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Have you ever seen a car that has been in an accident and tried to imagine what happened? Often it is possible to work backwards from the current shape of an object to deduce what happened to it, e.g., a head on collision with a tree. This reasoning requires a spatial cognitive skill - a mental transformation of an object. Mental transformation refers to the ability to alter an internal representation of an object in order to imagine what that object used to look like before some event or what it might look like in the future.

We are studying how people develop this skill. One avenue of our research has been to study mental transformation in experts. Strong mental transformation skills are essential in the field of geology. Geology is a historical science that takes what is observable and tries to deduce what has happened over time to result in the current state of affairs. In particular, geologists use the present spatial relations to figure out what transformations have occurred. This mental reasoning may take place at many scales, from tectonic to microscopic. For example, field geologists study the deformational history of rocks and regions by studying the spatial configuration of geological features in an outcrop and how they fit with other observations in a surrounding area. Just as the bent and rent metal of a car tells a story, so too the geological history is revealed by the bends and breaks, folds and faults, in rocks. (see fig. 1).

The current line of research aims to understand how expert geologists reason about mental transformations. Geologists self-report that they look at an outcrop and play back in their mind the sequence of transformations, mentally animating the transformations from the present spatial configurations back to horizontal sedimentary layers. An initial study examined if geologists are objectively able to make such mental transformations, and, if they are, is the skill domain specific or domain general. Previous studies of chess expertise (Chase & Simon, 1973) suggest that expert reasoning is domain specific, in which case geologists should only be able to perform mental transformations on objects that have been altered in geologically relevant ways. In contrast, if geologists are able to perform mental transformations on any object independent of the type of alteration it suggests they have a domain general skill.

Geologists (n=16) were compared to two control groups from other academic fields. All groups had the same level of education (Ph.D.). One control group came from another science that requires spatial reasoning (Chemists, n=14) and one that requires verbal reasoning (English Professors, n=10). The participants were presented with words that were transformed in one of three ways, and asked to identify the word. To make the task more demanding additional characters were added in between each letter of the word (see fig. 2). Words were broken up into pieces along diagonal lines. These pieces were translated as if faulted (see fig. 3) or were randomly displaced (see fig. 4).

Geologists were significantly better than both control groups suggesting the geologists have a domain general ability to make mental transformations that is superior to novices (Shipley et al, 2009). One explanation for this skill is that geologists are particularly good at disembedding - finding and attending to specific structures within a complex array. We tested this with another set of words where the transformation separated all of the pieces making it easier to see which pieces belonged together and thus mentally undo the transformation (see fig. 5).

All three groups performed better on these words, however Geologists still outperformed both control groups. This finding suggests that while disembedding is helpful for this task, it is not the sole explanation for the Geologist’s skill.

Geologists report that students often have trouble mentally transforming spatial structures. By characterizing this skill, we should be able to help educators provide students with strategies for visualizing such transformations. However, it is not yet clear what about geoscience education produces this skill. Future studies will examine how mental transformation skills develop, and study its importance for student retention and achievement.

References

• ♦Chase and Simon. (1973). Perception in Chess. Cognitive Psychology, 4.
• ♦Shipley, T., Manduca, C., Resnick, I. & Schilling, C. (2009, November). Expertise in Spatial Visualization: Can Geologists Reverse Time? Psychonomic Society, Boston.

LINK TO PRESENTATION:
Breaking the Mold: Altering Preschoolers’ Concepts of Geometric Shapes

Children’s early shape concepts represent the building blocks for later mathematical knowledge (Clements & Sarama, 2007). As preschoolers begin labeling shapes in their environment, they must distinguish features and patterns and create abstract categories of each shape. Yet young children find this very difficult! Preschool children start out categorizing shapes by visual similarity and orientation irrespective of geometric properties (Burger & Shaughnessy, 1986). These concepts are global and holistic in nature, in which the most salient shape properties bind together to form an overall feature or a ‘gestalt view’ of each shape (Ganel & Goodale, 2003; Keil, 1989; Smith, 1989; Tada & Stiles, 1996). For instance, the angle on top of a typical triangle is the most distinguishing feature and thus defines the overall concept for the child (e.g., triangles have a point on top and wide horizontal ‘bottoms’). If children see a triangle that is turned on its side or has irregular angles (e.g., obtuse, scalene triangles), they will say it is not a true triangle. Only later do they shift to rule-based classification systems that rely on the number of sides or angles for shape identification (Clements, Swaminathan, Hannibal, & Sarama, 1999; Keil, 1989).

