Initiative 2:
Understand tools for spatial learning

Initiative Coordinators: Dedre Gentner (Co-PI), Susan Goldin-Meadow (Co-PI), Terry Regier

There is a large literature on improving spatial skills using a wide variety of techniques. One important project that SILC conducted early on was a meta-analysis (Uttal et al., in press. Temporary Link.) to bring us up to date on what was known so far. We needed to know how much improvement is possible, whether improvement lasts, whether it transfers to other skills or contexts, and whether it works equally well for children and for adults and for men and women. This meta-analysis showed us that previous research provides answers to some important questions. For example, there are moderate-to-large effects of spatial interventions that have proven durable and showed transfer. However, we also found that more focused research was needed, particularly concerning the effects of spatial tools on spatial learning and how they produced their effects. Prior research had focused either on simple practice or had utilized real-world interventions (such as taking courses) that constitute a "package" of techniques that are not well specified or analyzed.

The goal of Initiative 2 is to discover which tools can most effectively be applied to spatial problems. We chose the specific tools we study – analogy, language, gesture, sketching, and maps/diagrams – because they highlight the role of relational information that is at the core of spatial reasoning. Importantly, different tools do this in different ways, some primarily highlighting the quantitative, continuous nature of spatial information (gesturing, sketching, maps and diagrams), others primarily highlighting the qualitative categorical nature of spatial information (language), and yet others highlighting both (analogy). An important goal that extends from Initiative 2 into Initiative 3 is to understand which tools, and which combinations of tools, are optimal for solving particular kinds of spatial problems. Initiative 2 focuses on characterizing the tools themselves and testing whether and how they promote spatial learning, providing crucial information for Initiative 3, exploring which tools and combinations of tools are most effective for improving spatial learning for different groups and for different stages of learning.

We begin with a very general tool: analogical reasoning. Analogical comparison and mapping is a powerful domain-general learning mechanism for causal and conceptual learning. We are systematically investigating its application to spatial learning. A central notion of analogy is the alignment of two structures, an idea that is particularly appropriate for spatial learning and transfer. When two situations are compared, their common relational structure is highlighted, facilitating transfer to new contexts. Our goal is to exploit the spatial alignment of two structures to facilitate learning. For example, we have found that providing children with two model buildings that can be spatially aligned makes it more likely that the children will discover how important a diagonal brace is in creating a stable structure. Analogical processing is also crucial in mapping from spatial structure to other domains, as in graphs and diagrams. For example, explicit instruction in analogy can help children learn how to relate the spatial dimensions in a graph to the corresponding dimensions in the world.

The second tool––language––is also very general and widely used in non-spatial domains. Learning particular words, and activating those words during problem solving, has been shown to facilitate thinking in non-spatial domains (Gentner & Goldin-Meadow, 2003). But language has two aspects that make it potentially relevant for spatial learning. First, languages contain words that convey spatial relations (e.g., in, on, under, through, etc. in English). These words impose categorical structure on the spatial world. Learning and using these words is likely to affect how spatial relations are categorized and thus has the potential to facilitate (or hinder) spatial thinking. Second, syntactic devices that organize words into frames can be applied to spatial situations (e.g., the sentence, the cat is on the mat, focuses attention on the figure, cat, which is situated in relation to the ground, mat; in contrast, the sentence, the mat is under the cat, focuses attention on the mat as figure, and situates it in relation to the cat as ground). Thus, language can be used to organize space in a particular way, which could serve as a tool for spatial thinking. Indeed, cross-linguistic research suggests that the way a language describes spatial relations may influence the particular spatial reference frame that speakers of that language routinely use (e.g.,  Levinson, 2000;  Haun et al.,  2005).

The third tool we are exploring is naturally produced with high frequency when we speak about spatial or non-spatial situations: gesture. Gesture is inherently spatial, as it is produced in a spatial format. Gesture is interesting as a spatial learning tool because it can capture the imagistic and continuous aspects of space that are often lost when a spatial situation is described in language (e.g., saying turn right indicates the direction the listener should take but does not convey whether the turn is a hard or soft right, information that can easily be conveyed in gesture). Gesture can thus add continuous information to the categorical information in language. With respect to young children who are learning spatial language, gesturing that accompanies spatial terms may be particularly helpful because it often transparently conveys the meanings of these terms. For example, in the context of talking about a tall building, an accompanying gesture that reaches over the head or that points to the top of the building can help teach the child the meaning of tall (e.g., Cartmill et al., 2010). Moreover, when learners are encouraged to gesture while explaining their solutions to a math problem, they are subsequently more likely to profit from a lesson in how to solve the problem than if they are not told to gesture (Broaders et al., 2007). Since gesture is frequently produced when describing spatial situations, it is a resource that has the potential to be harnessed in the service of spatial learning.

