain involves
multiple topographical features (e.g., undulating and intersecting river
valleys wandering among hills of varying heights). Nevertheless, experienced navigators report that they seek to use the “lay of the land”
along with other cues to maintain their spatial orientation in natural
environments.
How accessible is slope as a spatial cue? Most research to date has
focused on experimental settings where there is a simple unidirectional
tilt. Slope is a potent cue in studies using pigeons, the most extensively
studied species1 , who learn a spatial search task about three times faster
on a floor sloped at 20 degrees than on a flat surface (Nardi & Bingman
2009) and who rely heavily on slope information, even when other
sources of information have more predictive power (Nardi et al. 2010).
Rats also appear to use a unidirectional slope, specifically a slope of
10 degrees, in spatial search tasks (Miniaci et al. 1999). In human
experiments, slope has been limited to 5 degrees for safety reasons,
and, perhaps as a consequence, it has seemed less accessible than in
the studies with pigeons and rats. But slope is still useful, supporting
above-chance spatial search, although there is a male advantage in using it (Nardi et al. 2011), which appears in 8- to 10-year-old children
as well as adults (Holmes et al. in press). Unfortunately, we have very
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Nora Newcombe et al.
little information for any species about more complex environments,
in which slope varies unpredictably to define complex systems of valleys and hills. But tellingly for the surmise that slope may be a difficult
navigational cue to use, only people who self-rated as better navigators
were able to use slope information to learn about complex terrain in a
virtual reality study (Weisberg & Newcombe 2014).
Overall, we can conclude that, although slope is potentially a helpful
spatial cue, it may only be variably encoded by humans even in fairly
simple situations, and that extracting the “lay of the land” for navigating
more complex terrain is likely to be yet more challenging. Perhaps for
that reason, humans have created tools to measure slope and elevation,
and have also devised symbolic representations such as topographic
maps that store and integrate those measurements. But these tools are
themselves not easy to learn to use, a topic to which we now turn.
2. SYMBOLIC REPRESENTATION OF TOPOGRAPHY
Slope and elevation are both relational concepts.
Elevation is
related to slope but is not at all the same thing.
Consider
alpine plateaus or mesas, flat structures that occur at high elevations. Elevation is seemingly simply defined as distance above
sea level, but it is actually a complex measurement to make,
partly because sea level is not as constant as one might imagine –
see http://www.youtube.com/watch?v=q65O3qA0-n4. Topographic
maps represent earth’s surfaces using contour lines, which join locations
with equal values of elevation. Slope is defined by relations among the
lines, i.e., contour lines need to be related and integrated in order to visualize the terrain. Learning to read topographic maps is difficult (e.g.
Clark et al. 2008; Rapp et al. 2007), yet skill with them is essential to
geoscience, architecture, urban design, and landscape planning (Petcovic et al. 2009), and for emergency responders, e.g., when asked to
find landing sites for rescue helicopters (Wilkening & Fabrikant 2011).
Efforts to devise ways to facilitate acquisition of skills with topographic maps have often focused on providing additional visual information, such as various kinds of shaded relief (e.g. Phillips et al. 1975;
Pingel & Clarke 2014; Potash et al. 1978), stereo effects (Rapp et al.
2007), color-enhanced contour lines (e.g., Taylor et al. 2004) or direct
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The Lay of the Land
color coding of slope (Wilkening & Fabrikant 2011). Such efforts have
typically achieved significant effects, but limited ones in terms of the
size of the performance boost and/or generalization (e. g., when the
cues are removed, contour map reading returns to baseline).
One source of guidance for how best to boost performance is descriptions of expert performance. Experienced topographic map users
report that they look for meaningful patterns rather than focusing on
individual contour lines (e.g. Chang et al. 1985; Gilhooly et al. 1988).
For example, Pick and colleagues (1995) found that when asked to locate their position in the world on a topographic map, experienced topographic map users try to match structures in the terrain (e.g. valleys and ridges) to structures on the map and vice versa. McGuigan
(1957) found that novice topographic map users who saw terrain images paired with topographic maps showed better performance than six
other groups that received alternative types of instruction on both contour interpretation (e.g. absolute and relative height judgments) and
contour visualization (e.g. determine the direction of slope). Furthermore, participants’ skill in pattern recognition was strongly correlated
with their proficiency in contour interpretation.
Guided by these descriptions, we have made several efforts to improve students’ ability to read topographic maps, all based on the idea
of using cognitive tools to support learning, rather than modifying the
materials or changing the mapping conventions. In this article, we will
briefly report on three interventions. The first two were conducted in
parallel and used gesture or analogy to support learning. Building on
the lessons learned from the first two, the third aimed to use instructional language to focus attention on one of two concepts, either forming a concept of elevation and the meaning of contour lines, or using
the contour lines to visualize the shape of the terrain. Overall, these interventions can be seen as efforts to scaffold a transition from action-toabstraction, along a continuum of progressive abstraction. These studies led us to a deeper understanding of the components of topographic
map understanding, which will require future research to evaluate fully.
