Spatial Intelligence and Learning Center
NSF Science of Learning Center
This section highlights the research done in 2009 by our SILC Members in connection with our Spatial Intelligence and Learning Center project.
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Narrative is a powerful way of making sense of the world: Through it, we string together our experiences with pieces of our prior knowledge, and formulate coherent causal explanations. Especially for novices, this can make complex systems such as evolution more cognitively accessible. At the same time, these narrative understandings are often pruned of crucial details, and riddled with misconceptions. Indeed, writers on science education have identified narrative as the language of folk theories.
But narrative is not a purely verbal phenomenon. Images also tell stories, and that much of science is publicly communicated through visual representations - including diagrams, charts, graphs, animations, and interactive multimedia - points to a need to better understand the interactions between the viewer and the visual in the construction of understanding.
In a series of related projects, we investigate what learners understand from visual representations intended to communicate scientific concepts. Specifically, what narrative understandings do they hold, and how are those narratives re-constructed through their interactions with media? Findings from these studies will inform the design of educational multimedia that we will develop to facilitate people's understandings of scientific concepts.
In one project, we consider the cladogram - a specialized diagram used by biologists to represent phylogenetic relationships among taxa. Students experience notorious difficulty when reasoning with them, and it may be that the visual structure too readily invites the misconceived narratives associated with naïve explanations of evolution (see Fig. 1). In these studies, we alter the presentation of the cladogram through animation, and thus impose narratives that counter the upward linear progression people tend to interpret. In clinical interviews, we then ask students to reason with these cladograms, and so attempt to tease apart the processes by which their narrative understandings interact with specific visual features of the diagram as they construct an interpretation of it. Follow-up studies will further investigate the influence of canonical folk understandings on interpretations of the diagram, and the graphic symbols students will intuitively draw to visually represent relationships. These findings will inform the design of an educational multimedia intervention to teach students how to view cladograms.
In another study, we consider animated cartoons as media for communicating concepts of speciation and biogeography. These animations, on display at a natural history museum in Chicago, make use of a number of cinematic devices to compress complicated concepts into short, entertaining viewing times. In some cases, the animated depictions may literally contradict accurate portrayals of the underlying science (see Figure 2). How do design strategies such as anthropomorphism, temporal compression, and exaggeration, which are used to tell compelling narratives, interact with viewers' prior understandings of the concepts communicated? Interviews with students and museum visitors reveal different interpretations from viewers with little prior knowledge, compared to viewers with more solid understandings. Knowledge of how viewers construct meaning from watching these cartoons may inform more effective designs of educational animations.
Have you ever struggled to put together furniture that you ordered with "some assembly required"? Have you ever watched in awe as the instructor of introductory organic chemistry talked with bewildering rapidity and some mysterious board markings about molecules fit together? Visualization is an essential component of both everyday life and the development of scientific expertise. It has often been considered relatively fixed, or at best a skill that can be painfully acquired in specific areas, but without generalization to similar domains. However, two recent studies have just appeared that show that large, durable and generalizable improvements in visualization skill are possible.
In one study, Terlecki, Newcombe & Little (2008) asked undergraduates to participate in semester-long weekly practice with the Mental Rotations Test (MRT), a widely-used assessment of visualization. Additionally, some of them played the videogame Tetris. Both groups showed large improvements in mental rotation and these gains were maintained several months later. Videogame training transferred to two other spatial tasks at levels exceeding the effects of practice, and this transfer advantage was still evident after several months. In another study, Wright, Thompson, Ganis, Newcombe & Kosslyn (2008) tested undergraduates on two spatial tasks: mental rotation task and mental paper-folding. Each individual then participated in daily practice sessions with either mental rotation or mental paper folding over 21days. Participants showed practice gains to novel stimuli for the practiced task, as well as transfer to the other, non-practiced, spatial task. Thus, practice effects were process-based, not instance-based.
