In two experiments, we investigated the efficacy of a brief intervention that used interactive animation to trainstudents to infer the two-dimensional cross section of a virtual three-dimensional geometric figure. Under-graduates with poor spatial ability were assigned to receive the intervention or to a control group. Comparedto the control group, trained participants improved significantly on stimuli viewed during the intervention anddemonstrated transfer to untrained stimuli. Results were considered with respect to two accounts ofperformance gains and transfer after spatial visualization training, an instance-based account and a process-based account. The instance-based account attributes performance gains to a larger store of memories andpredicts no transfer to new stimuli or new spatial processes. The process-based account attributes performancegains to increased efficiency of mental processes and predicts transfer to new stimuli and tasks that share thesame mental processes. The results of these experiments cannot be accounted for by an instance-based accountalone. Performance gains and transfer in these experiments suggest that interactive animation and virtual solidsare promising tools for training spatial thinking in undergraduates.
A geology student observes an outcrop of rocks and tries to visualizethe cross-sectional structure of the landforms beneath it. An anatomystudent examines a two-dimensional slice of liver tissue, notes its keyspatial features, and infers that it is a longitudinal, rather than lateralsection of the organ. A mechanical engineering student sketches aschematic diagram of a building's heating and electrical systems,anticipating the angles at which exhaust vents and electrical cableswill cross. Each student is using spatial thinking skills to mentallyrepresent a two-dimensional cross section, or slice, of a three-dimensional object or structure. The ability to infer the external shapeand internal features of sections of objects and structures plays animportant role inmany domains of scientific thinking. It is a fundamen-tal skill in geology, where it has been referred to as “visual penetrationability” (Kali & Orion, 1996; Orion, Ben-Chaim, & Kali, 1997). Anatomystudents must learn to visualize, section, and rotate cross sections ofphysical structures, and learn to recognize these structures (Chariker,
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rty, M., Visualizing cross secti014), http://dx.doi.org/10.10
Naaz, & Pani, 2011; Rochford, 1985; Russell-Gebbett, 1985). In orderto comprehend and use technologies, such as X-rays and magneticresonance imagining (MRI), radiologists and other medical profes-sionals must learn to infer the shapes of cross sections (Hegarty,Keehner, Cohen, Montello, & Lippa, 2007). Furthermore, understandingthe cross-sectional structure of materials and mechanisms is afundamental skill in engineering (Sorby, 2009).
On face value, identifying the cross section of a three-dimensionalobject appears to require spatial visualization abilities, which werecharacterized by Carroll (1993) as ability to encode spatial informationand maintain it in working memory while transforming it. Previousstudies determined that the ability to infer a cross section of anobject is positively correlated with spatial visualization ability (Cohen& Hegarty, 2012; Kali & Orion, 1996; Keehner, Hegarty, Cohen,Khooshabeh, & Montello, 2008). Unfortunately, not all individuals areequally equipped with spatial visualization ability. There are largeindividual differences in spatial abilities (Hegarty & Waller, 2005;Voyer, Voyer, & Bryden, 1995), aswell as evidence that deficits in spatialthinking affect high school and university students' performance in bio-logy, 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 interpretcross sections of three-dimensional structures is an example of howindividuals with low spatial ability might be at a disadvantage inlearning science.
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2. Mutability and training of spatial thinking
Piaget proposed that children develop spatial thinking skills byphysically interacting with objects in their environment (Piaget &Inhelder, 1967). Meta-analyses investigating the malleability of spatialthinking provide evidence that such skills can be improved throughtraining and experience (Baenninger & Newcombe, 1989; Linn &Petersen, 1985; Uttal et al., 2013). This evidence has led U.S. scientistsand educators to call for systematic education of spatial thinking skillsat all levels of education (National Research Council, 2006, p. 10).
Questions remain about how to best train spatial thinking skills andthe nature of the learning that occurs as a result of training.Which toolsand instructional methods lead to performance gains and transfer?What are the psychological mechanisms that account for improvedperformance and transfer after training? Motivated by evidence forthe mutability of spatial thinking and by a need to develop newmethods to train spatial thinking skills, we developed a brief inter-vention to train cross-sectioning skill. The stimuli in our experimentsare derived from simple geometric solids (cone, cube, cylinder, prismand pyramid), which are among the most elementary recognizablethree-dimensional forms (Biederman, 1987; Pani, Jeffries, Shippey, &Schwartz, 1996). We hypothesized that effective training for this taskwould permit participants to discover and encode the shapes of two-dimensional cross sections of geometric solids. We evaluate differentaccounts of what is learned from this training.
3. Cognitive analysis of the criterion task
In our experiments participants are asked to predict the two-dimensional cross section that will result when a simple or complexgeometric solid is sliced by a cutting plane (see Fig. 1). Individuals canaccomplish spatial thinking tasks such as this by using an imagisticapproach (forming and manipulating mental images), and/or by usinganalytic strategies, such as comparing the features of two stimuli(Cohen & Hegarty, 2007, 2012; Hegarty, 2010; Schultz, 1991). Herewe propose an informal task analysis of the steps in an imagisticapproach to perform this task. One step is to encode the spatialcharacteristics of the figure, such as the shape of the geometric solidand the orientation of the cutting plane. Another step is to imagineslicing the object and removing the section of the sliced geometricsolid between the viewer and the cutting plane. A further step is tocreate 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 cross-sectional shape that would result from the intersection of the cutting plane and thegeometric solid. The correct answer is (c).