In a series of studies we explore how different learning experiences influence children’s developing shape concepts. In one such study, we examine how dialogic inquiry (i.e., questions that pose a dilemma/prompt curiosity) and physical exploration influence preschool children’s shape learning.

Preschool children were randomly assigned to one of three groups. In guided play, the experimenter helped children ‘discover’ each shape’s features by asking questions and prompting physical exploration of circles, triangles, rectangles, and pentagons (+dialogic inquiry, + physical exploration). In direct instruction, children were taught rule-based classifications for shapes in a passive learning style (- dialogic inquiry, -physical exploration). In the control condition, children participated in a dialogic reading activity for approximately the same amount of time as the shape lessons. To assess shape knowledge, groups were asked to complete a shape sorting task (Satlow & Newcombe, 1998). Children were shown 10 novel instances of typical, atypical, and nonvalid forms of each shape (40 total) and asked to place ‘real’ instances of each shape in a special box and the ‘fake’ shapes in a trashcan.

To determine the extent children’s category decisions were guided by rule-based classification systems versus visual similarities, rates of rejection were calculated across typical, atypical, and nonvalid shapes. As hypothesized, children in the control condition appeared to rely on visual similarity when sorting shapes, signified by small rejection rates of typical shapes and larger rejection rates for atypical and nonvalid shapes (see Figure 1). Conversely, children in both experimental conditions used rule-based classification systems to sort shapes, indicated by small rejection rates for typical and atypical shapes. Also, guided play showed a slight advantage over direct instruction. In Figure 2, guided play and direct instruction appear equal in learning outcomes for simple, familiar shapes (e.g., circles), yet children in the guided play condition showed significantly superior geometric knowledge for a novel, highly complex shape (pentagon).

These results suggest both direct instruction and playful learning approaches promote rule-based shape concepts; however, guided play may be more advantageous for complex concepts. Future research should explore how guided play may facilitate knowledge acquisition and concept formation for complex concepts in other domains. Additional research should explore the differential impact of dialogic inquiry and active exploration on the learning process.

Recent research shows that the spatial language parents use when talking to their children predicts their child's spatial language development (Pruden & Levine, in preparation). But parent spatial talk does not fully account for child spatial language. This study investigates whether the gestures parents produce along with spatial language have added value in predicting children's acquisition of spatial language, over and above spatial language alone.

There are several reasons to expect that this may be the case. First, with respect to language acquisition in general, children are sensitive to the gestures of others in both conversational and pedagogical situations (Goldin-Meadow, 2003). At home, parents' gestures predict children's gestures and, in turn, their vocabulary size (Rowe & Goldin-Meadow, 2009). In instructional situations, children learn more from spoken instruction if it is accompanied by gesture than if it is not (Church, Ayman-Nolley, & Mahootian, 2004; Valenzeno, Alibali, & Klatzky, 2003). Moreover, children can learn from gesture even when it conveys information that is not conveyed in speech (Singer & Goldin-Meadow, 2005). Second, gesture may be particularly good at conveying spatial information as it itself is highly spatial and thus has the potential to highlight and enhance the spatial information encoded in speech. That is, gesture may be particularly well suited to helping the child acquire spatial language because, unlike language, it easily captures the continuous nature of spatial information. For example, when talking about a "tall building," it is possible to provide cues to the meaning of the word "tall" by producing an over-the-head gesture, or by pointing to the top of the building. Finally, parents routinely produce gestures along with their spatial talk, providing children with the opportunity to learn from gesture (Levine, Ratliff, Huttenlocher, & Cannon, under review).

Using data from 52 parent-child dyads, we examined parent spatial talk, and the gestures that accompanied this talk, produced during naturalistic interactions at home recorded at 8 time points from 14-42 months of age. We focused our analysis on deictic and iconic gestures as they had the greatest potential to represent space or indicate spatial features of the environment. We also examined the child's use of spatial language during these interactions. For both parents and children, we focused on three categories of spatial talk: dimensional adjectives (e.g., big, little, tall, short), shape terms (e.g., circle, square), and spatial features (e.g., straight, curved, bent, flat). We addressed two specific questions: (1) Do parents differ in the amount of gesture used during spatial language? (2) If so, do differences in how often parents use spatial language with gesture, compared to how often they use it without gesture, provide added value in predicting children's spatial language production?

