Visualizing cross sections: Training spatial thinking ...

Learning and Individual Differences 33 (2014) 63–71

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Learning and Individual Differences journal homepage: www.elsevier.com/locate/lindif

Visualizing cross sections: Training spatial thinking using interactive animations and virtual objects☆ Cheryl A. Cohen ⁎, Mary Hegarty University of California, Santa Barbara, United States

a r t i c l e

i n f o

Article history: Received 11 February 2013 Received in revised form 29 March 2014 Accepted 2 April 2014 Keywords: Individual differences Spatial ability Spatial training Interactive animation Virtual models STEM education

a b s t r a c t In two experiments, we investigated the efficacy of a brief intervention that used interactive animation to train students to infer the two-dimensional cross section of a virtual three-dimensional geometric figure. Undergraduates with poor spatial ability were assigned to receive the intervention or to a control group. Compared to the control group, trained participants improved significantly on stimuli viewed during the intervention and demonstrated transfer to untrained stimuli. Results were considered with respect to two accounts of performance gains and transfer after spatial visualization training, an instance-based account and a processbased account. The instance-based account attributes performance gains to a larger store of memories and predicts no transfer to new stimuli or new spatial processes. The process-based account attributes performance gains to increased efficiency of mental processes and predicts transfer to new stimuli and tasks that share the same mental processes. The results of these experiments cannot be accounted for by an instance-based account alone. Performance gains and transfer in these experiments suggest that interactive animation and virtual solids are promising tools for training spatial thinking in undergraduates. © 2014 Elsevier Inc. All rights reserved.

1. Introduction A geology student observes an outcrop of rocks and tries to visualize the cross-sectional structure of the landforms beneath it. An anatomy student examines a two-dimensional slice of liver tissue, notes its key spatial features, and infers that it is a longitudinal, rather than lateral section of the organ. A mechanical engineering student sketches a schematic diagram of a building's heating and electrical systems, anticipating the angles at which exhaust vents and electrical cables will cross. Each student is using spatial thinking skills to mentally represent a two-dimensional cross section, or slice, of a threedimensional object or structure. The ability to infer the external shape and internal features of sections of objects and structures plays an important role in many domains of scientific thinking. It is a fundamental skill in geology, where it has been referred to as “visual penetration ability” (Kali & Orion, 1996; Orion, Ben-Chaim, & Kali, 1997). Anatomy students must learn to visualize, section, and rotate cross sections of physical structures, and learn to recognize these structures (Chariker,

☆ Support for the completion of this manuscript was provided by grant SBE-0541957 from the National Science Foundation. ⁎ Corresponding author at: Department of Psychology, Behavioral Sciences Building, University of Illinois at Chicago, 1007 W. Harrison Street, Chicago, IL 60607, United States. E-mail address: [email protected] (C.A. Cohen).

http://dx.doi.org/10.1016/j.lindif.2014.04.002 1041-6080/© 2014 Elsevier Inc. All rights reserved.

Naaz, & Pani, 2011; Rochford, 1985; Russell-Gebbett, 1985). In order to comprehend and use technologies, such as X-rays and magnetic resonance imagining (MRI), radiologists and other medical professionals must learn to infer the shapes of cross sections (Hegarty, Keehner, Cohen, Montello, & Lippa, 2007). Furthermore, understanding the cross-sectional structure of materials and mechanisms is a fundamental skill in engineering (Sorby, 2009). On face value, identifying the cross section of a three-dimensional object appears to require spatial visualization abilities, which were characterized by Carroll (1993) as ability to encode spatial information and maintain it in working memory while transforming it. Previous studies determined that the ability to infer a cross section of an object is positively correlated with spatial visualization ability (Cohen & Hegarty, 2012; Kali & Orion, 1996; Keehner, Hegarty, Cohen, Khooshabeh, & Montello, 2008). Unfortunately, not all individuals are equally equipped with spatial visualization ability. There are large individual differences in spatial abilities (Hegarty & Waller, 2005; Voyer, Voyer, & Bryden, 1995), as well as evidence that deficits in spatial thinking affect high school and university students' performance in biology, anatomy, engineering, geology and physics (e.g., Kozhevnikov, Motes, & Hegarty, 2007; Orion et al., 1997; Rochford, 1985; Sorby, 2009). Thus, difficulty in understanding how to infer or interpret cross sections of three-dimensional structures is an example of how individuals with low spatial ability might be at a disadvantage in learning science.