Please cite this article as: Cohen, C.A., & Hegarty, M., Visualizing cross sectiobjects, Learning and Individual Differences (2014), http://dx.doi.org/10.10
orientation that is orthogonal to the cut surface. We hypothesized thatthis step could be accomplished by mentally rotating the visualizedcut geometric figure, by changing view perspective, or by retrievingfrom memory an image of a cross section of a similarly shaped object.In summary, mentally representing the cross-section of an object is amulti-step process. The sequence of the proposed steps may vary byindividual.
Visuospatial working memory is the cognitive system that facili-tates the formation and manipulation of mental images, and theordering of steps in complex spatial visualization tasks. (Baddeley,1992; Miyake, Rettinger, Friedman, Shah, & Hegarty, 2001). Theoriesof mental imagery suggest that spatial visualization ability can becharacterized as differences in the ability to encode, retrieve fromlong-term memory, or transform mental images through dynamicmental processes, including rotation, translation, scanning and pars-ing (Kosslyn, Brunn, Cave, & Wallach, 1984). One possibility is thatindividuals with limited visuospatial ability have had less experienceencoding and manipulating spatial images. As a result they mighthave a limited store of spatial images in long-term memory. Theymight also be less facile in basic imagery processes such as rotationand parsing. Here we examine how experience interacting with avirtual model affects both storage and processing of visuospatialstimuli.
4. Accounts of improved performance after spatial training
Studies in cognitive psychology and education show support fortwo accounts of the nature of learning after spatial visualizationtraining. An instance-based account proposes that performancegains reflect an increased store of images accumulated during train-ing (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 rotationproblems improved performance only on trained objects at theirtrained orientations. Sims and Mayer (2002) found that practice onTetris, a computer game that involves the mental rotation of specificshapes, did not transfer to other mental rotation stimuli. Kail andPark (1990) found that practice on two-dimensional letter rotationsdid not transfer to mental rotation of unfamiliar letters. The authorsaccounted for these results by reference to instance theory (Logan,1988), which proposes that practice on a task increases the strengthand/or the number of memory representations of to-be-learnedmaterial, but not the underlying processes governing the transfor-mation. The instance-based account predicts no transfer to newstimuli after training.
The process-based account of learning proposes that performancegains after spatial training can be accounted for by enhanced mentalprocessing, 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 accountpredicts wide transfer of the trained processes to new stimuli. Forexample, Leone et al. (1993) found that mental rotation practice onsimple figures transferred to the mental rotation of more complexfigures. The authors proposed that participants learned to rotatestimuli around their principal frames of reference rather rotatingthe entire object or its segments. Wallace and Hofelich (1992)found that mental rotation practice improved performance on atwo-dimensional task that did not require mental rotation. Situatingtheir results within Kosslyn et al.'s (1984) model, the authorsattributed improvement on the distal task to the fact that it sharedmental transformation processes with the trained task. Similarly,Wright et al. (2008) found transfer from mental rotation topaper folding and attributed the transfer effects to participants'improved ability to encode stimuli and initiate the transformationprocess.
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5. Tools and methods for spatial training
5.1. Physical and virtual models
The active manipulation (vs. passive viewing) or physical models ofobjects has led to performance gains and transfer in the context of spa-tial visualization training (Brinkmann, 1966; Lord, 1985; Talley, 1973).Virtual models also can effectively represent three-dimensional struc-tureswhen physicalmodels are impossible or impractical to use. For ex-ample, Duesbury and O'Neil (1996) used manipulable virtual objects totrain engineering students to identify three-dimensional objects fromtheir two-dimensional views. Further, Sorby and Baartmans (1996)were successful in training spatial visualization in a semester-longcourse,which incorporated virtual geometric objects that can be rotatedand sliced. Virtual objects can also be used to train specific mentalprocesses. For example, Pani, Chariker, Dawson, and Johnson (2005)used a virtual model of a novel object to improve performance on aparticularly challenging three-dimensional rotation task.
Viewing and manipulating virtual models is particularly beneficialfor learning the spatial configuration of complex objects, such asanatomical 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 usedin our study) is to allow students to pass a plane through a complex vir-tual model of an anatomical structure and observe the resulting crosssections. However, viewing a complex model from unlimited perspec-tives may overwhelm the visuospatial working memory capacity ofnovice learners. Levinson et al. (2007) found that constraining noviceanatomy learners to key views (anterior, inferior, lateral and superior)of a brain model with limited degrees of freedom of manipulation wasmore beneficial than unrestricted access to multiple views (see Garget al., 2002 for similar results). In a longitudinal study with novice anat-omy learners, Chariker et al. (2011) compared two approaches forlearning sectional views of brain anatomy. Participants who learnedwhole brain anatomy from a three-dimensional model before learningsectional anatomy outperformed participants who learned two-dimensional sections alone. According to the authors, having a three-dimensional mental representation of the entire brain helped partici-pants organize the locations of two-dimensional anatomical sections.