Parents varied widely in how often they produced gestures along with their spatial utterances. On average, parents gestured with 16% of their spatial utterances, but some parents never gestured and one gestured 44% of the time. Using a multiple linear regression, we found that the number of spatial utterances parents produce accompanied by gesture significantly predicted children's spatial word types, controlling for parent spatial utterances without gesture and parent non-spatial utterances (Β = .65, p < .01).

Using a multiple linear regression analysis, we found that parent spatial utterances with gesture, parent spatial utterances without gesture, and parent non-spatial utterances as predictors of children's spatial types. Model 1 showed that the total number of parent spatial utterances that were accompanied by gesture significantly predicted children’s spatial types from 14 to 42 months and accounted for over 34% of the variance in children’s spatial types (Β = .60, p < .001). Models 2 and 3 show that parent spatial utterances with gesture remained a significant predictor of child spatial types even after we controlled for parent spatial utterances without gesture and parent non-spatial utterances.

Gesture may be even more helpful in the context of spatial words than in other contexts. Unlike spoken language, gesture is well suited to capturing the continuous information of the spatial world. For example, gesture has the potential to play a targeted role in the acquisition of spatial language by illustrating the spatial notions reflected in speech—producing a curved gesture while saying that the puzzle piece is curved could help the child figure out what the word curved means.

Our findings demonstrate that parent gesture produced in the context of spatial talk is related to children's spatial language. However, this relationship is correlational: the findings do not show that parent gesture produced along with spatial talk plays a causal role in fostering child spatial language. Our current research attempts to explore the causal role between these variables by manipulating the type of input children receive in a spatial context—puzzle play— to better identify the respective contributions of spatial language and gesture in children's acquisition of spatial language.

Cross-sectioning, also referred to as “penetrative” thinking (Kali & Orion, 1996), is a particular spatial visualization skill that involves inferring a 2D representation of a 3D structure, and vice versa (Cohen & Hegarty, 2007). This imaginary slicing of a 3D object to a 2D plane is an essential skill for many of the sciences, ranging from anatomical cross-sections in biology and neuroscience to cross-sections of landforms in geology (Cohen & Hegarty, 2008). However, the development of cross-sectioning ability has not been uniquely identified in relation to other measures of spatial ability (e.g., mental rotation), in part because of a lack of adequate measures and the unknown age at which this ability emerges. Thus, we do not know the developmental trajectory of cross-sectioning skills and how this skill relates to spatial ability more broadly.

In our current study, we created a new method for assessing cross-sectioning skills in young children by using brightly colored foam shapes as the stimuli (see Figure 1 for the sample item). We also measured children’s performance on a mental rotation task and the water-level task. Finally, we contrasted cross-sectioning performance using the real 3D objects with a 2D method using photographs of the actual shapes. Thus, we aim to successfully measure children’s cross-sectioning skills to determine a) how cross-sectioning skills develop between the ages of 3 and 9 years, b) the association between cross-sectioning skills and other spatial reasoning tasks, and c) how the method of assessment impacts performance.

Children successfully completed the cross-sectioning task using both the 3D and 2D methods. This suggests that children do reason about cross-sections and this ability can be assessed. Further, this ability develops over time as evidenced by a significant increase in performance with age. Difficulty of test items generally represented two categories: congruent items were easier in that the cross-section resulted in a similar shape to the overall object (e.g., cone cut vertically to result in a triangle cross-section), whereas incongruent items were harder due to the cross-section resulting in a different shape than the overall object (e.g., pyramid cut horizontally to result in a square cross-section).

Positive correlations between the mental rotation and cross-sectioning tasks were present across the 5 to 8 year age range. However, when controlling for age, mental rotation was not a significant predictor of cross-sectioning performance, which suggests these tasks are not measuring the same skills, particularly in children younger than 8 years old. Further, there was no significant correlation between performance on the cross-sectioning and water-level tasks. Thus, cross-sectioning ability is somewhat independent of both spatial perception and mental rotation. Additionally, there was a benefit of using the 3D task but only for 5-, 6-, and 7-year-olds. The 3- to 4-year-olds and 8- to 9-year-olds performed equally well using both versions of the task. We are currently examining if preschool children rely on a simple shape matching strategy rather than a spatial visualization process, and whether cross-sectioning is related to a more general spatial visualization skill by comparing cross-sectioning performance to performance on a version of a paper folding task that is appropriate for young children.