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C.A. Cohen, M. Hegarty / Learning and Individual Differences 33 (2014) 63–71

2. Mutability and training of spatial thinking Piaget proposed that children develop spatial thinking skills by physically interacting with objects in their environment (Piaget & Inhelder, 1967). Meta-analyses investigating the malleability of spatial thinking provide evidence that such skills can be improved through training and experience (Baenninger & Newcombe, 1989; Linn & Petersen, 1985; Uttal et al., 2013). This evidence has led U.S. scientists and educators to call for systematic education of spatial thinking skills at all levels of education (National Research Council, 2006, p. 10). Questions remain about how to best train spatial thinking skills and the nature of the learning that occurs as a result of training. Which tools and instructional methods lead to performance gains and transfer? What are the psychological mechanisms that account for improved performance and transfer after training? Motivated by evidence for the mutability of spatial thinking and by a need to develop new methods to train spatial thinking skills, we developed a brief intervention to train cross-sectioning skill. The stimuli in our experiments are derived from simple geometric solids (cone, cube, cylinder, prism and pyramid), which are among the most elementary recognizable three-dimensional forms (Biederman, 1987; Pani, Jeffries, Shippey, & Schwartz, 1996). We hypothesized that effective training for this task would permit participants to discover and encode the shapes of twodimensional cross sections of geometric solids. We evaluate different accounts of what is learned from this training.

orientation that is orthogonal to the cut surface. We hypothesized that this step could be accomplished by mentally rotating the visualized cut geometric figure, by changing view perspective, or by retrieving from memory an image of a cross section of a similarly shaped object. In summary, mentally representing the cross-section of an object is a multi-step process. The sequence of the proposed steps may vary by individual. Visuospatial working memory is the cognitive system that facilitates the formation and manipulation of mental images, and the ordering of steps in complex spatial visualization tasks. (Baddeley, 1992; Miyake, Rettinger, Friedman, Shah, & Hegarty, 2001). Theories of mental imagery suggest that spatial visualization ability can be characterized as differences in the ability to encode, retrieve from long-term memory, or transform mental images through dynamic mental processes, including rotation, translation, scanning and parsing (Kosslyn, Brunn, Cave, & Wallach, 1984). One possibility is that individuals with limited visuospatial ability have had less experience encoding and manipulating spatial images. As a result they might have a limited store of spatial images in long-term memory. They might also be less facile in basic imagery processes such as rotation and parsing. Here we examine how experience interacting with a virtual model affects both storage and processing of visuospatial stimuli.

4. Accounts of improved performance after spatial training 3. Cognitive analysis of the criterion task In our experiments participants are asked to predict the twodimensional cross section that will result when a simple or complex geometric solid is sliced by a cutting plane (see Fig. 1). Individuals can accomplish spatial thinking tasks such as this by using an imagistic approach (forming and manipulating mental images), and/or by using analytic strategies, such as comparing the features of two stimuli (Cohen & Hegarty, 2007, 2012; Hegarty, 2010; Schultz, 1991). Here we propose an informal task analysis of the steps in an imagistic approach to perform this task. One step is to encode the spatial characteristics of the figure, such as the shape of the geometric solid and the orientation of the cutting plane. Another step is to imagine slicing the object and removing the section of the sliced geometric solid between the viewer and the cutting plane. A further step is to create an image of the cross section of the geometric figure from an

Fig. 1. Sample cross-section test problem. The participant is asked to choose the crosssectional shape that would result from the intersection of the cutting plane and the geometric solid. The correct answer is (c).