Actively manipulating (vs. passively viewing) three-dimensionaldisplays may be particularly beneficial to individuals with spatial ability(Hoffler, 2010; Meijer & van den Broek, 2010). For example, a recentmeta-analysis revealed that individuals with low spatial ability be-nefitted more than those with moderate and high abilities frominteracting with three-dimensional rather than two-dimensionaldisplays (Hoffler, 2010). The authors suggested that the attentionaldemands of active manipulation might induce low spatial participantsto spendmore time encoding the visuospatial features of virtual objectsthan they would spend if they were viewing a two-dimensional non-manipulable 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 depictspatial transformations of objects making it well suited to simulatethe dynamic cognitive processes that occur in visuospatial workingmemory during spatial transformations (Kosslyn et al., 1984). Althoughanimation shows promise as a training tool for spatial thinking,transient dynamic images can prove challenging for learners to encodeand integrate into long-term memory (Lowe, 1999). The perceptualsaliency ofmaterial in a display (e. g., the size or color of objects, locationof key information, and/or direction of movement in an animation) candirect users' attention toward or away from the most relevant material(Lowe, 1999, 2008). Complicated interfaces can also tax the capacity
Please cite this article as: Cohen, C.A., & Hegarty, M., Visualizing cross sectiobjects, Learning and Individual Differences (2014), http://dx.doi.org/10.10
and processing limits of visuospatial working memory, impairingusers' ability to encode key information (Chandler, 2004).
Interactive interfaces that permit users to pause, rewind, and restarta dynamic display can address someof the challenges posedby the tran-sience of animation (Schwan & Riempp, 2004; Sweller & Chandler,1994). Another advantage of interactive animation is that it permitsthe integration of complementary learning activities and feedback intoinstruction. One such complementary activity is drawing (Ainsworth,Prain, & Tyler, 2011; Gobert & Clement, 1999; Zhang & Linn, 2011).Drawing gives students the opportunity to externalize their internalrepresentations of scientific phenomena, and to subsequently getcorrective feedback. In the case of training spatial thinking, drawingmay also provide neural feedback that supports learning. Gonzalezet al. (2011) found that themotoric feedback fromdrawing and copyingshapes helped students encode accurate information about spatialconfigurations.
5.3. Training protocol using virtual models and interactive animation
Our intervention used interactive animation, integrated with draw-ing and feedback, to train participants to identify the two-dimensionalcross sections of three-dimensional objects. Participants were firstshown a simple geometric figure that was sliced by a cutting planeand were asked to draw its cross section. Next, participants checkedthe accuracy of their drawings by advancing an interactive cuttingplane through a virtual three-dimensional solid that represented theobject shown in the drawing trial. As the participant advanced thecutting plane, the correct cross-sectional shape of the drawing trialwas revealed and the participant copied the correct shape adjacent totheir drawing. We hypothesized that visual feedback provided byobserving the correct cross-sectional shape would improve perfor-mance. Whereas previous studies have reported performance gainsafter extended practice on spatial tasks, we examine learning after ashort duration of direct instruction (12 min or less). We predictedthat participants who received our intervention would significantlyoutperform a control group on the test figures they viewed duringtraining. If learning is only instance based, they should not showtransfer to untrained figures. If learning is process based, they shouldshow transfer to new figures.
6. Experiment 1
6.1. Method
6.1.1. ParticipantsTwenty undergraduate students (approximately one-third of those
screened)whomet a criterion for low spatial ability (≤15 items correcton the cross-section measure) were recruited from an undergraduatepsychology class. The screening criterion represented the 50th percen-tile of scores from an earlier administration of the cross-section test.Participants were randomly assigned to an intervention group (8females and 2 males) and a control group (9 females and 1 male). AMann–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. Allparticipants 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 performancemeasure. Test stimuli are two-dimensional images of single or com-pound geometric solids, intersected by a cutting plane. As shown inthe sample problempictured 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 cuttingplane; b) a joined figure with an orthogonal cutting plane; and c) an embedded figurewith an oblique cutting plane.
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.
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from four answers the two-dimensional shape that would result if thethree-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 arecomposed of two simple figures joined at their edges. Embedded figuresare composed of one simple figure enmeshed inside of another. Half ofthe figures have cutting planes that are orthogonal (horizontal or verti-cal) to the figure's main vertical axis; the other half have cutting planesthat are oblique to the main vertical axis. All of the figures are orientedwith their vertical axes perpendicular to an imagined horizontal table-top. The entire test and its subscales demonstrated satisfactory internalreliability (Cohen & Hegarty, 2012). Cronbach's Alpha computed acrossall items was .91 and for the major subscales of the test was: simplefigures, α = .79; joined figures, α = .80; embedded figures, α = .73;orthogonal figures, α = .84; and oblique figures, α = . 85.
Fig. 3. Screen shot from the orthogonal (horizontal) cone training animation.
Please cite this article as: Cohen, C.A., & Hegarty, M., Visualizing cross sectiobjects, Learning and Individual Differences (2014), http://dx.doi.org/10.10
digital video viewer. Ten interactive animations (orthogonal andoblique sections of the five primary simple figures) were used to trainparticipants in Experiment 1.
7.3. Drawing trials
Each drawing trial was a two-dimensional color image of one of the10 simple figures represented in the interactive training animations.The two-dimensional images included highlights, shadows andperspective cues to indicate depth in the third dimension. Fig. 4a is asample drawing trial.
8. Procedure
8.1. Spatial ability screening
Participants were individually screened for spatial ability bycompleting the Santa Barbara Solids Test. Those who met the criterionfor low spatial ability were randomly assigned to the trained or controlcondition and completed the experiment during the same testingsession. Those who did not meet the criterion were thanked for theirparticipation and dismissed.