Further work is underway to identify the processes that change, and to isolate the training conditions that are necessary to achieve such effects. For now, however, these studies show that there is reason to be optimistic that people can learn better spatial skills, both for assembling furniture and for learning science.
Example of Mental Paper Folding:
.jpg "Eg. Mental Paper Folding")
How does spatial reasoning work? Does it vary across cultures? Researchers at the Spatial Intelligence and Learning Center (SILC) have used their CogSketch simulation of spatial reasoning to investigate these questions. Prior work by Dehaene and Spelke used a visual Oddity task, where participants identify which image of six is “odd” or “different”, to compare spatial reasoning in Americans and Mundurukú (a South American indigenous group). Andrew Lovett, Kate Lockwood, and Ken Forbus used CogSketch to simulate their findings. CogSketch was given as input the same Power Point files used to generate displays for human subjects. CogSketch automatically computes a variety of qualitative spatial relationships, such as whether lines are parallel or intersect. Analogical processing, based on SILC researcher Dedre Gentner’s structure-mapping theory, is used to compare images and compute generalizations from them, to find the “odd” one. CogSketch was able to solve most of the problems that human participants solved, and problems that were hard for people were also hard for the simulation. Moreover, the differences between Americans and Mundurukú were further explored by selectively ablating capabilities of the simulation, to make its performance correlate more strongly with one group or the other. The ablation study suggests that Mundurukú have more difficulty focusing on groups of shapes, and that they focus more on the individual edges of shapes -- possibly because Americans, unlike the Mundaruku, have names for shapes such as triangle and rectangle, which could invite a focus on the whole object. In addition to improving our understanding spatial reasoning in people, such simulation studies help provide the science base for creating educational software that can understand student sketches.
Relational terms (e.g., verbs and prepositions) are the cornerstone of language development, bringing together two distinct fields: linguistic theory and infants’ event processing. To learn relational terms, infants initially perceive and conceptualize spatial components within events such as path and manner, and then uncover how their ambient language packages these spatial constructs. We propose that infants trade spaces as the language-general nonlinguistic constructs are gradually refined and tuned to the requirements of the particular native language (Göksun, Hirsh-Pasek, & Golinkoff, in press).
Previous research suggests that preverbal infants from different language environments possess a general set of spatial and event components (e.g., containment, support, degree of fit, path, manner, source, goal) that form bases for learning relational terms. Our studies offer a new area of research, exploring infants’ processing of figures and grounds in dynamic events.
The figure in an event can follow any path or move from any source. The ground is a stationary setting with respect to a figure’s movement. For example, in the sentence “John is walking across the street,” John is the figure and the street is the ground. Importantly, languages encode figure and ground relations differently. Japanese ground-path verbs such as wataru “go across” or koeru “go over”, incorporate constraints on the physical geometry of the ground along with the direction of motion. For example, wataru “go across” implies that there is both a starting point and a goal and the ground should be a flat extended surface. The typical grounds for wataru “go across” are railroad, road, or bridge. In contrast, when the ground does not contain a barrier between two sides (e.g., a tennis court, grassy field) the verb tooru “go through,” rather than wataru “go across” is used (see Figure 1).
Figure 1. The grounds at the top panel (railroad track, street, road, and bridge) are encoded by the verb wataru “to cross” and grounds at the bottom panel (tennis court and grass) are not typically coded by the verb wataru “to cross,” but encoded by the verb tooru “go through” in Japanese.
In a series of studies, we examined how English-reared infants differentiate figures (e.g., a man or a woman crossing a railroad) and grounds (e.g., crossing a railroad vs. crossing a tennis court) in dynamic events. Results indicated that infants notice changes in figures and grounds by 11 and 14 months of age, respectively. Notably, the same infants distinguish grounds better when the comparison is between a wataru “go across” (e.g., railroad) ground and a tooru “go through” ground (e.g., tennis court) according to Japanese (Göksun, Hirsh-Pasek, & Golinkoff, 2009). Thus, preverbal infants are sensitive to the subtle distinctions of grounds that are not lexicalized in English. In a control study, we tested a potential confound, the color of the ground, on infants’ differentiation of these grounds. One might argue that the “greenness” of the grassy field or tennis court drew infants’ attention to prefer looking at those sides at test trial. However, results replicated the original findings with colored scenes suggesting that color of the ground is not a strong perceptual cue for infants’ discrimination of grounds.