2.1.
Topographic Map Assessment (TMA)
As a vital methodological prerequisite, we also developed a common
yardstick, a way to evaluate students’ ability to read and reason about
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Nora Newcombe et al.
topography that could be used across studies and hence allow for comparison among different labs and classrooms. The TMA was constructed
collaboratively by cognitive psychologists, educators, and geoscientists.
Items were created by gathering samples of topographic maps tests online and emulating the types of questions using maps gathered from
the United States Geological Survey web page http://www.usgs.gov/.
A geoscience educator checked the items for accuracy and for appropriateness for the ability levels of novices. The test consists of 23 items
with 28 possible points. (See Appendix A for the complete set of items,
and Appendix B for the scoring rubric.) It requires students to engage
with topographic maps in a variety of ways, potentially tapping multiple dimensions or levels of understanding. For example, some items
require participants to draw the direction a stream would flow between
two points, and the path it would take (e.g., items 2, 10, 11, and 12).
Other items require matching an image of a terrain to a location on a
topographic map (items 8, 15 and 16) or require knowledge about a
contour interval (the change in elevation between two contour lines;
items 5, 6, and 9). This variety taps much of the knowledge a student
would need to interact with topographic maps outside of a field setting.
We evaluated psychometric characteristics of the TMA in a large
sample of female psychology majors (N = 261), restricting ourselves to
women because they were much more common in psychology classes,
and because they showed wide variability in their ability to solve the
items, in part because they perform less well than men. In a sample that
included both sexes, we found a large gender difference on the TMA,
with men (M = 18.0, SD = 4.0) significantly outperforming women (M
= 15.2, SD = 4.1), t (78) = 3.00, p = .004, d = 0.68).
Reliability for the TMA was very high (α = .76). Furthermore, the
TMA exhibits a wide range of performance (Min = 4, Max = 27, M =
16.9, SD = 4.3) and item response theory analyses (Rasch model and
a 1-factor latent trait model) reveal that the assessment covers a broad
range of ability (see Figure 1). These are good indications that the
TMA is useful for assessing topographic map reading ability in novice
students.
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The Lay of the Land
Figure 1. IRT analyses and plots for the LTM model (top and lower left)
and Rasch model (lower right) show the test covers a broad range of
ability levels, and most items have high information (steep slopes of
items on the lower right graph). The test information function (top)
shows the test is calibrated mainly for novices, since the peak of the
curve is centered below zero.
2.2.
Can Gesture Improve Topographic Map Reading?
Gestures help novices solve complex 3D spatial problems such as understanding block diagrams in the geosciences (Atit et al. 2015), and translating between different 2D diagrams of organic molecules in chemistry
(Stull et al. 2012). The effect of gesture may be based on several factors.
First, gesture helps learners to focus attention on critical information
(Alibali & Kita 2010; Sauter et al. 2012) and to reduce cognitive load
(e.g. Goldin-Meadow et al. 2001). Second, in so far as gestures are actions, they provide an embodied grounding to learning, but they are not
just actions—they are also symbolic and hence are on the continuum lying between action and abstraction (Goldin-Meadow & Beilock 2010).
They can directly represent some complex spatial relations, such as rel-
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ative orientation and shape (Atit et al. 2014). Furthermore, they represent in a way that allows for symbolizing continuous and analogue,
not categorically (like language). Perhaps because of their abstraction
away from action, gestures are known to promote generalization and
retention (Novack et al. 2014).
Building on video analyses of expert geoscientists describing topography (Atit et al. 2013), we used two kinds of gestures to attempt to
highlight relevant information on topographic maps, using the map
shown in Figure 2. We presented gestures paired with the maps as well
as with physical models of the maps’ 3D structure, as shown in Figure
3, because of observations that models may support spatial learning
(Alles & Riggs 2011; Stieff 2011). That is, both interventions used the
models as part of the instructional package. One kind of gesture was
the pointing and tracing gestures often used to focus a listener’s attention to spatial information (e.g. Atit et al. 2014; Heiser et al. 2004;
Lozano & Tversky 2006), used here to highlight relevant patterns. The
pointing and tracing gestures were used to highlight relevant contour
patterns on topographic maps. The other kind of gesture was the hand
shapes shown below in Figure 4. The hand shapes were used to represent the 3D structure (also represented by a 3D model) of relevant
terrain features. There were two comparison groups, one that received
basic text-based instruction on topographic maps, and one that received
no instructions.