8.2. Training intervention
The participantwas seated at a desktop computer and asked to drawthe cross section of the figure shown in a drawing trial. After the partic-ipant completed his/her first drawing, the experimenter instructed theparticipant to advance the interactive cutting plane slowly throughthe figure three times, and to bring it to rest at the same position as
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shown in the drawing trial. The experimenter asked the participant tocopy the correct cross-sectional shape, as shown in the animation, be-neath the first drawing, and to compare the two drawings, indicatingwith a + or − sign if they were the same shape. The ellipse shown inFig. 4b is one participant's first attempt to draw the cross section ofthe cone bisected by the horizontal plane in Fig. 4a. After interactingwith the training animation, the same participant drew Fig. 4c andadded the minus sign in Fig. 4b to indicate that the drawings weredifferent shapes.
Participants were trained on the remaining nine figures with thesame procedure. If the participant drew an incorrect shape of any draw-ing trial, the participant was retrained with the interactive animationuntil s/he drew the correct shape for the trial. The 10-figure trainingcycle was repeated for all participants. Training was complete whenthe participant drew a correct cross section on first attempt duringa given training cycle. After training, the participant completed theposttest, which was identical to the pretest.
8.3. Control
Participants in the control condition read a section of non-fictionprose (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 itemwas removed from all remaining analyses. The remaining 29 testfigureswere classified into three categories (trained, similar and new) for anal-ysis of training and transfer. Trained (10) test figureswere 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 werecomposed 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 standarderrors for Experiment 1, by type of figure and condition. Given thatthe small sample sizes and restricted range of variance, we used thenon-parametric Mann–Whitney U test to assess group differencesacross the three categories of figures at pre- and posttest. At pretest,there were no significant differences between the intervention and
Fig. 5. Experiment 1: Performance means at pre-
Please cite this article as: Cohen, C.A., & Hegarty, M., Visualizing cross sectiobjects, Learning and Individual Differences (2014), http://dx.doi.org/10.10
control groups for trained figures, similar figures, new figures, or across29 figures (all p-values ≥ .22). In contrast, participants who completedthe animation training significantly outperformed the control at post-test on trained figures, p b . 01, similar figures, p = . 05, and across all29 scored figures, p = . 003. There were no significant differences inperformance 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 inter-vention group overall (p b .01) and for trained figures (p b .01), similarfigures (p b .01), and new figures (p b .05). The control group alsoshowed significant improvement overall from pre- to posttest (pb .05), but gains for this group for the sub-categories of trained figures(p = .06), similar figures (p = .07), and new figures (p = .25) werenot statistically significant. The overall improvement for the controlgroup suggests that merely viewing the test figures on two subsequentoccasions within a short period of time may confer some training bene-fit, as is typical for spatial tests (Uttal et al., 2013).
What was the nature of the learning in Experiment 1? The perfor-mance gains on trained figures suggest that, at a minimum, participantsin the intervention condition formed images of cross-sectional shapesduring training andwere able to retain these images long enough to rec-ognize them on the post-test. The performance gains on similar figuressuggest that trained participants could identify trained shapes as partsof more complex similar figures, a result which can be supported by ei-ther an instance or a process account of learning. It is noteworthy thatthese performance gains occurred after a relatively modest amount(10–12 min) of training.
Results for the new figures improved from pretest to posttest for theintervention group but not the control group, suggesting some transfer.However, the intervention group did not significantly outperform thecontrol group on new figures after training. A limitation of Experiment1 was that only three trials contained untrained (new) figures. Thisrestricted our ability to examine transfer, as new figures are the criticaltrials 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 thattraining was limited to animations of four figures (the orthogonal and
and posttest by type of figure and condition.
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oblique cross sections of the cone and the cube). Consequently, therewere 13 new figures to test transfer effects. Given the success of thetraining in Experiment 1, one goal of this studywas to test the effective-ness of an even shorter training intervention, with two rather than fivegeometric figures. We chose the cone and the cube because they variedin both shape of base (circle vs. square) and whether or not the sideswere parallel, which were features on which the larger group of shapesvaried. Transfer is not predicted by an instance-based account of learn-ing alone, as this account presumes that learning is confined to theformation of memories of the specific stimuli seen during training. Incontrast, process-based theory predicts transfer to new figures, becauseit suggests that the more general processes of encoding the spatialfeatures of an object, mentally slicing the object and imagining thecross section are trained.
10.1. Method
10.1.1. ParticipantsAs in Experiment 1, prospective participants were screened for low
spatial ability, using the same criterion (≤15 items correct on thecross-section test). Participants were randomly assigned to an interven-tion group (11 females) and a control group (11 females and onemale).A Mann–Whitney U test showed no significant difference (p= .57) be-tween the pre-test scores of the intervention (M = .35, SD = .09) andcontrol (M = .36, SD = .12) groups. All participants received coursecredit for their participation.
10.1.2. MaterialsThe materials were identical to those used in Experiment 1, with
the exception that only four interactive animations (orthogonal andoblique cutting planes of the cone and the cube) and four correspondingdrawing trials were used to train participants.
10.2. Procedure
10.2.1. Spatial ability screeningParticipants were screened in pairs. Those who met the screening
criteria were randomly assigned to the trained or control conditions.
Fig. 6. Experiment 2: Performance means at pre-
Please cite this article as: Cohen, C.A., & Hegarty, M., Visualizing cross sectiobjects, Learning and Individual Differences (2014), http://dx.doi.org/10.10
10.2.2. Training and controlThe training procedure was identical to that used in Experiment 1,
with the exception that trained participants interactedwith four anima-tions. Training with the four animations lasted 6–8 min. Participants inthe 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 theanalysis. The 29 remaining problems were reclassified into three cate-gories for analysis of transfer effects. The four trainedfigureswere singlesolids (orthogonal and oblique views of the cone and cube), identical tothose used in the interactive animations. As in Experiment 1, similarfigures were composed of two solids, at least one of which had beentrained. Of the 11 similar figures, 9 were composed of one trainedsolid and one untrained solid and two were composed of two trainedsolids. Each of the 14 new figures was composed of two untrainedsolids.