Our current studies address two lines of inquiry. First, we attempt to tease apart the role of spatial and temporal interaction in these events. Do children process static scenes of the same dynamic events similarly? Relational term learning demands perceiving the spatial-temporal interaction inherent in dynamic events. Verbs, for example, can label a moment in time (as in kiss) or they unfold across time (as in run), or can represent the completion of a particular time frame (as in break). Eliminating the temporal aspect of an event might enhance or reduce children’s ability to distinguish different figures and grounds.
Second, to test our hypothesis of trading spaces for figure-ground relations, we investigate how Japanese-reared infants from two age groups (14 and 20 months of age) differentiate grounds in the same nonlinguistic dynamic events. The comparison of these children to their English-reared counterparts will provide crucial information on how language exposure might influence the attention to language-specific distinctions in events.
Language is a fundamental human ability that is impaired in approximately 75% of children diagnosed with an Autism Spectrum Disorder (ASD; Tager-Flusberg & Cooper, 1999). Most interventions for ASD children focus on teaching nouns, despite mounting evidence suggesting that acquiring a cadre of verbs is necessary for developing grammatical speech (Fernald, Perfors & Marchman, 2006). Learning most verbs and prepositions is harder than learning most nouns even for typically developing children because the referents of such words are temporally dynamic, perceptually variable, and name the spatial relations between objects rather than the objects themselves (Gentner & Boroditsky, 2001). Although learning relational words like verbs inherently requires children to process space/time relationships, the role of spatial and temporal processing in the language development of ASD children has hitherto not been explored.
A growing body of research suggests that to learn a verb or relational term, children must accomplish two tasks. First, they must discriminate and categorize semantic components (Talmy, 1985) within the flow of everyday events, which requires them to process space/time relationships. Second, children must combine these semantic components in language-specific ways and map a word onto their newly formed relational concepts (Gentner, 1982). Researchers have explored two key supports for helping children map verbs and relational terms onto referents in the world: social cues (Tomasello & Merriman, 1995) and linguistic cues (Fisher & Song, 2006). In typical children, social and linguistic cue understanding appear in synchrony but are recruited and weighted differently across developmental time (Hollich, Hirsh-Pasek & Golinkoff, 2000), which confounds any attempt to identify the separate contributions of each to word learning. However, the wide variability seen in ASD children in the areas of spatial/temporal processing (Dakin & Frith, 2005), social skills (Baron-Cohen, 1995) and linguistic skills (Tager-Flusberg, 2006) may enable us to clarify the individual contributions of these cues to learning verbs and relational words.
Why do ASD children have particular difficulty learning verbs and other relational terms? In collaboration with Robert Schultz, PhD and Sarah Paterson, PhD at the Center for Autism Research at the Children's Hospital of Philadelphia and the University of Pennsylvania, we will administer a series of four tasks and standardized language tests to typically developing children and ASD children with the goal of answering three questions: First, do ASD children have difficulty learning verbs and relational terms because they lack the necessary conceptual underpinnings? Task 1 addresses this question by examining the discrimination and categorization of two well-researched event components: path and manner. Second, do ASD children have trouble with verbs due to difficulty understanding the social intentions and goaldirectedness of others? Tasks 2 and 3 represent a multi-method approach investigating children's social intent and its relation to vocabulary outcomes. Task 2 examines infants' intentional understanding through imitation and the completion of failed intentions. Task 3 explores how children use temporal cues to detect social intent. Although Tasks 2 and 3 both draw upon children’s ability to detect social cues, Task 3 also incorporates a strong temporal component. Third, how do children's face processing skills interact with these other skills to impact verb and relational word learning? Task 4 examines face processing, which loads on both spatial-temporal and social cues. Our research calls for an analytic strategy that will deconstruct the various tasks to establish how spatial/temporal and social features contribute independently and jointly to language outcomes.