Pencil and paper worksheets are a staple of education. But drawings are hard to grade, and pencil and paper worksheets cannot provide feedback based on what a student is doing. A new technology developed by SILC researchers, sketch worksheets, uses artificial intelligence software to provide immediate feedback to students and help instructors with grading. For the first time Fall quarter, sketch worksheets were used as part of student work in a real course. This pilot experiment is a first step towards making sketch worksheets broadly available in education.

Why make sketch worksheets? Results from artificial intelligence in education research indicate that software tutors can provide significant benefits for students, in part by providing immediate feedback. Unfortunately, intelligent educational software has rarely been built for spatial domains. A major barrier is that the software needs to be able to see a student’s sketch the way a teacher would. SILC research is tackling this problem head-on, by creating CogSketch, a new kind of sketch understanding system. CogSketch incorporates models of human visual processing and spatial reasoning, based on cognitive science research in AI, cognitive psychology, and vision science. (For an example of CogSketch's visual processing abilities in action, please see the April 2009 showcase.)

Understanding the sketch is half of the problem. The other half is providing feedback to students, and assessment information to instructors. Sketch worksheets incorporate a hidden sketch, made by an instructor, providing a kind of “answer key” for the worksheet. This sketch is compared against the student’s work. The similarities and differences between them provide the basis for feedback. The comparison process itself is based on a cognitive model of human analogical matching, also developed by SILC researchers. Worksheet authors can specify what feedback CogSketch should provide to students based on this comparison, as well as provide grading rubrics for assessment.

To refine the software, the CogSketch team worked with Prof. Brad Sageman, Professor of Earth and Planetary Sciences of Northwestern University, to create sketch worksheets for his Physical Geology course. The first assignment was for extra credit, involving worksheets where students identified faults and their properties in photographs of geological sections, and reconstructed a sequence of geological processes based on a diagram. The first assignment went sufficiently well that a second assignment, this time required, was developed, where students sketched the reservoirs and flows of the carbon cycle, annotating it with the magnitudes of the flows. Students were able to use sketch worksheets with only minimal training, and the CogSketch team got valuable feedback that has helped them refine the software to make it better for future users.

This is the first step on a long journey: Many further studies will be required to improve the software and the cognitive models it relies on, to find out how we can best improve student learning. We hope that this journey leads to sketch-based educational software that helps students learn spatially.

To find out more:

CogSketch is publicly available from SILC’s web site (www.spatiallearning.org). The download contains sample worksheets and the full worksheet authoring environment.

A paper on sketch worksheets will be presented at the Innovative Applications of Artificial Intelligence conference in July.

• ♦Yin, P., Forbus, K., Usher, J. Sageman, B., and Jee, B. (2010). Sketch Worksheets: A Sketch-based Educational Software System. 22nd Annual Conference on Innovative Applications of Artificial Intelligence, July, Atlanta.

• ♦Forbus, K., Usher, J., Lovett, A., Lockwood, K. & Wetzel, J. (2008). CogSketch: Open-domain sketch understanding for cognitive science research and for education. In the Proceedings of the Fifth Eurographics Workshop on Sketch-Based Interfaces and Modeling. Annecy, France.

When was the last time you got lost? Have you ever travelled to a new place without a map only to find that minutes later you were wandering around desperately looking for a familiar landmark or a person who can orient you? Have you ever taken the subway to a different part of town and exited to the street level only find yourself completely disoriented? Why is it that we all have that friend who is constantly getting lost sometimes even in his/her hometown? At the same time, why is it that some of us are just not only naturally good at navigating but actually enjoy the thrill of exploring and learning about our environment? The project detailed below touches on some of these questions by investigating how individuals differ in their acquisition and development of spatial knowledge.

Classical frameworks on the acquisition and development of spatial knowledge (Shemyakin, 1962; Siegel and White, 1975) suggest that individuals first learn landmarks followed by the routes that connect them, eventually integrating these into a more holistic and metric survey level representation. During the last decade, it has been proposed that spatial microgenesis does not always follow a strict stage-like development but rather proceeds in a more continuous or quantitative fashion (Montello, 1998). The continuous framework proposes that some individuals are capable of integrating complex spatial information that allows them to perform accurate metric calculations with minimal exposure in the environment.