Fig. 6 shows and posttest performance means for Experiment 2, bytype of figure and condition. At pretest, there were no significant differ-ences in performance between the two groups for trained (4) figures,similar (11) figures, or new (14) figures (all p-values≥ .09). In contrast,therewere significant differences between the intervention and controlgroups at posttest for trainedfigures, p b . 001; similarfigures, 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 inter-vention group overall (p b .01) and for trained figures (p b .01), similarfigures (p b .01), and new figures (p b .01). In contrast, the controlgroup showed no significant improvement overall (p = .17), or fortrained (p = 1.0), similar (p = .51), or new figures (p = .16).
Participants who received the intervention in Experiment 2 weretrained on orthogonal and oblique cross sections of only two figures (acone and a cube), yet they outperformed the control group on untrainedshapes (orthogonal and oblique cross sections of cylinders, prismsand pyramids). The results of this experiment are consistent with aprocess-based account of visuospatial learning and cannot be accountedfor by instance theory alone. Although instance-based learning mighthave occurred, it appears that participants also learned a more generalprocess that could be applied to new objects. Finally, it is notable that
and posttest by type of figure and condition.
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the training intervention in Experiment 2 was even shorter than that inExperiment 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 an-imation and virtual models to train a specific spatial visualization skill—inferring the shape of cross sections of a three-dimensional object. Bothexperiments demonstrated significant performance gains for trainedparticipants on trained and untrained figures and significant differencesin posttest performance between trained and control participants ontrained figures. In Experiment 2, trained participants also outperformedcontrol participants on untrained figures on the posttest, providingstrong evidence for transfer. While previous studies (e.g., Charikeret 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 predictedcross section and using the virtualmodels to provide feedback on draw-ings. Our results show that large performance gains can be achievedafter 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), interac-tion with the virtual object figures in these experiments substitutesfor the experience of slicing a physical object and viewing its internalstructure. The interactive displays used in our experiments have simple,yet flexible, interfaces that can be paused and advanced atwill, allowingusers to explore the virtual object at a self-determined order and pace.In addition, multiple training animations (e.g., orthogonal and obliqueslices of cones) can be viewed simultaneously. Supportive instructionalactivities, such as drawing and copying shapes, can be easily integratedinto instruction with the interactive interface.
12.1. Accounts of improved performance after spatial training
We framed our study with respect to two theoretical accounts ofspatial learning. Instance-based learning proposes that improved per-formance after spatial training results from an increase in the strengthand/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-basedlearning (Leone et al., 1993; Wallace & Hofelich, 1992; Wright et al.,2008) proposes that performance gains after training reflect thestrengthening of existing mental processes (e.g., the ability to rotatestimuli around object-centered frames of reference) and/or the acquisi-tion of new spatial transformation processes. This theory predicts trans-fer 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 explanationfor our results. Participants in the experimental conditions of bothexperiments showed significant pre- to post-test increases in their per-formance on new stimuli (geometric figures they had not manipulatedduring training), and in Experiment 2, participants in the experimentalcondition outperformed those in the control group on new (untrained)stimuli in the posttest. These results indicate that training transferred tountrained stimuli, a result that cannot be accounted for by instancelearning alone, but which is consistent with process-based learning.
Whilewe observed transfer of training to novel stimuli, we acknowl-edge that our stimuli were simple geometric solids and we tested onlynear transfer to other stimuli made up of simple (if different) geometricsolids. It remains to be seen whether training on the simple geometricfigures used here would transfer to real-world cross-sectioning taskssuch as interpreting X-rays and MRI images and predicting the cross-sections of geologic structures.
A process-based account of learning predictswide transfer of trainedskills. According to this account, our training intervention with simple
Please cite this article as: Cohen, C.A., & Hegarty, M., Visualizing cross sectiobjects, Learning and Individual Differences (2014), http://dx.doi.org/10.10
geometric solids should transfer to imagining of cross sections of morecomplex objects. However, a third account of spatial learning predictsmore circumscribed transfer, and is worthy of testing in future experi-ments. This intuition account of spatial learning (Pani, Zhou, & Friend,1997; Pani et al., 2005, 1996) proposes that we organize our perceptsof the spatial properties of objects and their transformations in frame-works that allow us to predict similar transformations of similar objectsat similar orientations, but does not predict general transfer to allobjects. For example, this account would predict that after learningthe shapes of horizontal and oblique cross-sections of a cone (a circleand ovoid shape, respectively) participants could predict the shapes ofhorizontal and oblique cross-sections of other cones or cone-likestructures, but would not be able to predict the results of sections ofless similar objects (such as irregular geological structures). An intuitionaccount proposes that improved performance results from developing anew set of spatial intuitions, rather than from learning new spatialtransformation processes or strengthening existing processes.
In summary, it is clear from our results that an instance-basedaccount alone cannot explain the results of training. Another account,either process- or intuition-based, is required to explain the pattern ofresults in our experiments. To test the claims of intuition theory againstthe claims of process theory, we would need to examine transfer to lesssimilar and more complex stimuli. This is an important goal for futureresearch.