This series of four studies will investigate how spatial ability and temporal processing interact with social cognition to predict verb and relational word learning in TD and ASD children. We hypothesize that aspects of spatial-temporal processing and social cognition contribute individually and jointly to the process of learning relational words like verbs, and expect that these studies will produce valuable data regarding the necessary and sufficient conditions for acquiring these types of words. Importantly, our multi-pronged investigation into the underpinnings of verb development will allow us to create individual profiles of spatialtemporal and social skills in ASD children, which can then be used to aid in diagnosis and to inform strategic language intervention.
Animals are remarkably skilled in their capacity to use a range of environmental features to orient in space once they have lost track of where they are, a process called reorientation. Among the types of cues that animals can use, one that has received little attention is the information extractable from a terrain extending in the vertical dimension, such as a geographical slant or slope (Miniaci et al., 1999; Proffitt et al., 1995; Restat et al., 2004). A slope gradient is a source of directional information (Jacobs & Schenk, 2003), enabling a navigator to establish an allocentric reference frame based on the vertical axis (up and down) and the derived orthogonal axis (left-right) of the slope (Restat et al., 2004).
The use of slope for reorientation and goal location has been shown in non-human animals (rats: Miniaci et al., 1999; pigeons: Nardi & Bingman, 2009). The present research aimed to study, for the first time, if humans can reorient by a geographical slant in a real-world environment. This is an ecologically relevant question because terrain slope is part of the lay of the land in natural environments. Furthermore, although it is a perceptually salient cue, as it provides potentially redundant, multimodal sensory activations (visual, proprioceptive, kinesthetic and vestibular stimuli), hill slants tend to be misjudged, and the conscious awareness of slope seems to be highly variable, depending, for example, on physiological and psychosocial resources (Proffitt et al., 1995; Schnall et al., 2008).
The experimental enclosure used consisted of an 8 x 8 ft, wooden platform with a PVC pipe frame on top (see Figure A). The enclosure was tilted to a 5° inclination by raising one side on wooden blocks. Twenty male and twenty female Temple undergraduate students took part to the experiment. Subjects saw the experimenter hide a target in one of the four corners of the experimental enclosure. After having lost their sense of orientation by being spun blindfolded on a swivel chair, they had to find the target. This procedure was repeated for 4 trials, with the target always in the same corner.
Because the enclosure was completely symmetrical and featureless, and no external cue could be seen or heard (participants wore earphones to cover outside noise), the only way to locate the goal was using the slope gradient.
Both genders performed significantly above chance, males: t(19) = 14.33, p < .0001; females: t(19) = 2.41, p < .05 (see Figure B). In order to do so, subjects not only were able to encode the goal's vertical coordinate (up-down axis), but also its orthogonal coordinate on the slope (left-right axis). Only by using such an allocentric, bi-coordinate representation was it possible to successfully locate the goal. This ability has been shown in rats and pigeons (Miniaci et al., 1999; Nardi & Bingman, 2009), therefore it was not a surprise that also humans could succeed in such a task.
However, surprisingly males performed substantially and significantly better than females, t(38) = 4.43, p < .0001 (see Figure B). This effect size is large, d = 1.4, with means differing for more than 1 SD.
The psychometric test literature shows, in general, a male superiority in visual perception tasks that require engaging the horizontal-vertical reference frame, such as the Water-level Task and the Rod-and-Frame Test (Linn & Peterson, 1985). However, these gender differences are often eliminated under haptic and proprioceptive versions of the tests, where vision is irrelevant (Proffitt et al., 1995; Robert & Longpre, 2005). This suggests that males might surpass females in spatial tasks that emphasize visual stimuli.