We have been working on a project investigating the behavioral and neural correlates of the acquisition and development of spatial knowledge of an unfamiliar university campus (Ambler campus of Temple University) over a period of three weeks, with particular emphasis on individual differences. In their first visit to the campus, subjects learned two routes located at different areas of the campus and were asked to remember the name and position of several buildings on each route. During the following weeks, subjects learned these routes for a second and third time together with a connecting route. At each stage, their integrated configurational knowledge was probed by asking them to complete a variety of online and offline tasks including direction estimation, distance estimation and sketch mapping (see figure 1). A subset of subjects also participated in an fMRI experiment where a recognition task was used to probe the subject's memory for buildings around the campus.

Behavioral results revealed large individual differences in the initial acquisition of spatial knowledge, suggesting that spatial microgenesis does not necessarily follow a stage-like development (as proposed by classical frameworks) but proceeds in a continuous fashion. This was particularly true during initial acquisition (first session) where several subjects showed evidence of metric knowledge and developed accurate representations of the environment with minimal exposure. Data from the fMRI experiment further complemented these results. A whole brain analysis that looked at performance-related activations revealed an exclusive activation of the retrosplenial cortex (RSC) among the top performers. It seems that while both top and bottom performers were able to accurately recall buildings from the Ambler campus (recognition accuracy was above 85% for both groups) the top performers were not only identifying these buildings but possibly situating them within their mental representation of the campus. This is consistent with the role of the RSC in supporting mechanisms that allow for situating a scene within the broader spatial environment (Epstein, 2008; Wolbers & Wolbers & Büchel, 2005) by integrating egocentric spatial information into a survey-level representation during navigation.

Virtual Ambler

Perhaps one of the main drawbacks of the real-world study was that the testing procedure was too long (9 hours distributed over 3 weeks) and required a certain amount of commitment from the participants. In an effort to collect more data from different samples of the population, we created a virtual model of the Ambler campus (see figure 2). The model was created using Google Sketchup¹ and later exported to the gaming engine Unity 3D² allowing subjects to actively navigate around the virtual campus. We are now currently working in developing web-based application which will structure the virtual world and the different spatial tasks together in an immersive videogame-like experience. Although subjects tested in the desktop virtual reality environment will not benefit from proprioception, pre-pilot testing suggests that the previous three-week testing procedure can be reduced to a 90 minute session. Having the real-world data as a basis for comparison, we hope that Virtual Ambler will allow us to test a larger sample of the population and answer specific questions regarding individual differences in spatial ability and knowledge transfer.

¹http://sketchup.google.com/
²http://unity3d.com/

References

• ♦Epstein, R.A. (2008). Parahippocampal and retrosplenial contributions to human spatial navigation. Trends in Cognitive Science, 12, 388-306.
• ♦Ishikawa, T. & Montello, R. D. (2006). Spatial knowledge acquisition from direct experience in the environment: Individual differences in the development of metric knowledge and the integration of separately learned places. Cognitive Psychology, 52, 93-129.
• ♦Montello, R. D. (1998). A new framework for understanding the acquisition of spatial knowledge in large-scale environments. In J. M. Egenhofer & G. R. Golledge (Eds.), Spatial and temporal reasoning in geographic information systems (pp. 143-154). New York: Oxford University Press.
• ♦Shemyakin, F. N. (1962) Orientation in space. In B. G. Ananyev (Ed.), Psychology in the Soviet Union (pp. 186-255). Washington: US Office of Technical Reports.
• ♦Wolbers, T. & Büchel, C. (2005). Dissociable retrosplenial and hippocampal contributions to successful formation of survey representations. Journal of Neuroscience, 25, 3333-3340.

How do we remember locations and find our way back to them? After all, we regularly find our way, even, like our ancestors, without a GPS. Avoiding getting lost matters, as does finding your car in the middle of the night after getting off the airport shuttle, jet-lagged and weighted down with baggage. In addition to being able to represent locations spatially, we can also talk about them, using language like prepositions, which tell us about the relationship between things. For example, in the real world, you could walk to or point to the car's location in Figure 1, and also describe its position as under the tree beside the flowers and in front of the house. Does spatial language bear any relationship to our non-spatial representations of where things are? How do these systems (verbal and non-verbal) develop in relationship to each other?

There are different ways people can remember locations and navigate to them. One is ego-centric (related to ourselves), and another is truly spatial. You can remember that something is on the left of you (egocentric), and you can also remember that it is north (spatial). If you walk out the door of our infant lab, for example, the parking lot is on your left, and also to the west. No matter where you face, the parking lot will always be west of the lab, but if you turn 180 degrees to face the door, the parking lot will now be on your right. Place learning, the interest of this study, is the ability to calculate spatial locations using distances and directional information from distant features, regardless of egocentric information (Newcombe, Huttenlocher, Drummey & Wiley, 1998; Sluzenski, Newcombe, & Satlow, 2004).