The Lay of the Land
10
Figure 2. An image of the Sample Map used during instruction, a topographic map adapted from Bennison & Moseley (2003) that contains contour patterns representing a hill, a valley, and steep and gentle
slopes.
Figure 3. Images of the three aligned models of the structures represented on the Sample Map: from left to right, hill, valley, and steep and
gentle slopes.
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2.3.
Figure 4. Images of the gestures used by the experimenter during instruction for the 3D Visualization group: from left to right, the gesture
of a hill, the gesture of a valley, and the gesture representing slope (the
angle of the hand varied depending on whether a steep or gentle slope
was represented).
We found that the basic textual instruction was helpful: students
who read the passage did better on the TMA than students who dived
into the TMA without preparation. But the Point-and-Trace group, where
gestures were used to draw attention to contour patterns, performed
better than either control group. The 3D Visualization group, where
gestures represented the 3D shapes directly, performed better than the
No Instruction group, but its performance did not significantly exceed
the Text-based Instruction group. On the other hand, its performance
was also not significantly lower than the Point-and-Trace group, suggesting some modest level of effect not large enough to detect even
with a substantial sample.
One possible reason why Point-and-Trace was most clearly helpful
is that these gestures draw attention to the contour lines that define
elevation categories, in the same way that color highlighting or shading
does. Because they are active delineations of the lines and their shapes,
these gestures may both solidify the notion of elevation and encourage
the abstraction of the visual patterns collectively defined by the lines
and how they map onto terrain shape. Speculatively, discriminating the
terrain features that are captured by the shape gestures could be a skill
that emerges later in the acquisition of fluency in reading topographic
maps.
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The Lay of the Land
Can Analogy Improve Topographic Map Reading?
Our other initial intervention study aimed to capitalize on the role of
analogy and comparison in spatial learning (e.g., Markman & Gentner
2001). Participants were randomly assigned to one of two groups. In a
Topomap group, participants were shown sets of images of virtual environment 3D terrains and their corresponding topographic maps (i.e.,
numbers 1-4 in Figure 5 were shown at one time; then a second set
of four images was shown depicting a different type of terrain). They
were then asked to write down similarities and differences between the
3D terrains and between the topographic maps for each set of four images. In a Verbal group, participants were given a verbal analogy quiz
as a filler task, and asked to complete as many analogies as they could.
Timing was yoked to the amount of time a participant in the Topomap
group took on the comparison task. Both groups then completed the
TMA. But unfortunately, the two experimental groups did not significantly differ on the TMA. Why did the analogy intervention not work?
One possibility is that it was insufficiently strong. Participants did not
receive many problems, and never explicitly compared the topographic
maps with the corresponding 3D visualizations.
Figure 5. Sample stimulus for Analogy Study
However, there was one intriguing result of this study. We analyzed the language used to describe the similarities and differences in
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Nora Newcombe et al.
the Topomap group during the comparison task, with particular attention to the words ’elevation’, ’shape’, ’color’, ’slope’, ’height’, and ’line’.
We then tested whether participants in the Topomap group who used
a specific spatial word (e.g., ’elevation’) performed better (or worse)
than participants who did not use that word. Using a Bonferroni correction for multiple comparisons, the only word that showed a significant difference was ’elevation.’ That is, participants who used the word
elevation in describing the similarities or differences between the two
maps performed significantly better than participants who did not use
that word, and significantly better than the Verbal group. These findings were intriguing, but only correlational. We could not determine
whether participants who used the word elevation already understood
topographic maps, and were using appropriate language to describe
the knowledge they had, or if the comparison drew some participants’
attention to a relevant feature (’elevation’), but not other participants.
In addition, participants who used the term ’elevation’ performed
better on a particular subset of items from the TMA. Particular items
from the TMA differentially focus on analyzing the concept of elevation
or on visualizing the terrain in 3D. Two cognitive psychologists and two
expert geoscientists coded each item for whether it was more likely to
require knowledge about Elevation or knowledge about the Shape of
the terrain. There was consensus for the four coders on 16 out of 28
items, 9 of which were coded as Shape, 7 of which were coded as Elevation. Participants who did use the term elevation outperformed control
participants on Elevation items, but not Shape items. Participants who
did not use the term elevation performed worse than control participants specifically on items requiring knowledge about elevation, but
equally on items requiring visualization.
2.4.
Analyzing Elevation or Visualizing Terrain?