Studies in cognitive psychology and education show support for two accounts of the nature of learning after spatial visualization training. An instance-based account proposes that performance gains reflect an increased store of images accumulated during training (Heil, Rosler, Link, & Bajric, 1998; Kail & Park, 1990; Sims & Mayer, 2002; Tarr & Pinker, 1989). For example, Heil et al. (1998) and Tarr and Pinker (1989) found that training on mental rotation problems improved performance only on trained objects at their trained orientations. Sims and Mayer (2002) found that practice on Tetris, a computer game that involves the mental rotation of specific shapes, did not transfer to other mental rotation stimuli. Kail and Park (1990) found that practice on two-dimensional letter rotations did not transfer to mental rotation of unfamiliar letters. The authors accounted for these results by reference to instance theory (Logan, 1988), which proposes that practice on a task increases the strength and/or the number of memory representations of to-be-learned material, but not the underlying processes governing the transformation. The instance-based account predicts no transfer to new stimuli after training. The process-based account of learning proposes that performance gains after spatial training can be accounted for by enhanced mental processing, rather than just a more robust store of encoded images (Leone, Taine, & Droulez, 1993; Wallace & Hofelich, 1992; Wright, Thompson, Ganis, Newcombe, and Kosslyn (2008). This account predicts wide transfer of the trained processes to new stimuli. For example, Leone et al. (1993) found that mental rotation practice on simple figures transferred to the mental rotation of more complex figures. The authors proposed that participants learned to rotate stimuli around their principal frames of reference rather rotating the entire object or its segments. Wallace and Hofelich (1992) found that mental rotation practice improved performance on a two-dimensional task that did not require mental rotation. Situating their results within Kosslyn et al.'s (1984) model, the authors attributed improvement on the distal task to the fact that it shared mental transformation processes with the trained task. Similarly, Wright et al. (2008) found transfer from mental rotation to paper folding and attributed the transfer effects to participants' improved ability to encode stimuli and initiate the transformation process.


5. Tools and methods for spatial training 5.1. Physical and virtual models The active manipulation (vs. passive viewing) or physical models of objects has led to performance gains and transfer in the context of spatial visualization training (Brinkmann, 1966; Lord, 1985; Talley, 1973). Virtual models also can effectively represent three-dimensional structures when physical models are impossible or impractical to use. For example, Duesbury and O'Neil (1996) used manipulable virtual objects to train engineering students to identify three-dimensional objects from their two-dimensional views. Further, Sorby and Baartmans (1996) were successful in training spatial visualization in a semester-long course, which incorporated virtual geometric objects that can be rotated and sliced. Virtual objects can also be used to train specific mental processes. For example, Pani, Chariker, Dawson, and Johnson (2005) used a virtual model of a novel object to improve performance on a particularly challenging three-dimensional rotation task. Viewing and manipulating virtual models is particularly beneficial for learning the spatial configuration of complex objects, such as anatomical structures (Chariker et al., 2011; Garg, Norman, Eva, Spero, & Sharan, 2002; Levinson, Weaver, Garside, McGinn, & Norman, 2007). A common strategy for teaching sectional anatomy (also used in our study) is to allow students to pass a plane through a complex virtual model of an anatomical structure and observe the resulting cross sections. However, viewing a complex model from unlimited perspectives may overwhelm the visuospatial working memory capacity of novice learners. Levinson et al. (2007) found that constraining novice anatomy learners to key views (anterior, inferior, lateral and superior) of a brain model with limited degrees of freedom of manipulation was more beneficial than unrestricted access to multiple views (see Garg et al., 2002 for similar results). In a longitudinal study with novice anatomy learners, Chariker et al. (2011) compared two approaches for learning sectional views of brain anatomy. Participants who learned whole brain anatomy from a three-dimensional model before learning sectional anatomy outperformed participants who learned twodimensional sections alone. According to the authors, having a threedimensional mental representation of the entire brain helped participants organize the locations of two-dimensional anatomical sections. Actively manipulating (vs. passively viewing) three-dimensional displays may be particularly beneficial to individuals with spatial ability (Hoffler, 2010; Meijer & van den Broek, 2010). For example, a recent meta-analysis revealed that individuals with low spatial ability benefitted more than those with moderate and high abilities from interacting with three-dimensional rather than two-dimensional displays (Hoffler, 2010). The authors suggested that the attentional demands of active manipulation might induce low spatial participants to spend more time encoding the visuospatial features of virtual objects than they would spend if they were viewing a two-dimensional nonmanipulable image. 5.2. Animation as a tool for spatial training Animation combines static images into a dynamic visualization, allowing viewers to perceive continuous change (Betrancourt & Tversky, 2000; Lowe, 2008). Animation is frequently used to depict spatial transformations of objects making it well suited to simulate the dynamic cognitive processes that occur in visuospatial working memory during spatial transformations (Kosslyn et al., 1984). Although animation shows promise as a training tool for spatial thinking, transient dynamic images can prove challenging for learners to encode and integrate into long-term memory (Lowe, 1999). The perceptual saliency of material in a display (e. g., the size or color of objects, location of key information, and/or direction of movement in an animation) can direct users' attention toward or away from the most relevant material (Lowe, 1999, 2008). Complicated interfaces can also tax the capacity