12.2. Applications to training and transfer for STEM disciplines
The stimuli used in our study were quite simple, compared to themore complex spatial structures that need to be considered in STEMdo-mains such as anatomy, engineering and geology. However, our pretestscores indicated that imagining cross sections of simple geometric solidswas challenging for adults with poor spatial abilities, justifying the useof these stimuli. Use of these stimuli may address a need to train spatialskills in younger students. The National Council of Teachers of Mathe-matics (NCTM, 2000) recommends incorporating training in geometricthinking into K-12 education,with instruction starting as early as gradesK-2. Skills specified by the NCTM as intrinsic to geometric thinking in-clude recognizing the attributes of two-and three-dimensional shapes,creating mental images of geometric shapes, and recognizing shapesfrom different view perspectives (NCTM, 2000). The present protocoland stimuli may be appropriate for very young populations, as there isevidence that children as young as 5 years of age have the kinestheticand motor skills to effectively use computer mouse interfaces in non-speeded tasks (Lane & Ziviani, 2010).
Furthermore, similar methodologies (including drawing and receiv-ing feedback from models) have recently used to train student to infercross sections of geological structures (Gagnier, Atit, Ormand, &Shipley, 2014) and to train representational competence in organicchemistry (Padalkar & Hegarty, 2012), demonstrating the applicabilityof our approach to adult STEM learning. There are also ways in whichthe current intervention might be enhanced to meet the challenges oftraining more complex spatial skills. More time manipulating virtualmodels could increase participants' encoding of the spatial features ofthe stimuli (Wright et al., 2008). Training with a greater variety ofobjects, including more complex objects, and with training sessionsdistributed over time has been effective in other studies (Charikeret al., 2011; Pani et al., 2005; Sorby & Baartmans, 1996). Manipulatingphysical models of the trained figures may also improve performance,given the evidence for the shared neural substrates of haptic and visualsystems 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 beimportant to disambiguate which aspects of a real model (e. g., betterdepth cues, more naturalistic manipulation) offer an advantage whenused instead of, or in combination with, virtual models. Finally, verbal
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instructions, including reference to spatial features of themodels, couldprovide an instructional benefit beyond that provided by interactiveanimation alone (Mayer, 2008).
13. Limitations
This study is limited in thatwe examined only short-term learning. Itis important for future studies to test the longer-term learning effects ofour intervention. Our study is also limited in that we examined only onecriterion task, which was a multiple-choice test. Future research shouldtest if training on the present stimuli would transfer to other tasks, suchas 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 printedstimuli to depict the three-dimensional figures on the pre- and post-tests. Two-dimensional projections of three-dimensional stimuli arefundamentally ambiguous, and this ambiguity might be somewhatresponsible for the poor performance of participants in our pretest. Inthe future, physical models of the simple geometric solids couldalso be provided to resolve any possible ambiguity about three-dimensional perspective cues in the two-dimensional images. Alterna-tively, presenting spatial ability tests on computers using virtual realitydisplays could provide depth cues such as stereoscopic viewing, and theability to rotate the figures (providing motion-based depth cues). Bysimulating three-dimensional space, augmented and virtual reality test-ing environmentsmay offer amore ecologically valid tool formeasuringspatial skills. The use of computer-based virtual reality displays to testand train spatial ability offers a number of additional benefits, includingthe ability to collect response latencies and information about solutionstrategies (Kaufmann et al., 2008).
14. Conclusion
In conclusion, this study introduces a short training intervention thatwas highly effective and can easily be adapted to the training of simplespatial skills with children or more complex spatial skills with adults.The results of our experiments add to evidence that interventionsusing virtual models and interactive animations is can be promisingmethodologies for training spatial skills, and alleviating one of thedifficulties faced by low-spatial individuals in learning science.
References
Ainsworth, S., Prain, V., & Tyler, R. (2011). Drawing to learn science. Science, 333,1096–1097.
Amedi, A., Malach, R., Hendler, T., Peled, S., & Zohary, F. (2001). Visuo-haptic object-related activation in the ventral visual pathway. Nature Neuroscience, 4(3), 324–330.
Baddeley, A. (1992). Working memory. Science, 255, 556–559.Baenninger, M., & Newcombe, N. (1989). The role of experience in spatial test perfor-
mance: A meta-analysis. Sex Roles, 20(5–6), 327–344.Betrancourt, M. M., & Tversky, B. B. (2000). Effect of computer animation on users' perfor-
mance: A review. Travail Humain: A Bilingual and Multi-Disciplinary Journal in HumanFactors, 63(4), 311–329.
Biederman, I. (1987). Recognition-by-components: A theory of human image under-standing. Psychological Review, 94(2), 115–147.
Brinkmann, E. H. (1966). Programmed instruction as a technique for improving spatial vi-sualization. Journal of Applied Psychology, 50(2), 179–184.
Carroll, J. B. (1993). Human cognitive abilities: A survey of factor analytic studies.Cambridge; New York: Cambridge University Press.
Chandler, P. (2004). The crucial role of cognitive processes in the design of dynamic visu-alizations. Learning and Instruction, 14, 355–357.
Chariker, J. H., Naaz, F., & Pani, J. R. (2011). Computer-based learning of neuroanatomy: Alongitudinal study of learning, transfer and retention. Journal of EducationalPsychology, 103(1), 19–31.
Cohen, C. A., & Hegarty, M. (2007). Sources of difficulty in imagining cross sections of 3Dobjects. In D. S. McNamara, & J. G. Trafton (Eds.), Proceedings of the Twenty-Ninth An-nual Conference of the Cognitive Science Society (pp. 179–184). Austin TX: CognitiveScience Society.