In young children, there is long developmental trajectory of spatial skill development. Initially, infants develop an awareness of their own movements, (Landau & Spelke, 1988; Lepecq & Lafaite, 1989; Rieser & Heiman, 1982; Tyler & McKenzie, 1990), and this egocentric information gradually is supplemented with spatial coding. In the second year of life, place learning emerges between 20-24 months (Newcombe et al., 1998; Sluzenski et al., 2004). For example, when children are faced with the task of finding a hidden object after a position change, only children older than 22 months can use external features (the skill involved in place learning) to increase the accuracy of their searches (Newcombe et al., 1998).

Developmentally, there are different theories of how language and spatial concepts emerge. The specificity hypothesis (Gopnik & Meltzoff, 1986; 1987) suggests that during the single word acquisition period of language development (15-24 months) there is a relationship between the emergence of linguistic skills and non-linguistic skills that rely on shared foundational knowledge (e.g. spatial navigation and spatial language skills). Prepositions, specifically, have been discussed as emerging from and capturing infants' perceptions of spatial relations, such as the locations of objects, as well as the path component of action events. For example, actions that involve going in or moving out will be captured as the prepositions "in" and "out" (Mandler, 2006). By these accounts, similar domains in cognition and language would be expected to show a relationship to each other during development.

The purpose of this experiment was to explore the relationship between prepositions and place learning at an age when both are emerging, looking at how children are able to begin to remember locations, and whether or not this spatial awareness can be seen in their first words. Children were tested using a spatial task adapted from the Morris water maze (Morris, 1984), and the MacArthur Communicative Development Inventory. In the place learning task, children were placed in a round enclosure and a puzzle was hidden under the floor at one location. Before each trial, children were spun, to disorient them, and placed down at a different starting position, and asked to find the hidden puzzle. Their search types and success at finding the puzzle were coded.

What we found was that older children had significantly larger expressive vocabularies than younger. In addition, they had significantly stronger spatial skills, as shown by searching in the correct area of the pool more often than younger children, as well as pinpointing the goal location (place learning) (see Figure 3). Although language and place learning both correlated with age, once age was partialled, there was no correlation between them. The crucial exception was prepositions, the acquisition of which was correlated with place learning. The finding of a spatial- specific language linkage, as both language and place learning undergo rapid change, suggests an intriguing story about the interaction between various cognitive systems, beginning as early in development as when the systems themselves emerge.

References

• ♦Gopnik, A. & Meltzoff, A. (1986). Relations between semantic and cognitive development in the one-word-stage: The specificity hypothesis. Child Development, 57, 1040-1053.
• ♦Gopnik, A. & Meltzoff, A. (1987). The development of categorization in the second year and its relation to other cognitive and linguistic developments. Child Development, 58, 1523-1531.
• ♦Landau, B. & Spelke, E. (1988). Geometric complexity and object search in infancy. Developmental Psychology, 24, 512-521.
• ♦Lepecq, J.C. & Lafaite, M. (1989). The early development of position constancy in a no-landmark environment. British Journal of Developmental Psychology, 7, 289-306.
• ♦Mandler, J.M. (2006). Actions organize the infant's world. In K. Hirsh-Pasek & R. Golinkoff (Eds.), Action meets word: How children learn verbs (pp. 111-133). New York: Oxford University Press, 2006.
• ♦Morris, R. (1984). Developments of a water-maze procedure for studying spatial learning in the rat. Journal of Neuroscience Methods, 11, 47–60.
• ♦Newcombe, N., Huttenlocher, J., Drummey, A. & Wiley, J.G. (1998). The development of spatial location coding: Place learning and dead reckoning in the second and third years. Cognitive Development, 13, 185-200.
• ♦Rieser, J. & Heiman, M. (1982). Spatial self-reference systems and shortest-route behavior in toddlers. Child Development, 53, 524-533.
• ♦Sluzenski, J. Newcombe, N. & Satlow, E. (2004). Knowing where things are in the second year of life: Implications for hippocampal development. Journal of Cognitive Neuroscience, 16, 1443-1451.
• ♦Tyler, D. & McKenzie, B. (1990). Spatial updating and training effects in the first year of human infancy. Journal of Experimental Child Psychology, 50, 445-461.