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and processing limits of visuospatial working memory, impairing users' ability to encode key information (Chandler, 2004). Interactive interfaces that permit users to pause, rewind, and restart a dynamic display can address some of the challenges posed by the transience of animation (Schwan & Riempp, 2004; Sweller & Chandler, 1994). Another advantage of interactive animation is that it permits the integration of complementary learning activities and feedback into instruction. One such complementary activity is drawing (Ainsworth, Prain, & Tyler, 2011; Gobert & Clement, 1999; Zhang & Linn, 2011). Drawing gives students the opportunity to externalize their internal representations of scientific phenomena, and to subsequently get corrective feedback. In the case of training spatial thinking, drawing may also provide neural feedback that supports learning. Gonzalez et al. (2011) found that the motoric feedback from drawing and copying shapes helped students encode accurate information about spatial configurations. 5.3. Training protocol using virtual models and interactive animation Our intervention used interactive animation, integrated with drawing and feedback, to train participants to identify the two-dimensional cross sections of three-dimensional objects. Participants were first shown a simple geometric figure that was sliced by a cutting plane and were asked to draw its cross section. Next, participants checked the accuracy of their drawings by advancing an interactive cutting plane through a virtual three-dimensional solid that represented the object shown in the drawing trial. As the participant advanced the cutting plane, the correct cross-sectional shape of the drawing trial was revealed and the participant copied the correct shape adjacent to their drawing. We hypothesized that visual feedback provided by observing the correct cross-sectional shape would improve performance. Whereas previous studies have reported performance gains after extended practice on spatial tasks, we examine learning after a short duration of direct instruction (12 min or less). We predicted that participants who received our intervention would significantly outperform a control group on the test figures they viewed during training. If learning is only instance based, they should not show transfer to untrained figures. If learning is process based, they should show transfer to new figures. 6. Experiment 1 6.1. Method 6.1.1. Participants Twenty undergraduate students (approximately one-third of those screened) who met a criterion for low spatial ability (≤15 items correct on the cross-section measure) were recruited from an undergraduate psychology class. The screening criterion represented the 50th percentile of scores from an earlier administration of the cross-section test. Participants were randomly assigned to an intervention group (8 females and 2 males) and a control group (9 females and 1 male). A Mann–Whitney U test showed no significant difference (p = .16) between the mean pre-test scores of participants in the intervention (M = .31, SD = .10) and control (M = .38, SD = .10) groups. All participants received course credit. 7. Materials 7.1. Performance measure The Santa Barbara Solids Test (SBST) (Cohen & Hegarty, 2012) served as the screening test and the pre- and post-training performance measure. Test stimuli are two-dimensional images of single or compound geometric solids, intersected by a cutting plane. As shown in the sample problem pictured in Fig. 1, the participant is asked to identify

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Fig. 2. Figure from the cross-section test: a) a simple figure with an orthogonal cutting plane; b) a joined figure with an orthogonal cutting plane; and c) an embedded figure with an oblique cutting plane.

from four answers the two-dimensional shape that would result if the three-dimensional object were sliced at the indicated plane. The 30 test figures comprise three levels of geometric complexity (see Fig. 2). Simple figures are single geometric solids (a cone, cube, cylinder, three-sided prism, or four-sided pyramid). Joined figures are composed of two simple figures joined at their edges. Embedded figures are composed of one simple figure enmeshed inside of another. Half of the figures have cutting planes that are orthogonal (horizontal or vertical) to the figure's main vertical axis; the other half have cutting planes that are oblique to the main vertical axis. All of the figures are oriented with their vertical axes perpendicular to an imagined horizontal tabletop. The entire test and its subscales demonstrated satisfactory internal reliability (Cohen & Hegarty, 2012). Cronbach's Alpha computed across all items was .91 and for the major subscales of the test was: simple figures, α = .79; joined figures, α = .80; embedded figures, α = .73; orthogonal figures, α = .84; and oblique figures, α = . 85. 7.2. Interactive training animations Each interactive animation displayed a simple virtual figure (a cone, a cube, a cylinder, a three-sided prism or a pyramid) intersected by either an orthogonal or oblique cutting plane. The virtual figure was stationary throughout the course of the animation, while the cutting plane was advanced through the figure by way of a computer mouse. As the cutting plane sliced through the figure, an image of the resulting two-dimensional cross section appeared on the left side of the display (see Fig. 3). The interactive animations could be paused and advanced at will, allowing users to explore the virtual object at a selfdetermined pace. The animations were displayed in a QuickTime©