In the present experiment, the four corners of the enclosure were visually almost identical. On the contrary, vestibular and kinesthetic cues could be readily used to perceive the slope gradient and solve the task. Therefore, the fact that females were outperformed by males is remarkable because it shows a robust gender effect in the use of a multimodal cue in which kinesthetic and vestibular information – as opposed to visual information – play a crucial role.
Current research is investigating the factors underlying such a gender difference in slope use. One line of research is examining whether drawing attention to the tilt of the floor might eliminate the male advantage. Another line is testing if the gender difference is related to a differential perception of the kinesthetic and vestibular cues of the sloped floor.
A. Schematic representation of the experimental enclosure viewed from above. The experimenter hid the target under one of the bowls in the corners. Participants were spun on the swivel chair blindfolded and then had to find the target. Note that the chair's axis of rotation was perpendicular to the earth. B. Mean percentage of correct choices (± SD) during the 4 trials on the slope (chance is 25%). Both genders performed above chance. However, males performed significantly better than females (p < .0001).
Measurement links the abstract world of numbers and the concrete world of physical objects. However, measurement skills lag behind all other mathematics topics for American students (National Center for Education Statistics, 1996). One underlying factor associated with this trend is a lack of understanding of units. Where students have difficulty often involves measuring with a ruler when an object is not aligned with the zero-point. In this case, students simply either read off the number where the object ends or count the number of hash marks between the start and endpoint of the object (Bragg & Outhred, 2004; Ellis, Siegler, & Van Voorhis, 2001; Lehrer et al., 1998), demonstrating an apparent lack of unit understanding.
.jpg "pre-post stimuli")
Researchers at the Spatial Intelligence and Learning Center (SILC) at the University of Chicago conducted a training study designed to highlight the importance of units on a ruler. Second grade students were shown how and what needs to be counted (e.g., the intervals on the ruler, rather than the numbers themselves) by using discrete units, placed directly on the ruler, when they were measuring items that were not aligned with the zero-point. Objects were then moved back to the start of the ruler and measured again (with units on the ruler) to “check” the answer. Another group of students received a control condition (1), which replicated traditional measurement instruction from mathematics curricula using the same ruler with aligned items or units from the training condition but not both together. Another group of students received control condition 2, where unit pieces were placed directly on the ruler but only to measure aligned objects.
.jpg "experimental condition")
.jpg "measurement training")
Strategy differences also related to performance. Children who used the ruler simply as a tool to read off the number where an item ends (regardless of where it starts on the ruler), did not improve after training, whereas the children who counted hash marks showed dramatic improvement. Thus, the training effectively shifted the strategy of students who counted hash mark to counting units.
The combination of measuring misaligned items in conjunction with using discrete objects superimposed on a ruler is an effective method for teaching measurement. Moreover, the more typical instruction used in classrooms (e.g., separate activities of using aligned ruler measurement and measuring with discrete units) is not as effective in promoting the understanding of interval units. Additionally, children who count hash marks on misaligned ruler problems are more prepared to learn about interval units than those who merely read off the rightmost number on the ruler. The training technique is likely more effective because it highlights the fact that units are countable by making each unit extremely salient and has direct implications for instruction in mathematics, whereby emphasizing unit intervals (e.g. using units in conjunction with a ruler to measure misaligned items) can effectively enhance children’s understanding of linear measurement units. Ongoing research is examining whether experience with misaligned then aligned items, as in the training condition, would be effective without the use of discrete units. Additionally, we plan to extend these findings to examine how children measure objects that fall within inch markers (e.g., fractional parts) of both aligned and misaligned objects.
.jpg "results")
In our daily lives, we are always on the move. Successful navigation requires two components (when a GPS unit isn’t at hand), a map-like representation, and some knowledge of your current position on the map. From time to time, perhaps after travelling underground in the subway, or by being distracted by a phone conversation, we lose track of the "I am here" sticker on our mental map. Before we are able to carry on with our travels, we must first update our current position on our mental map. Thus, the processing of reorientation, or updating the current spatial position, can be viewed as the first step in the navigation process. This is the process that we will be discussing in this Showcase.