Cohen, C. A., & Hegarty, M. (2012). Inferring cross sections of 3D objects: A new spatialthinking test. Learning and Individual Differences, 22, 868–874.
Please cite this article as: Cohen, C.A., & Hegarty, M., Visualizing cross sectiobjects, Learning and Individual Differences (2014), http://dx.doi.org/10.10
Duesbury, R., & O'Neil, H. (1996). Effect of type of practice in a computer-aided design en-vironment in visualizing three-dimensional objects from two-dimensional ortho-graphic projections. Journal of Applied Psychology, 81(3), 249–260.
Easton, R. D., Greene, A. J., & Srinivas, K. (1997). Transfer between vision and haptics:Memory for 2-D patterns and 3-D objects. Psychonomic Bulletin & Review, 4(3),403–410.
Gagnier, K. M., Atit, K., Ormand, C. J., & Shipley, T. F. (2014, March). Understanding 3D:Generating diagrams from 3D models improves diagrammatic reasoning. Talk pre-sented at the American Educational Research Association annual meeting, Philadelphia,PA.
Garg, A. X., Norman, G. R., Eva, K. W., Spero, L., & Sharan, S. (2002). Is there any real virtueof virtual reality?: The minor role of multiple orientations in learning anatomy fromcomputers. Academic Medicine, 77, S97–S99.
Gobert, J. D., & Clement, J. J. (1999). Effects of student-generated diagrams versus student-generated summaries on conceptual understanding of causal and dynamic knowl-edge in plate tectonics. Journal of Research in Science Teaching, 36(1), 39–53.
Gonzalez, C., Anderson, J., Culmer, P., Burke, M. R., Mon-Williams, M., &Wilkie, M. (2011).Is tracing or drawing better when learning to reproduce a pattern? Experimental BrainResearch, 208, 459–465.
Harman, K. L., Humphrey, G. K., & Goodale, M. A. (1999). Active manual control of objectviews facilitates visual recognition. Current Biology, 9(22), 1315–1318.
Hegarty, M. (2010). Components of spatial intelligence. In B. H. Ross (Ed.), The psychologyof learning and motivation. Advances in research and theory, Vol. 52. (pp. 265–297). .San Diego, CA. US: Elsevier Academic Press.
Hegarty, M., Keehner, M., Cohen, C., Montello, D. R., & Lippa, Y. (2007). The role of spatialcognition in medicine: Applications for selecting and training professionals. In G.Allen (Ed.), Applied spatial cognition (pp. 285–315). Mahwah, NJ: Lawrence ErlbaumAssociates.
Hegarty, M., & Waller, D. (2005). Individual differences in spatial abilities. In P. Shah, & A.Miyake (Eds.), The Cambridge handbook of visuospatial thinking (pp. 121–167). NewYork: Cambridge University Press.
Heil, M., Rosler, F., Link, M., & Bajric, J. (1998). What is improved if a mental rotation is re-peated—The efficiency of memory access, or the speed of a transformation routine?Psychological Research, 61, 99–106.
Hoffler, T. N. (2010). Spatial ability: Its influence on learning with visualizations—a meta-analytic review. Educational Psychology Review, 22(3), 245–269.
James, T. W., James, K. H., Humphrey, G. K., & Goodale, M. A. (2006). Do visual and tactileobject representations share the same neural substrate? In A. Heller, & SoledadBallesteros (Eds.), Touch and blindness: Psychology and neuroscience (pp. 139–155).Mahwah, NJ: Lawrence Erlbaum Associates.
Kail, R., & Park, Y. -S. (1990). Impact of practice on speed of mental rotation. Journal ofExperimental Child Psychology, 49(2), 227–244.
Kali, Y., & Orion, N. (1996). Spatial abilities of high-school students in the perception ofgeologic structures. Journal of Research in Science Teaching, 33, 369–391.
Kaufmann, H., Csisinko, M., Strasser, I., Strauss, S., Koller, I., & Gluck, J. (2008). Design of avirtual reality supported test for spatial abilities. Proceedings of the International Con-ference on Geometry and Graphics, August 4th—8th, Dresden, Germany (pp. 2008).
Keehner, M., Hegarty, M., Cohen, C. A., Khooshabeh, P., & Montello, D. R. (2008). Spatialreasoning with external visualizations: What matters is what you see, not whetheryou interact. Cognitive Science, 32, 1099–1132.
Kosslyn, S., Brunn, J., Cave, K., & Wallach, R. (1984). Individual differences in mental im-agery ability: A computational analysis. Cognition, 18, 195–243.
Kozhevnikov, M., Motes, M., & Hegarty, M. (2007). Spatial visualization in physics prob-lem solving. Cognitive Science, 31, 549–579.
Lane, A. E., & Ziviani, J. M. (2010). Factors influencing skilled use of the computer mouseby school-aged children. Computers & Education, 55(3), 1112–1122.
Leone, G., Taine, M., & Droulez, J. (1993). The influence of long-term practice on mentalrotation of 3D objects. Cognitive Brain Research, 1, 241–255.
Levinson, A. J., Weaver, B., Garside, S., McGinn, H., & Norman, G. R. (2007). Virtual realityand brain anatomy: A randomized trial of e-learning instructional designs. MedicalEducation, 41(5), 495–501.
Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences inspatial ability: A meta-analysis. Child Development, 56(6), 1479–1498.
Logan, G. D. (1988). Toward an instance theory of automatization. Psychological Review,95(4), 492–527.
Lord, T. (1985). Enhancing the visuo-spatial aptitude of students. Journal of Research inScience Teaching, 22, 395–405.
