A growing body of research indicates spatial visualization skills are important to success in many STEM disciplines, including several engineering majors that rely on a foundation in engineering mechanics. Many fundamental mechanics concepts such as free-body diagrams, moments, and vectors are inherently spatial in that application of the concept and related analytical techniques requires visualization and sketching. Visualization may also be important to mechanics learners’ ability to understand and employ common mechanics representations and conventions in communication and problem solving, a skill known as representational competence. In this paper, we present early research on how spatial abilities might factor in to students’ conceptual understanding of vectors and associated representational competence.
We administered the Mental Cutting Test (MCT), a common assessment of spatial abilities, in the first and last week of the term. We also administered the Test of Representational Competence with Vectors (TRCV), a targeted assessment of vector concepts and representations, in week one and at mid-term. The vector post-test came after coverage of moments and cross products. We collected this assessment data in statics courses across multiple terms at three different colleges. To understand how spatial skills relate to the development of representational competence, we use a multiple regression model to predict TRCV scores using the pre-class MCT scores as well as other measures of student preparation in the form of grades in prerequisite math and physics coursework. We then extend the analysis to consider both MCT and TRCV scores as predictors for student performance on the Concept Assessment Test in Statics. We find that spatial abilities are a factor in students’ development of representational competence with vectors. We also find that representational competence with vectors likely mediates the importance of spatial abilities to student success in developing broader conceptual understanding in statics. We conclude by discussing implications for mechanics instruction.
Eric Davishahl serves as professor and engineering program coordinator at Whatcom Community College in northwest Washington state. His current project involves developing and piloting an integrated multidisciplinary learning community for first-year engineering. More general teaching and research interests include designing, implementing and assessing activities for first-year engineering, engineering mechanics, and scientific computing. Eric has been an active member of ASEE since 2001. He was the recipient of the 2008 Pacific Northwest Section Outstanding Teaching Award, chaired the PNW Section 2017-2019, served on the ASEE Board of Directors as Zone IV Chair 2022-2024. and currently serves as Program Chair for the Two-Year College Division.
Todd Haskell is a cognitive scientist interested in learning and the development of expertise, especially in STEM fields. He is currently Associate Professor of Psychology at Western Washington University. In previous projects Dr. Haskell has worked on understanding how chemistry novices and experts navigate between macroscopic, symbolic, and small particle representations, and how pre-service elementary teachers translate an understanding of energy concepts from physics to other disciplines.
Lee Singleton is a professor at Whatcom Community College, in Bellingham, WA. He holds a BS in mathematics from Harding University, a MS in mathematics and PhD in biomedical mathematics from Florida State University. His current interests include 3D-prin
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