We can investigate the reorientation process in the lab. First, participants are introduced to a controlled environment, where we can manipulate the types of cues that are available to participants. Then participants are shown a goal location, and asked to remember where it is. To induce the state of disorientation (mimicking the subway travel scenario), participants are asked to spin in a circle with their eyes closed. Once they have stopped spinning, then they are allowed to open their eyes, and are asked to return to the goal location. Based on the types of information that we provide to participants, we can investigate how people are able to reorient.
One type of information that is often displayed is a feature cue, such as a uniquely colored landmark. Young children, even toddlers, have been shown to use feature cues for reorientation (Learmonth, Nadel, & Newcombe, 2002). However, it is debated how these feature cues are used by the reorientation system. Lee, Shusterman, and Spelke (2006) have argued that when young children are using feature cues, they do so in an associative manner, to beacon towards a goal location. This is an important point, because from this position, it is argued that the young children are able to partially navigate, without recovering a sense of where they are in the environment. To test this hypothesis, four year old children were introduced to a circular enclosure with an equilateral array of hiding locations. In this array, one of the hiding locations was a red cylinder, while the other two points of the triangle were identical blue rectangular boxes. Thus, the red cylinder could serve as a landmark for reorientation. If this is true, then the four year old children should be successful finding the sticker in any of the locations after disorientation. However, if children are depending on a beaconing strategy, and cannot use features at all for reorientation, then children should succeed when the sticker is at the unique red location, and randomly divide search at the two identical blue containers. Perhaps surprisingly, the second situation was found by Lee et al (2006). Children were able to retrieve the sticker about 80-90% of the time at the unique container, and were only 50% successful at the blue containers. These finding were taken as support of a two-step account of reorientation. In the first step of the reorientation system, participants are hypothesized to reorient based on the available geometry of the environment. In a second step, people can associatively beacon to a target location based on the non-geometric (i.e. feature) properties of the environment. This view of spatial cognition is modular in nature, and leaves little room for the role of experience, malleability, or training.
The alternative position to modularity is adaptive combination. From this theoretical position, the mind is able to use potentially any available cue that may aid the reorientation system. Saliencies, initial tendencies, as well as a past history of success or failure will bias a participant to use one particular type of cue over another when a decision is required. From this framework, there is an alternative explanation of the Lee et al (2006) finding. We believe that since the feature cue was small, portable, and part of the array, it would be a poor landmark choice to determine one’s position in the environment. When we are determining heading, cues that are large, stable, and more distal to the task would be better cues for reorientation.
Therefore, in this set of experiments, we ask if four year old children are able to use features for true reorientation (rather than just as beacons to a target location) when the feature cue is mounted on a wall, rather than as part of the array. In the first portion of the experiment, children were asked to search within an equilateral triangle search array, with identical shaped and colored goal locations. The feature cue was mounted on the circular boundary.
In contrast to Lee et al, children were able to retrieve the goal at all three positions at above chance levels. However, it is possible that the children were able to infer geometry between the three hiding locations and the feature curtain hanging on the circular wall. To rule out this possibility, the feature served as one point of the equilateral triangle, and then children we asked to search between two containers (composing the rest of the triangle) equidistant from the feature wall. The two-step associative account predicts that children should search equally often at each of the hiding locations. In contrast, four-year-old children in our experiment were able to focus search on the correct hiding location. Therefore, we provide evidence that young children can use features as more than just beacons, as landmarks in the reorientation system.
In summary, we have provided one piece of evidence that bolsters the case the adaptive combination approach to spatial cognition. One point to note is that although children performed at above chance levels, their performance was not impressively high, and therefore it seems that the reorientation system is developing beyond four years of age. As points of future research, it would be interesting to determine the developmental trajectories of each type of reorientation cue, as well as to understand how children resolve situations of conflicting or ambiguous information. Additionally, it would be noteworthy to tie the cognitive data to the neural level. Specifically, it would be interesting to think about how developing neural systems, such as place cells, head direction cells, and boundary vector cells may support or be influenced by spatial development. Lastly, it would also be of interest to think about how this reorientation system relates to the other aspects of cognition and individual differences. Perhaps we might expect reorientation ability to correlate quite well with oriented navigation, and less well with other spatial tasks such as mental rotation. All of these points are open questions, and would be potentially fruitful avenues of future research.