The results of the gesture study suggested that point-and-trace gestures
are especially well-suited to supporting topographic map reading. One
possible reason is that they focus attention on the contour lines and encourage the formation of a concept of elevation. The importance of such
a concept is also potentially at the source of the correlation found in the
analogy study between use of the word elevation and better TMA performance. In addition, however, the point-and-trace gestures may have
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The Lay of the Land
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actually done a better job than the shape gestures of highlighting the
shape of the terrain. Following the contours with a finger may demonstrate their 2D shape and allow extraction of the 3D shape. Given this
reasoning, we decided to do a study in which we held gesture constant
and varied language in order to focus learners’ attention either on elevation or on shape.
We devised three conditions in a between-subject design. In the
Visualizing condition, participants were encouraged to focus on the
shape of the contour lines, and imagine how they might look in 3D.
In the Analyzing condition, participants were told that each contour
line represents one value of elevation, and to consider that the concept of elevation implies that as contour lines are closer together, elevation changes more quickly. In both conditions, participants imitated
pointing and tracing gestures (the same gestures as those used by the
Point-and-Trace group in the experiment described earlier) made by the
experimenter, and then answered questions about a sample map using
their own gestures. Participants in the control condition received no instruction, but saw the same stimuli, were asked open-ended questions
about each map, and were allowed to gesture if they chose (although
doing so was not specifically encouraged). Condition assignment was
pseudo-randomized and counter-balanced for map experience based on
reports of experience with topographic maps (on a scale of 1-7).
The Visualizing and Analyzing conditions both outperformed the
Open-ended condition on the overall TMA. However, the two groups
turned out not to have learned the same things. Using the same Shape
and Elevation item coding as before, participants in the Visualizing condition performed well on Shape items relative to other conditions, but
poorly on Elevation items, and conversely participants in the Analyzing condition performed poorly on Shape items but well on Elevation
items (see Figure 6). Data from the Open-ended condition showed that
participants in the Visualizing condition were at baseline for Elevation
items, whereas participants in the Analyzing condition were at baseline
for Shape items.
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The Lay of the Land
by clarifying the nature of the developmental or learning progression.
Is there in fact a sequence from perception (side views, aerial views, action) to 3D models to 3D ziggurat-like models (as we used) to schematic
depictions to gestures to symbolic representations (i.e., the conventions
of contour lines, or words such as elevation)? Does the order in which
gestures, models, and perspective views are offered affect the development of skills in topographic map understanding? For example, perhaps
first using pointing and tracing gestures to learn how to find contour
patterns followed by using 3D gestures and models to help visualize
the structures would be an effective progression, or perhaps shape and
elevation can be learned independently. We are only at the start of the
journey to understand how to understand the lay of the land.
Figure 6. Differential advantages for the Visualizing and Analyzing
groups on Shape versus Elevation items from the TMA.
3. CONCLUSIONS AND FUTURE DIRECTIONS
There are two broad types of future directions suggested by this research. There are many possible ways to help learners new to topographic maps. For example, we could begin the action-to-abstraction
sequence by embodied grounding in action, providing active slope experience on a tilted treadmill to instantiate what certain degrees of
slope feel like. Those degrees could be communicated perceptually
with visual images of those slopes in an actual landscape or videos of
mountain paths, schematically using tilted lines, or symbolically using
number of degrees or how close together contour lines would be for
that degree of slope. As another example, people might benefit from
using both point-and-trace and shape gestures while solving problems
on the TMA. As a third example, people working with TMA-type items
could be asked to predict observer view, or predict stream flow and so
forth, but then see the correct answer immediately, perhaps with an explanation. Prediction with feedback and explanation helps learning, as
does viewing worked examples.
Another, and complementary, avenue is to follow up these findings
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ACKNOWLEDGEMENTS
Authors marked with ∗ contributed equally. This work was supported
by National Science Foundation grant SBE 10-41707 to the Spatial Intelligence and Learning Center. Thanks to David Rapp for comments
on draft TMA items, and Dedre Gentner for discussion of the analogy
study.
Notes
1
This choice of species may seem odd: given that birds can fly, why would they make
extensive use of a ground-based cue? However, pigeons forage for food on the ground,
and spend a considerable amount of time on their feet rather than on wing. Furthermore,
their claws allow them to grip tightly even on steep inclines, allowing for the effect of
slope to be studied with a wide degree of variation.
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Topographi Map Assessment
Developed by Matt Ja ovina, Carol Ormand,
Thomas F. Shipley, & Steven Weisberg
Please
omplete this 18-item assessment. The assessment is not
timed. Try to answer ea h item to the best of your ability.
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APPENDIX B
Topographi Map Assessment
Developed by Matt Ja ovina, Carol Ormand,
Thomas F. Shipley, & Steven Weisberg
Please
omplete this 18-item assessment. The assessment is not
timed. Try to answer ea h item to the best of your ability.
www.thebalticyearbook.org
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