U.S. students' science proficiency markedly lags behind students' proficiency in other nations at the secondary level. This is particularly true in physics, where students encounter challenging concepts such as torque and angular momentum (Grigg et al., 2006). We explored whether direct experience with physics concepts (e.g., feeling forces – as opposed to reading about force, seeing forces being exerted on someone else, or even measuring forces with instruments) can enhance student understanding. Lab experiences where students feel physics quantities directly may lead to the recruitment of brain areas devoted to sensory and motor (sensorimotor) processing when students later think and reason about the physics concepts they experienced. Previous research suggests that when these sensorimotor areas are involved in thinking and reasoning tasks, people’s understanding of the concepts in question can improve (Beilock et al. 2008).

In the current experiment, we compared seeing a demonstration of angular momentum and torque with feeling the effects of a spatial change to angular momentum on students' understanding of force quantities. College-age participants (N=44) completed the experiment in randomly assigned pairs.

First, participants read a short qualitative description of angular momentum and the factors that affect it. In this description, angular momentum was also connected to the familiar concept of linear momentum. The description went so far as to include the following explicit instruction: Tilting a spinning wheel from vertical to horizontal changes the direction in which the wheel is spinning in the world, so completing this “tilt” leads to forces that would not occur if the wheel was still – and these forces are the result of the wheel’s angular momentum.

Students then completed a baseline assessment of their understanding of the relation between (a) the size/weight of spinning wheels (defined an object's moment of inertia) and the speed of the spinning wheels and (b) the amount of torque (i.e., rotational force) that is exerted when tilting the wheels. Understanding these relations is an integral part of understanding the concepts of angular momentum and torque. In this Baseline Force Judgment Task (FJT), two figures are presented on the screen (Figure 1). The avatar on the left (identified to the participants as the "template") was always holding an apparatus with one larger wheel and one smaller wheel. Both wheels spun at 1 revolution per second. On the right, an avatar (identified as "Woody") was holding an apparatus in which one or more of three potential wheel factors (i.e., either the wheels' spin direction, spin speed, or size) might differ from the template's apparatus. The participant could view animations of the two figures for up to 30 seconds. The goal was to understand how the figures differed.

Each video clip was followed by the question, “Did Woody experience more or less force than the template?” Participants responded by pressing a "more" or "less" key on the keyboard in front of them. The participant then pressed a key to begin the next trial. This design allowed us to record participants' ability to understand the relations between factors of a multi-dimensional physical system. Increases in response accuracy indicate participants have learned the qualitative relations between the size, speed, and directions of wheel spin, as well as how these relations impact the amount of rotational force that is exerted when tilting the wheels. Participants performed 52 video clip trials in the Baseline FJT.

Following the completion of the Baseline FJT, some participants (randomly assigned to the sensorimotor group) were told they would be completing a task similar to the one on the video clips. Other participants (randomly assigned to the observation group) were told they would watch another participant complete the task. During this Training Experience, the experimenter told the observer what the other person was about to experience (e.g., wheel spin directions and speeds, with the size of the wheels apparent prior to the start of each trial). Importantly, we equated the visual feedback both groups received. To do this, a laser pointer was mounted along the axis around which the wheels spun. The sensorimotor group was told to tilt the wheels so that the red dot of the laser followed a straight target line on the wall. They were told to tilt the wheels from vertical to horizontal and back to vertical, 5 times in 5 seconds. Errors, which were directly related to the forces exerted by the apparatus when it was tilted, were visible to both participants (via the laser pointer deviation from the target line). Nine combinations of wheel spin direction, speed, and size were completed to demonstrate the relevance of these factors in influencing angular momentum magnitude and direction.

After completion of the Training Experience, each participant completed the Test FJT. This task was identical to the one completed prior to training.

As seen in Figure 2, the results of this experiment suggest that experiencing forces leads to greater learning about the qualitative relationships that underlie angular momentum than the observation of someone else experiencing them. An Analysis of Variance (ANOVA) revealed a significant effect of Session (F(1,42)=4.25, p=0.05), that was qualified by a significant Group × Session interaction, F(1,42)=4.33, p=0.04).

