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The Inside Story: Biases in Student Perception of Cross-Sectional Views
When you look at the figure below, do you see the brown swirl (indicated by the red line) as being present only on the surface of the object, extending into the object in 3-dimensions or do you think the answer is unknowable?
Clearly the dark brown region (cinnamon swirl) is 3D and extends into the object, however from this 2D view, a cross-section, the 3D shape is unknowable. To infer the 3D shape of the region, one would have to view the region from another side. Inferring 3D shape from cross-sections is particularly important for STEM disciplines such as radiology, neuroscience and geoscience, which focus on making 3D spatial inferences from 2D views. However, a common sentiment among geoscientists (Kali & Orion, 1996) is that students do not recognize they need to seek out additional information to know the true 3D shape from a cross-section and are biased to assume that regions on the surface extend straight back into the object.
To move beyond anecdotal accounts, we examined undergraduate students perceptions of cross-sections. We showed two groups of undergraduate psychology students cross-sections of common objects (wood, rocks, fruits). For each cross-section, students indicated if a highlighted region appeared to a) be visible only on the surface, b) extend into the object or if the answer was c) unknowable. If they viewed the region as extending in, they used a rod attached to an inclinometer to show the angle of extension. Students then completed three measures of spatial reasoning: 1) the Geologic Block Cross-sectioning Test (GBCT; Ormand et al, 2013), a measure of visualizing 3D forms, 2) the Object Perspective Taking Test, a measure of perspective taking (Kozhevnikov & Hegarty, 2001), and 3) the Peters et al (1995) Mental Rotation Test.
Participants were fairly confident that the 3D orientation was knowable from a cross-sectional view and only reported that the answer was unknowable on 7% of the trials. Participants showed a clear bias to assume regions in the cross-section extended straight back into the object. Figure 2 shows the mean dip estimate and the correct dip angle for each picture (collapsed across both groups). As can be seen, although the true dip angle varies widely, participants saw these regions as extending straight back. This bias was evident in almost all observers; 87% of the responses fell within 10° of 90°.
There were individual differences in cross-section perception that were accounted for by performance on a measure of 3D spatial reasoning. Performance on the Geologic Block Cross-sectioning Test (shown in Figure 3), predicted whether or not students recognized the inherent uncertainty in a cross-sectional view. Thus, recognizing the uncertainty in a single cross-section appears related to the skill of integrating multiple cross-sections.
Figure 2. The mean dip estimates (maroon) for each picture along with the correct dip angle for each picture (light pink). Dip angle is defined relative to the plane of the picture. A bias to perceive regions as continuing “straight back” would be a dip estimate of 90°.
Figure 3. A problem from the Geologic Block Cross-Sectioning Test (Ormand et al, 2013). Students select which of the multiple choice options best represents the cross-section produced by the pictured cut through the geologic block diagram. The correct answer is A.
In sum, we found clear and systematic biases in student perception of cross-sections. On average, students did not recognize that the 3D shape is unknowable from a cross-sectional view. There was a bias to assume that regions of a cross-section extend straight back into the object and there were individual differences in reasoning about uncertainty of cross-sections. This bias has implications for our understanding of visual perception as well as for STEM education, as many STEM fields require some amount of reasoning about the inside of a volume from surface information. It is important for teachers to recognize and address students’ bias to assume that regions extend straight back into the objects. Our research is the first step in understanding biases in perceptions of cross-sections, which is important for developing interventions that help students overcome this bias.