Fig. 4. (a) Drawing trial for the orthogonal cone figure; (b) participant's first and (c) second attempts to draw the orthogonal horizontal) cross section of the cone.

digital video viewer. Ten interactive animations (orthogonal and oblique sections of the five primary simple figures) were used to train participants in Experiment 1. 7.3. Drawing trials Each drawing trial was a two-dimensional color image of one of the 10 simple figures represented in the interactive training animations. The two-dimensional images included highlights, shadows and perspective cues to indicate depth in the third dimension. Fig. 4a is a sample drawing trial. 8. Procedure 8.1. Spatial ability screening Participants were individually screened for spatial ability by completing the Santa Barbara Solids Test. Those who met the criterion for low spatial ability were randomly assigned to the trained or control condition and completed the experiment during the same testing session. Those who did not meet the criterion were thanked for their participation and dismissed. 8.2. Training intervention

Fig. 3. Screen shot from the orthogonal (horizontal) cone training animation.

The participant was seated at a desktop computer and asked to draw the cross section of the figure shown in a drawing trial. After the participant completed his/her first drawing, the experimenter instructed the participant to advance the interactive cutting plane slowly through the figure three times, and to bring it to rest at the same position as


shown in the drawing trial. The experimenter asked the participant to copy the correct cross-sectional shape, as shown in the animation, beneath the first drawing, and to compare the two drawings, indicating with a + or − sign if they were the same shape. The ellipse shown in Fig. 4b is one participant's first attempt to draw the cross section of the cone bisected by the horizontal plane in Fig. 4a. After interacting with the training animation, the same participant drew Fig. 4c and added the minus sign in Fig. 4b to indicate that the drawings were different shapes. Participants were trained on the remaining nine figures with the same procedure. If the participant drew an incorrect shape of any drawing trial, the participant was retrained with the interactive animation until s/he drew the correct shape for the trial. The 10-figure training cycle was repeated for all participants. Training was complete when the participant drew a correct cross section on first attempt during a given training cycle. After training, the participant completed the posttest, which was identical to the pretest. 8.3. Control Participants in the control condition read a section of non-fiction prose (a biography) for 10 min and then completed the posttest. 9. Results and discussion There was an error in one item on the cross-section and this item was removed from all remaining analyses. The remaining 29 test figures were classified into three categories (trained, similar and new) for analysis of training and transfer. Trained (10) test figures were simple solids, identical to those used in the interactive animations. Similar figures (16) were composed of two solids, at least one of which had been trained (thirteen were composed of two trained solids and three were composed of one trained and one untrained solid). New figures (3) were composed of two untrained solids. Fig. 5 shows pre- and posttest performance means and standard errors for Experiment 1, by type of figure and condition. Given that the small sample sizes and restricted range of variance, we used the non-parametric Mann–Whitney U test to assess group differences across the three categories of figures at pre- and posttest. At pretest, there were no significant differences between the intervention and