Our fourth tool––sketching––is inherently spatial, and, like gesture, can easily capture continuous information. Sketching, however, leaves a permanent trace, allowing students and teachers to externalize and communicate ideas naturally within an intrinsically spatial format. Indeed, teachers in STEM disciplines often use sketches in instruction, and state that students’ sketches are deeply revealing of their degree of understanding. Yet up to now, the great potential value of sketching in STEM instruction has not been realized. This is partly because scoring sketches is extremely time-consuming for instructors, but also because the time course of drawing is lost when pencil and paper are used to sketch. Recent studies show that the order in which students draw the parts of a diagram is highly revealing of their understanding (e.g., Jee et al, 2009). Moreover, there is ample evidence that intelligent tutoring systems and learning environments can provide significant benefits to learners. But such systems are rarely developed for spatial learning, in part because the science base needed to support sketching for interaction is missing. Consequently, one of SILC’s strategic goals is the creation of a platform for sketch-based educational software. The system we are creating, CogSketch, has two interlocking and synergistic purposes. First, CogSketch is a cognitive science research instrument. In laboratory experiments, it enables us to gather data more effectively to explore how sketching can be used in assessing and improving learning. In computational simulation experiments, it enables us to model spatial skills and learning processes. These efforts help accelerate our research, but as an added benefit, provide improvements to the system’s processing and interfaces that are needed to support its educational role. The second purpose, supporting STEM education, is described in Initiative 4.

Our fifth tool is spatial displays that often begin with sketches, but which are typically developed and codified using social conventions. Displays of this kind---maps and diagrams––are, like gesture, inherently spatial. However, as with language, maps and diagrams also have systematized conventions that, once understood, can facilitate learning. Understanding how external media such as maps and diagrams influence spatial learning and reasoning is crucial to improving spatial learning. Maps highlight spatial relations that can be difficult or even impossible to perceive on the basis of direct experience. For example, by looking at a map, one can easily see the relative spatial position of several cities across the United States, information that would be difficult to acquire directly from experience. The unique perspective and scale of maps make spatial relations that are not directly perceptible cognitively tractable. Maps can also be used to convey non-spatial information as a function of locations in space (e.g., precipitation as a function of location). Diagrams and charts take this process one step further; they allow us to display any type of information in a spatial format. Understanding the spatial conventions needed to interpret maps and diagrams is essential to becoming proficient in the STEM disciplines. For example, developing skill in geoscience depends on knowing how to understand and use complex maps, including Geographic Information System (GIS), that represent three-dimensional topography. Thus, one of the goals of SILC is to understand the challenges that learning from maps and other spatial representations present to learners.

Although we began by developing each tool on its own, our goal is also to understand how these tools can be used together to create synergies in spatial learning. For example, understanding how to use a map involves aligning the map with the space it represents, a clear case of analogical reasoning. To extend the example, in certain cases it may be possible to use gesture or spatial language to make the alignment explicit, thereby facilitating the comparison process. Initiative 3 will further explore how to best combine our spatial learning tools for maximum effect.

SILC is exploring how these five tools, alone and in combination, can accelerate spatial learning. Importantly, we are also investigating how these spatial tools can be applied to non-spatial problems. Diagrams and graphs are an obvious example because they can convey non-spatial information in a graphic format that makes complex relations among categories relatively transparent and thus easier to understand and manipulate. For example, using a line graph to display average improvement after instruction in children ages 5 through 10 and in adults, with separate lines for males vs. females, would allow one to see at a glance whether males improve more than females, and whether the size of the gap increases, decreases or remains constant across age. In this case, spatializing the ideas has made them more tractable. Even our less conventional spatial tools can be used to spatialize ideas. For example, when talking about complex kinship relations, speakers have been found to use hand gestures to lay the kinship scheme out in the air, a kind of “air sketch” (Enfield, 2005). The gestures make it easier for listeners to grasp the system and understand who is related to whom; they may even make it easier for the speakers to describe the system. Thus, gesture has the potential to spatialize ideas that are not inherently spatial, allowing mechanisms that are particular to space to be brought to bear on these non-spatial ideas. One of the themes of SILC is that introducing tools that encourage learners to spatialize their ideas will have beneficial effects on thinking and learning.

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