Lowe, R. K. (1999). Extracting information from an animation during complex visuallearning. European Journal of Psychology of Education, 14, 225–244.
Lowe, R. (2008). Learning from animation:Where to look, when to look. In R. Lowe, &W.Schnotz (Eds.), Learning from animation: Research implications for design (pp. 49–68).Cambridge, UK: Cambridge University Press.
Mayer, R. E. (2008). Research-based principles for learning from multimedia. In R. Lowe,& W. Schnotz (Eds.), Learning from animation: Research implications for design. Cam-bridge, UK: Cambridge University Press.
Meijer, F., & van den Broek, E. L. (2010). Representing 3D virtual objects: Interaction be-tween visuo-spatial ability and type of exploration. Vision Research, 50(6), 630–635.
Miyake, A., Rettinger, D. A., Friedman, N. P., Shah, P., & Hegarty, M. (2001). Visuospatialworking memory, executive functioning and spatial abilities. How are they related?Journal of Experimental Psychology: General, 130, 621–640.
National Council of Teachers of Mathematics (2000). Principles and standards for schoolmathematics. Reston, VA: National Council of Teachers of Mathematics.
National Research Council (2006). Learning to think spatially: GIS as a support system in K-12 curriculum. Washington: National Research Council Press.
Orion, N., Ben-Chaim, D., & Kali, Y. (1997). Relationship between earth science educationand spatial visualization. Journal of Geoscience Education, 45, 129–132.
ons: Training spatial thinking using interactive animations and virtual16/j.lindif.2014.04.002
9C.A. Cohen, M. Hegarty / Learning and Individual Differences xxx (2014) xxx–xxx
Padalkar, S., & Hegarty, M. (2012). Improving representational competence with model-based feedback. In N. Miyake, R. Cooper, & D. Peebles (Eds.), Proceedings of the AnnualConference of the Cognitive Science Society (pp. 2162–2167).
Pani, J. R., Chariker, J. H., Dawson, T. E., & Johnson, N. (2005). Acquiring new spatial intu-itions: Learning to reason about rotations. Cognitive Psychology, 51, 285–333.
Pani, J. R., Jeffries, J. A., Shippey, G. T., & Schwartz, K. J. (1996). Imagining projective trans-formations: Aligned orientations in spatial organization. Cognitive Psychology, 31(2),125–167.
Pani, J. R., Zhou, H., & Friend, S. M. (1997). Perceiving and imagining Plato's solids: The gen-eralized cylinder in spatial organization of 3D structures. Visual Cognition, 4(3), 225–264.
Piaget, J., & Inhelder, B. (1967). The child's conception of space. New York: W. W. Norton.Reales, J. M., & Ballesteros, S. (1999). Implicit and explicit memory for visual and haptic
objects: Cross-modal priming depends on structural descriptions. Journal ofExperimental Psychology: Learning, Memory, and Cognition, 25, 1–20.
Rochford, K. (1985). Spatial learning disabilities and underachievement among universityanatomy students. Medical Education, 19, 13–26.
Russell-Gebbett, J. (1985). Skills and strategies: Pupils' approaches to three-dimensionalproblems in biology. Journal of Biological Education, 19(4), 293–298.
Schultz, K. (1991). The contribution of solution strategy to spatial performance. CanadianJournal of Psychology, 45(4), 474–491.
Schwan, S., & Riempp, R. (2004). The cognitive benefits of interactive videos: Learning totie knots. Learning and Instruction, 14, 293–305.
Sims, V. K., &Mayer, R. E. (2002). Domain specificity of spatial expertise: The case of videogame players. Applied Cognitive Psychology, 16(1), 97–115.
Please cite this article as: Cohen, C.A., & Hegarty, M., Visualizing cross sectiobjects, Learning and Individual Differences (2014), http://dx.doi.org/10.10
Sorby, S. (2009). Educational research in developing 3D spatial skills for engineering stu-dents. International Journal of Science Education, 31(3), 459–480.
Sorby, S., & Baartmans, B. (1996). A course for the development of 3D spatial visualizationskills. Engineering Design Graphics Journal, 60(1), 13–20.
Sweller, J., & Chandler, P. (1994). Why some material is difficult to learn. Cognition andInstruction, 12(3), 185–233.
Talley, L. H. (1973). The use of three-dimensional visualization as a moderator in thehigher cognitive learning of concepts in college level chemistry. Journal of Researchin Science Teaching, 10(3), 263–269.
Tarr, M. J., & Pinker, S. J. (1989). Mental rotation and orientation-dependence in shaperecognition. Cognitive Psychology, 21(2), 233–282.
Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., et al. (2013). Themalleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin,139, 352–402.
Voyer, D., Voyer, S., & Bryden, M. (1995). Magnitude of sex differences in spatial abilities:A meta-analysis and consideration of critical variables. Psychological Bulletin, 117,250–270.
Wallace, B., & Hofelich, B. (1992). Process generalization and the prediction of perfor-mance on mental imagery tasks. Memory & Cognition, 20(6), 695–704.
Wright, R., Thompson, W. L., Ganis, G., Newcombe, N. S., & Kosslyn, S. M. (2008). Traininggeneralized spatial skills. Psychonomic Bulletin & Review, 15(4), 763–771.
Zhang, Z. H., & Linn, M. C. (2011). Can generating representations enhance learningwith dynamic visualizations? Journal of Research in Science Teaching, 48(100),1177–1198.
ons: Training spatial thinking using interactive animations and virtual16/j.lindif.2014.04.002