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control groups for trained figures, similar figures, new figures, or across 29 figures (all p-values ≥ .22). In contrast, participants who completed the animation training significantly outperformed the control at posttest on trained figures, p b . 01, similar figures, p = . 05, and across all 29 scored figures, p = . 003. There were no significant differences in performance between the two groups on new figures, p = .28. Analyses of within-subject improvement from pre- to post test (Wilcoxon Signed Rank Tests) showed significant effects for the intervention group overall (p b .01) and for trained figures (p b .01), similar figures (p b .01), and new figures (p b .05). The control group also showed significant improvement overall from pre- to posttest (p b .05), but gains for this group for the sub-categories of trained figures (p = .06), similar figures (p = .07), and new figures (p = .25) were not statistically significant. The overall improvement for the control group suggests that merely viewing the test figures on two subsequent occasions within a short period of time may confer some training benefit, as is typical for spatial tests (Uttal et al., 2013). What was the nature of the learning in Experiment 1? The performance gains on trained figures suggest that, at a minimum, participants in the intervention condition formed images of cross-sectional shapes during training and were able to retain these images long enough to recognize them on the post-test. The performance gains on similar figures suggest that trained participants could identify trained shapes as parts of more complex similar figures, a result which can be supported by either an instance or a process account of learning. It is noteworthy that these performance gains occurred after a relatively modest amount (10–12 min) of training. Results for the new figures improved from pretest to posttest for the intervention group but not the control group, suggesting some transfer. However, the intervention group did not significantly outperform the control group on new figures after training. A limitation of Experiment 1 was that only three trials contained untrained (new) figures. This restricted our ability to examine transfer, as new figures are the critical trials for discriminating between instance and process-based accounts. We address this limitation in Experiment 2. 10. Experiment 2 Experiment 2 was identical to Experiment 1 with the exception that training was limited to animations of four figures (the orthogonal and

Fig. 5. Experiment 1: Performance means at pre- and posttest by type of figure and condition.

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oblique cross sections of the cone and the cube). Consequently, there were 13 new figures to test transfer effects. Given the success of the training in Experiment 1, one goal of this study was to test the effectiveness of an even shorter training intervention, with two rather than five geometric figures. We chose the cone and the cube because they varied in both shape of base (circle vs. square) and whether or not the sides were parallel, which were features on which the larger group of shapes varied. Transfer is not predicted by an instance-based account of learning alone, as this account presumes that learning is confined to the formation of memories of the specific stimuli seen during training. In contrast, process-based theory predicts transfer to new figures, because it suggests that the more general processes of encoding the spatial features of an object, mentally slicing the object and imagining the cross section are trained.

10.1. Method 10.1.1. Participants As in Experiment 1, prospective participants were screened for low spatial ability, using the same criterion (≤ 15 items correct on the cross-section test). Participants were randomly assigned to an intervention group (11 females) and a control group (11 females and one male). A Mann–Whitney U test showed no significant difference (p = .57) between the pre-test scores of the intervention (M = .35, SD = .09) and control (M = .36, SD = .12) groups. All participants received course credit for their participation.

10.1.2. Materials The materials were identical to those used in Experiment 1, with the exception that only four interactive animations (orthogonal and oblique cutting planes of the cone and the cube) and four corresponding drawing trials were used to train participants.

10.2. Procedure 10.2.1. Spatial ability screening Participants were screened in pairs. Those who met the screening criteria were randomly assigned to the trained or control conditions.

10.2.2. Training and control The training procedure was identical to that used in Experiment 1, with the exception that trained participants interacted with four animations. Training with the four animations lasted 6–8 min. Participants in the control condition read a section of non-fiction prose for 8 min.

11. Results and discussion As in Experiment 1, one flawed problem was eliminated from the analysis. The 29 remaining problems were reclassified into three categories for analysis of transfer effects. The four trained figures were single solids (orthogonal and oblique views of the cone and cube), identical to those used in the interactive animations. As in Experiment 1, similar figures were composed of two solids, at least one of which had been trained. Of the 11 similar figures, 9 were composed of one trained solid and one untrained solid and two were composed of two trained solids. Each of the 14 new figures was composed of two untrained solids. Fig. 6 shows and posttest performance means for Experiment 2, by type of figure and condition. At pretest, there were no significant differences in performance between the two groups for trained (4) figures, similar (11) figures, or new (14) figures (all p-values ≥ .09). In contrast, there were significant differences between the intervention and control groups at posttest for trained figures, p b . 001; similar figures, p = . 001; new figures, p b .001; and all figures, p b .001. Analyses of within-subject improvement from pre- to post test (Wilcoxon Signed Rank Tests) showed significant effects for the intervention group overall (p b .01) and for trained figures (p b .01), similar figures (p b .01), and new figures (p b .01). In contrast, the control group showed no significant improvement overall (p = .17), or for trained (p = 1.0), similar (p = .51), or new figures (p = .16). Participants who received the intervention in Experiment 2 were trained on orthogonal and oblique cross sections of only two figures (a cone and a cube), yet they outperformed the control group on untrained shapes (orthogonal and oblique cross sections of cylinders, prisms and pyramids). The results of this experiment are consistent with a process-based account of visuospatial learning and cannot be accounted for by instance theory alone. Although instance-based learning might have occurred, it appears that participants also learned a more general process that could be applied to new objects. Finally, it is notable that

