Summary of Key Findings on Spatial Thinking
and the Use of Representations

•   How students create, use, interpret, and translate between graphical and mathematical representations provides insight into their understanding of important concepts in a discipline. DBER highlights discipline-specific challenges that students face when using such representations.

•   Although equations, graphical displays, and other representations may seem easy to understand for undergraduate faculty who are domain experts, college students have difficulty extracting information from these representations, and constructing appropriate representations from existing information. College students also have difficulty relating and translating among different representations of the same entity or phenomenon.

•   There is contradictory evidence about the relationship between spatial ability and performance in science. Consistent with findings from cognitive science that students with low-spatial ability especially have difficulty relating two- and three-dimensional representations, some DBER studies show a relationship between measures of spatial ability and success on specific science or engineering tasks. Other studies do not provide evidence of that relationship.

•   The evidence on the effectiveness of animations is mixed: The use of animations has been shown to enhance learning in some circumstances, and to be ineffective or even detrimental to student learning in other situations.

Directions for Future Research on Spatial
Thinking and the Use of Representations

DBER and cognitive science have yielded many useful insights into how students use mathematical and graphical representations, but important gaps remain. For example, the research community, instructors, and those who develop representations would benefit from a deeper understanding of students’ use of representations as tools to enhance their learning, and studies along these lines should leverage what is already known about the basic cognitive and perceptual processes that students use to comprehend graphical representations.

The role of spatial ability also needs clarification. Spatial ability may be measured in many different ways, any one of which may be more or less relevant to any specific science or engineering task. Although several authors have proposed that many tasks (e.g., rotation tasks of three-dimensional models) require mental imagistic models, others have shown that many

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