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Scaffolding Spatial Abilities in Integral Calculus

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2022 ASEE Annual Conference & Exposition


Minneapolis, MN

Publication Date

August 23, 2022

Start Date

June 26, 2022

End Date

June 29, 2022

Conference Session

NSF Grantees Poster Session

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Paper Authors


Eric Davishahl Whatcom Community College


Lee Singleton

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Dr. Lee Singleton is currently Professor of mathematics at Whatcom Community College in Bellingham, WA, where he has been teaching since 2007. He earned his Ph.D. in Biomathematics at Florida State University in 2007 and is currently interested in the recent availability of 3d printing technologies, and how they can allow students to experience math with a much more hands-on approach. His latest research has been a joint NSF grant with engineering faculty at WCC, investigating the use of hands-on models in Calculus II and Statics. Dr. Singleton has been involved with national and local organizations such as Achieving the Dream, AMATYC (American Mathematical Association of Two-Year Colleges), and WAMATYC (Washington branch of AMATYC).

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Todd Haskell

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Kathryn Rupe Western Washington University

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Leslie Glen

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This NSF-IUSE exploration and design project began in fall 2018 and features cross-disciplinary collaboration between engineering, math, and psychology faculty to develop learning activities with hands-on models and manipulatives. We are exploring how best to design these activities to support learners’ development of conceptual understanding and representational competence in integral calculus and engineering statics, two foundational courses for most engineering majors. A second goal is to leverage the model-based activities to scaffold spatial skills development in the context of traditional course content. As widely reported in the literature, well-developed spatial abilities correlate with student success and persistence in many STEM majors. We provided calculus students in selected intervention sections taught by four instructors at three different community colleges with take-home model kits that they could reference for a series of asynchronous learning activities. Students in these sections completed the Purdue Spatial Visualization Test: Rotations (PSVT:R) in the first and last weeks of their course. We also administered the assessment in multiple control sections (no manipulatives) taught by the same faculty.

This paper analyzes results from fall 2020 through fall 2021 to see if there is any difference between control and intervention sections for the courses as a whole and for demographic subgroups including female-identifying students and historically-underserved students of color. All courses were asynchronous online modality in the context of the COVID-19 pandemic. We find that students in intervention sections of calculus made slightly larger gains on the PSVT:R, but this result is not statistically significant as a whole or for any of the demographic subgroups considered. We also analyzed final course grades for differences between control and intervention sections and found no differences.

We found no significant effect of the presence of the model-based activities leading to increased PSVT:R gains or improved course grades. We would not extend this conclusion to face-to-face implementation, however, due primarily to the compromises made to adapt the curriculum from in-person group learning to asynchronous individual work and inconsistent engagement of the online students with the modeling activities.

Davishahl, E., & Singleton, L., & Haskell, T., & Rupe, K., & Glen, L. (2022, August), Scaffolding Spatial Abilities in Integral Calculus Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--42091

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