Fig. 6. Experiment 2: Performance means at pre- and posttest by type of figure and condition.


the training intervention in Experiment 2 was even shorter than that in Experiment 1 (four learning trials in contrast with ten in Experiment 1), providing stronger evidence for the effectiveness of this approach. 12. General discussion These experiments investigated the benefits of using interactive animation and virtual models to train a specific spatial visualization skill— inferring the shape of cross sections of a three-dimensional object. Both experiments demonstrated significant performance gains for trained participants on trained and untrained figures and significant differences in posttest performance between trained and control participants on trained figures. In Experiment 2, trained participants also outperformed control participants on untrained figures on the posttest, providing strong evidence for transfer. While previous studies (e.g., Chariker et al., 2011; Levinson et al., 2007; Pani et al., 2005; Sorby & Baartmans, 1996) have used similar training interventions with virtual models, our intervention is novel in that it involves drawing the predicted cross section and using the virtual models to provide feedback on drawings. Our results show that large performance gains can be achieved after a short period of such training with simple objects. As in studies that used interactive models to teach anatomy (Chariker et al., 2011; Garg et al., 2002; Levinson et al., 2007), interaction with the virtual object figures in these experiments substitutes for the experience of slicing a physical object and viewing its internal structure. The interactive displays used in our experiments have simple, yet flexible, interfaces that can be paused and advanced at will, allowing users to explore the virtual object at a self-determined order and pace. In addition, multiple training animations (e.g., orthogonal and oblique slices of cones) can be viewed simultaneously. Supportive instructional activities, such as drawing and copying shapes, can be easily integrated into instruction with the interactive interface. 12.1. Accounts of improved performance after spatial training We framed our study with respect to two theoretical accounts of spatial learning. Instance-based learning proposes that improved performance after spatial training results from an increase in the strength and/or the number of memory representations of trained material, and predicts no transfer to new stimuli after training (Heil et al., 1998; Kail & Park, 1990; Logan, 1988; Tarr & Pinker, 1989). Process-based learning (Leone et al., 1993; Wallace & Hofelich, 1992; Wright et al., 2008) proposes that performance gains after training reflect the strengthening of existing mental processes (e.g., the ability to rotate stimuli around object-centered frames of reference) and/or the acquisition of new spatial transformation processes. This theory predicts transfer of training to new stimuli. While instance-based learning might have occurred in our studies, our results rule out an instance-based account as the sole explanation for our results. Participants in the experimental conditions of both experiments showed significant pre- to post-test increases in their performance on new stimuli (geometric figures they had not manipulated during training), and in Experiment 2, participants in the experimental condition outperformed those in the control group on new (untrained) stimuli in the posttest. These results indicate that training transferred to untrained stimuli, a result that cannot be accounted for by instance learning alone, but which is consistent with process-based learning. While we observed transfer of training to novel stimuli, we acknowledge that our stimuli were simple geometric solids and we tested only near transfer to other stimuli made up of simple (if different) geometric solids. It remains to be seen whether training on the simple geometric figures used here would transfer to real-world cross-sectioning tasks such as interpreting X-rays and MRI images and predicting the crosssections of geologic structures. A process-based account of learning predicts wide transfer of trained skills. According to this account, our training intervention with simple

