Visualizing Cross Sections: Training Spatial Thinking Using Interactive Animations and Virtual Objects

• In Event: Lesson Learned About Increasing Mathematics Achievement Through Spatial Instruction

Abstract

Rationale/Purpose: Spatial visualization is defined as the ability to encode and maintain spatial information in working memory while transforming it (Carroll, 1993). Identifying the 2D cross section of a 3D geometric solid is a spatial visualization task that predicts performance in STEM fields, including biology (Rochford, 1985), engineering (Sorby, 2009) and geology (Orion, Ben-chaim, & Kail, 1997). Motivated by evidence that spatial thinking skills are malleable (Uttal et al., 2013), we investigated the efficacy of an intervention that used interactive animation and virtual solids to improve the ability to infer cross sections of 3D objects. The design of the intervention was informed by theories of visuospatial working memory (Kosslyn, 1984), the benefits of active manipulation of virtual and physical models (Chariker et al., 2011) and learning from animation (Betrancourt & Tversky, 2000).

Methods. Undergraduate students with low spatial ability participated in two experiments. Materials included desktop computers, a pre-post multiple-choice measure of cross-sectioning skill, 2D drawing trials, and interactive animations. Each animation displayed a single geometric figure that was intersected by either an orthogonal or an oblique cutting plane. The geometric figure was stationary in the animation, while the cutting plane could be advanced by a mouse. As the cutting plane sliced through the figure, an image of the resulting cross section appeared next to the geometric figure.
Participants were trained individually. In both experiments, the participant first inferred and drew the cross section of a geometric solid shown in a drawing trial. Next, the participant manipulated the animated cutting plane until it revealed object’s cross section. The participant then copied the cross-sectional shape shown in the animation, and compared this shape to their first drawing. This cycle was repeated until the participant drew the correct cross-sectional shape on first attempt. After training, the participant took the post-test. Participants were trained on 10 geometric solids in Experiment 1 and on four geometric solids in Experiment 2. Training lasted 10-12 minutes in each experiment. Participants in the control group received no training, but completed the pre-and post-test measures.

Results
Compared to the control group, trained participants in both experiments improved significantly on stimuli viewed during the intervention, and demonstrated transfer to untrained stimuli.

Discussion/Significance
While previous studies have used interventions with virtual models, this training protocol is novel because participants drew the predicted cross section and used virtual models to get feedback on their drawings. The stimuli in our experiments were simple compared to complex spatial structures that need to be considered in many STEM fields. However, pre-test scores in both experiments indicated that imagining the cross sections of 3D objects is challenging for adults with poor spatial thinking skills. The present stimuli and protocol may be appropriate for very young populations, as there is evidence that children as young as five years of age have the kinesthetic and motor skills to use computer interfaces (Lane & Ziviani, 2010).

Authors

• Cheryl Ann Cohen, U.S. Department of Veteran Affairs

• Mary Hegarty, University of California - Santa Barbara