Thanks to Kristin Ratliff for inspiration for the title.
Many adults have anxieties about mathematics and these anxieties, over and above actual math ability, can negatively impact math performance (Ashcraft, 2002). Prior work has revealed that math anxiety disrupts the working memory (WM) that individuals need to carry out difficult mathematical computations. Working memory can be thought of as a short-term memory system involved in the control, regulation, and active maintenance of a limited amount of information immediately relevant to the task at hand (Miyake & Shah, 1999). If the ability of WM to maintain task focus is disrupted, performance may suffer (Ashcraft & Krause, 2007).
Working memory can not only be thought of as a general cognitive construct. It can also be thought of as an individual difference variable – meaning that some people have more of it than others. Usually, the higher one’s WM the better one’s performance on academic tasks ranging from reading comprehension to mathematical problem solving (Engle, 2002). However, it has been shown that individuals who are relatively high in WM (i.e. high span individuals) are most susceptible to poor math performance in anxiety-provoking situations (Beilock & Carr, 2005). This is because situation-induced anxieties compete for the WM resources that individuals with high WM capacity normally rely on for their superior performance (Beilock, 2008). As a result, math anxiety may serve to push the math performance of those higher in WM down to the level of their lower WM counterparts.
Though the findings outlined above have added much to our understanding of the negative impact of math anxiety on performance, less is know about whether there are other domainrelevant anxieties that can impact performance. In particular, while spatial ability is important for students' success in math and science, little work has been done to investigate the relation between students’ spatial anxiety and their spatial abilities (Delgado & Prieto, 2004; Govier & Feldman, 1999). Because individual differences in spatial ability begin to appear as young as kindergarten, we chose to investigate the possibility that spatial anxieties also emerge and impact children’s abilities at a young age (Levine, Huttenlocher, Taylor & Langrock, 1999).
For these reasons, the current work explored the relation between spatial anxiety (e.g., anxiety about performing spatial tasks in an evaluative context) and spatial ability (as measured via mental rotation ability) at the early elementary school level, where it is unknown whether spatial anxiety even exists. Specifically, we (1) explored the existence of spatial anxiety in young children and (2) examined how spatial anxieties related to young children’s spatial abilities as a function of individual differences in WM.
Measures of spatial anxiety, spatial ability, and working memory were obtained for 160 first and second grade students in the Chicago Public Schools during the first three months of the school year. Spatial anxiety was measured using a questionnaire adapted for 1st and 2nd graders from the Mathematics Anxiety Rating Scale for Elementary school students (Suinn, Taylor & Edwards, 1988). Spatial ability was assessed using the Thurstone mental rotation subtest. WM was measured using the total digit span which consists of forward and backward digit span (WISC III). Span scores averaged across the two tests ranged from 2-20. We took the bottom quartile to represent low WM students (M = 6.80, SE = .254), and the top quartile to represent high WM students (M = 13.25, SE=.250).
As seen in Figure 1, the relation between spatial anxiety and mental rotation ability was very different for lower WM and higher WM children. For lower WM children, there was no relation between spatial anxiety and mental rotation ability (r=-.02, n.s.). In contrast, for higher WM children, the higher one’s spatial anxiety, the lower one’s mental rotation ability (r=-.32, p<.04). Put another way, spatial anxiety was related to lower spatial ability, but only in children who were high in WM. High WM children with low spatial anxiety outperformed their low WM counterparts. However, high WM children with high spatial anxiety performed just like their low WM counterparts.