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geometric solids should transfer to imagining of cross sections of more complex objects. However, a third account of spatial learning predicts more circumscribed transfer, and is worthy of testing in future experiments. This intuition account of spatial learning (Pani, Zhou, & Friend, 1997; Pani et al., 2005, 1996) proposes that we organize our percepts of the spatial properties of objects and their transformations in frameworks that allow us to predict similar transformations of similar objects at similar orientations, but does not predict general transfer to all objects. For example, this account would predict that after learning the shapes of horizontal and oblique cross-sections of a cone (a circle and ovoid shape, respectively) participants could predict the shapes of horizontal and oblique cross-sections of other cones or cone-like structures, but would not be able to predict the results of sections of less similar objects (such as irregular geological structures). An intuition account proposes that improved performance results from developing a new set of spatial intuitions, rather than from learning new spatial transformation processes or strengthening existing processes. In summary, it is clear from our results that an instance-based account alone cannot explain the results of training. Another account, either process- or intuition-based, is required to explain the pattern of results in our experiments. To test the claims of intuition theory against the claims of process theory, we would need to examine transfer to less similar and more complex stimuli. This is an important goal for future research. 12.2. Applications to training and transfer for STEM disciplines The stimuli used in our study were quite simple, compared to the more complex spatial structures that need to be considered in STEM domains such as anatomy, engineering and geology. However, our pretest scores indicated that imagining cross sections of simple geometric solids was challenging for adults with poor spatial abilities, justifying the use of these stimuli. Use of these stimuli may address a need to train spatial skills in younger students. The National Council of Teachers of Mathematics (NCTM, 2000) recommends incorporating training in geometric thinking into K-12 education, with instruction starting as early as grades K-2. Skills specified by the NCTM as intrinsic to geometric thinking include recognizing the attributes of two-and three-dimensional shapes, creating mental images of geometric shapes, and recognizing shapes from different view perspectives (NCTM, 2000). The present protocol and stimuli may be appropriate for very young populations, as there is evidence that children as young as 5 years of age have the kinesthetic and motor skills to effectively use computer mouse interfaces in nonspeeded tasks (Lane & Ziviani, 2010). Furthermore, similar methodologies (including drawing and receiving feedback from models) have recently used to train student to infer cross sections of geological structures (Gagnier, Atit, Ormand, & Shipley, 2014) and to train representational competence in organic chemistry (Padalkar & Hegarty, 2012), demonstrating the applicability of our approach to adult STEM learning. There are also ways in which the current intervention might be enhanced to meet the challenges of training more complex spatial skills. More time manipulating virtual models could increase participants' encoding of the spatial features of the stimuli (Wright et al., 2008). Training with a greater variety of objects, including more complex objects, and with training sessions distributed over time has been effective in other studies (Chariker et al., 2011; Pani et al., 2005; Sorby & Baartmans, 1996). Manipulating physical models of the trained figures may also improve performance, given the evidence for the shared neural substrates of haptic and visual systems for encoding three-dimensional structure (Amedi, Malach, Hendler, Peled, & Zohary, 2001; Easton, Greene, & Srinivas, 1997; Harman, Humphrey, & Goodale, 1999; James, James, Humphrey, & Goodale, 2006; Reales & Ballesteros, 1999). If this is true, it would be important to disambiguate which aspects of a real model (e. g., better depth cues, more naturalistic manipulation) offer an advantage when used instead of, or in combination with, virtual models. Finally, verbal

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instructions, including reference to spatial features of the models, could provide an instructional benefit beyond that provided by interactive animation alone (Mayer, 2008).

13. Limitations This study is limited in that we examined only short-term learning. It is important for future studies to test the longer-term learning effects of our intervention. Our study is also limited in that we examined only one criterion task, which was a multiple-choice test. Future research should test if training on the present stimuli would transfer to other tasks, such as drawing cross sections; given that our intervention involves drawing, we might expect it to have even larger effect on drawing tasks. A final possible limitation is our use of two-dimensional printed stimuli to depict the three-dimensional figures on the pre- and posttests. Two-dimensional projections of three-dimensional stimuli are fundamentally ambiguous, and this ambiguity might be somewhat responsible for the poor performance of participants in our pretest. In the future, physical models of the simple geometric solids could also be provided to resolve any possible ambiguity about threedimensional perspective cues in the two-dimensional images. Alternatively, presenting spatial ability tests on computers using virtual reality displays could provide depth cues such as stereoscopic viewing, and the ability to rotate the figures (providing motion-based depth cues). By simulating three-dimensional space, augmented and virtual reality testing environments may offer a more ecologically valid tool for measuring spatial skills. The use of computer-based virtual reality displays to test and train spatial ability offers a number of additional benefits, including the ability to collect response latencies and information about solution strategies (Kaufmann et al., 2008).

14. Conclusion In conclusion, this study introduces a short training intervention that was highly effective and can easily be adapted to the training of simple spatial skills with children or more complex spatial skills with adults. The results of our experiments add to evidence that interventions using virtual models and interactive animations is can be promising methodologies for training spatial skills, and alleviating one of the difficulties faced by low-spatial individuals in learning science.

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Visualizing cross sections: Training spatial thinking ...

Visualizing cross sections: Training spatial thinking ...

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