Both groups exhibited limited knowledge (approximately 61% correct for each group – where random guessing should yield 50% correct) on the Baseline FJT. However, after the Training Experience, stark differences emerged. The sensorimotor groups' accuracy improved by about 10%. The observational groups' accuracy remained around 61% correct. Importantly, both sensorimotor experience and observation yielded information about the forces. This is because force-induced errors were visible in terms of the wheel apparatus's laser pointer deviating from the target line when the participant anticipated the need for more or less force than was actually required to tilt the axle. The observation group was instructed to pay attention to the laser pointer during training. An experimental debriefing session revealed that they did in fact do this.

Simply put, participants that had the opportunity to feel the effects of spatially changing angular momentum demonstrated better understanding of the qualitative relationships between factors which influence angular momentum and torque. We are currently conducting both behavioral and fMRI follow-up experiments to explore whether the sensorimotor group’s increased understanding of angular momentum is specifically due to the recruitment of sensorimotor systems when merely thinking and reasoning about the concept.

References

• ♦Beilock, S. L., Lyons, I. M., Mattarella-Micke, A., Nusbaum, H. C. & Small, S. L. (2008). Sports experience changes the neural processing of action language. Proceedings of the National Academy of Sciences, 105, 13269-13273.
• ♦Grigg, W., Lauko, M., Brockway, D., National Center for Education Statistics, National Assessment of Educational Progress (Project) & Institute of Education Sciences (U.S.). (2006). The nation's report card: Science 2005 assessment of student performance in grades 4, 8, and 12. Washington, DC: U.S. Dept. of Education, Institute of Education Science.

Learning about locations in space often involves the use of visual representations. As an example, first listen to the following description that an 8-year-olds is giving of the layout of space she has just learned:

What do you think this space looks like? The boxes could be in rows in the space. They could be on shelves. They might be adjacent to one another or they might be spread apart. Now watch the gestures that accompany this description:

Visual representations, such as gestures and drawings, can enhance verbal communication when words are not enough. Visual communication may be especially useful for children, as the majority of 6 year-olds, 8-year-olds, and 10-year-olds in our studies have verbally described space in the same manner as the girl you just heard. Although gesture can be beneficial for enhancing their descriptions, many of the younger children (6-year-olds and 8-year-olds) never used their hands while describing the space. We’ve found two methods that encourage children to better communicate spatial information, and also gain a deeper, more integrated understanding of the space.

Maps: In one of our studies, half of the children saw a map of the animals' locations before entering the space. The other half saw photos of the animals (and received no spatial information). The children then navigated a route through the space and learned the locations of the animals. Then, they had to describe what they had learned to their parent, who had never seen the space before but would need to be able to find all of the animals later. The children who saw a map communicated more spatial information, mainly in gesture. The map may have provided them with a portable, tractable, representation of the space that was easy to convert to a gesture model. Gestures and maps are similar in that they both permit us to communicate spatial relations and scale large spaces to a more manageable size.

The children who saw a map also gained a deeper knowledge of the space. When later asked to make relational inferences about the locations of the animals (e.g., knowing who was diagonal from the frog), children who saw a map made significantly more correct inferences than those who did not see a map. Maps often give us a perspective not normally found in navigation (Blaut, 1991; Woord, 1992) and can impact our representation of the space (Uttal, 2000, 2005).

Drawing: Children who make their own drawings of the space also show the same advantage as children who see maps. When asked to communicate the space to their parents, children were also given the chance to draw while they explained. Many children drew maps, which communicated the layout of the space and the locations of the animals. Like the children who saw a map, they also demonstrated a deeper knowledge of the space as evidenced by the inference questions.

In summary, visual representations play a critical role in helping children learn to think spatially. In SILC we investigate the role that these representations play in spatial learning and education more generally.

References

• ♦Blaut, J. (1991). Natural mapping. Transations of the Institute of British Geographers, 16(1), 55-74.
• ♦Liben, L. S. (2001). Thinking through maps. In M. Gattis (Ed.), Spatial schemas and abstract thought (pp. 45-78). Cambridge, MA: MIT Press.
• ♦Uttal, D. H. (2000). Seeing the big picture: Map use and the development of spatial cognition. Developmental Science, 3, 247-286.
• ♦Uttal, D. H. (2005). Spatial symbols and spatial thought: Cross-cultural, developmental, and historical perspectives on the relation between map use and spatial cognition. In L. Namy (Ed.), Symbol use and symbolic representation: Developmental and comparative perspectives (pp. 3-23). Mahwah, NJ: Erlbaum.
• ♦Wood, D. (1992). The power of maps. New York: Guilford Press.