The significance of these results is heightened by the fact that spatial ability is thought to be an important component of early mathematical processing (Casey, Kersh & Young, 2004; Casey, Nuttall & Pezaris, 2001; Kyttälä, Aunio, Lehto, Van Luit & Hautamäki, 2003). If high WM children with spatial anxiety have lower spatial abilities than they are capable of achieving, this may carry consequences for their success in math and related disciplines. These results suggest the importance of examining spatial anxieties as well as spatial abilities in young children as both have the potential to impact achievement in the STEM disciplines.
How can we help children learn spatial concepts? Previous research has shown structural alignment is a powerful tool in helping both children and adults learn novel spatial relations (Christie & Gentner, in press; Gentner & Namy, 1999; Kotovsky & Gentner, 1996). Our goal in this project was to test whether these ideas could be applied to support children's learning of mechanical principles. To do this, SILC partnered with the Chicago Children's Museum to investigate whether structural alignment can facilitate the acquisition of stable construction principles: specifically, diagonal bracing (a subcase of the general principle that triangles confer stability in construction). This study also drew on our prior findings that alignable differences—differences that relate to the common structure between a pair—are particularly salient (Gentner & Sagi, 2006; Markman & Gentner, 1993). In this study, children were presented with pairs of model buildings; one building was made with diagonal braces which gave the structure stability and the other had horizontal crosspieces which provided no structural support. There were two training groups: high-alignability [HA] and low-alignability [LA], which differed according to whether their pairs were highly similar and thus easily aligned, or were superficially different, and thus more difficult to align (See Figures 1a. and 1b.) A third group received no training [NT]. During the training, children were shown that the building with the diagonal brace was more stable (harder to wiggle) than the other building.
The predictions were (1) that the two training groups would show better understanding than the no-training group; and (2) that the children in the high alignability group would learn best, because for them the diagonal brace should emerge as an alignable difference, thus helping them focus on how a diagonal brace helps make building stable.
Following training, children and their families built their own skyscraper. Upon completion, children were asked to complete a Brace Placement task to assess their understanding of diagonal bracing. In the Brace Placement task children were presented with an unstable building frame (approximately 1 foot tall) and were asked to help make it more stable by adding a piece to it. We coded the orientation of the child's added piece (with respect to the building's frame) as either diagonal, horizontal or vertical. The results of the Brace Placement task, shown in Figure 2, bear out the predictions. Children who received training generated more diagonal braces than those who did not; and children in the high-alignability condition generated more diagonal braces than those in the low-alignability condition. These findings indicate that the analogical principle of high alignment, shown to be effective in laboratory studies, can be impactful in noisy, real world learning environments.
.jpg "Figure 1a")
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The spatial categories of our native language seem natural to us – but other languages sometimes partition the spatial world differently (Levinson & Meira, 2003). For example the four spatial relations shown below are all instances of a single spatial category in English: the letters are on the shirt, the strap is on the bag, the book is on the shelf, and the coat is on the hook. But these spatial relations fall in different categories in Dutch (solid outlines), and in Yélî-Dnye (dashed outlines).
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Some spatial categories appear to be genuinely natural to humans, in that they are expressed linguistically in one or more languages – while other spatial categories are less natural, in that they do not appear in any language yet studied. Why is this? What makes a spatial category natural?
Recently, we identified a possible answer to this question (Khetarpal et al., 2009). We proposed that there is a universal similarity space of spatial meanings, and that languages reflect near-optimal partitions of this space. We obtained an approximation to a universal similarity space by asking speakers of English and Dutch to sort spatial scenes such as those above into piles based on the similarity of the spatial relation portrayed, and taking the frequency with which two scenes were sorted into the same pile as an index of their similarity. Given these similarities, we took an optimal categorical partition of the corresponding space to be one in which similarity is maximized within categories and minimized across categories (Garner, 1974). We found that the spatial systems of 9 unrelated and dissimilar languages were all near-optimal when assessed in this space. This account suggests why certain patterns of spatial naming appear in the world's languages and others do not. It also suggests which kinds of spatial categories may be particularly easy or difficult to learn – a suggestion we intend to test empirically in the near future.
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