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Targeting Representational Competence and Spatial Skills Development with Hands-on Models in Calculus and Statics

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Conference

2019 ASEE PNW Section Conference

Location

Corvallis, Oregon

Publication Date

March 20, 2019

Start Date

March 20, 2019

End Date

March 22, 2019

Permanent URL

https://peer.asee.org/31896

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Paper Authors

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Eric Davishahl Whatcom Community College Orcid 16x16 orcid.org/0000-0001-9506-2658

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Eric Davishahl is assistant professor and engineering program coordinator at Whatcom Community College. His teaching and research interests include developing, implementing and assessing active learning instructional strategies and auto-graded online homework. Eric has been a member of ASEE since 2001. He currently serves as chair of the Pacific Northwest Section and was the recipient of the 2008 Section Outstanding Teaching Award.

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Todd R Haskell Western Washington University

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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.

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Lee Singleton Whatcom Community College

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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-printing, active learning, and infusing more physical activity into mathematics courses. Recent grant positions include principal investigator on the NSF-funded grant “EAGER: MAKER: Engaging Math Students with 3D-Printing for STEM Success and co-PI on the NSF-funded grant "Collaborative Research: Improving Representational Competence by Engaging with Physical Modeling in Foundational STEM Courses".

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Abstract

In this presentation, we will outline a new project that features cross-disciplinary collaboration between engineering, math, and psychology faculty to determine how to leverage hands-on active learning with physical models to improve spatial skills and develop representational competence in calculus and engineering statics. 3D printing technologies provide a readily available and affordable tool to develop learning aids that target these specific learning outcomes. There are three primary project goals: (1) Develop physical models and associated curriculum that embeds spatial skills training with activities designed to develop representational competence in multiple content areas in statics and integral calculus. (2) Assess the effectiveness of the models and activities on improving representational competence and relevant spatial skills. (3) Identify the characteristics of modeling activities that make them effective for all learners and/or subgroups of learners. The project began in fall 2018 with model and associated curriculum development work, pilot activities in classrooms, and a lab study exploring activity design parameters. Years two and three will feature a longitudinal study of students in intervention and control sections of both statics and calculus. This presentation will include an overview of the research design, applications of the theory of representational competence to engineering mechanics, and targeted assessment instruments. We will also demonstrate an example modeling activity with emphasis on design elements intended to foster representational competence. The term representational competence refers to the ability to interpret, switch between, and appropriately use multiple representations of a concept as appropriate for learning, communication and analysis. Science education literature identifies representational competence as a marker of true conceptual understanding and as key to knowledge transfer across topics and disciplines. When teaching engineering subjects, we use multiple representations (e.g. include graphics, diagrams, symbols, numbers and narrative) to develop concepts and analysis techniques. Through years of study as students, researchers, and teachers, we develop a fluency with representations rooted in a deep conceptual understanding of what each representation communicates. Many novice learners, however, struggle to gain such understanding and rely on superficial mimicry of the problem solving procedures we demonstrate in examples. Spatial thinking connects to representational competence in that internal mental representations (i.e. visualizations) facilitate work using multiple external representations. A growing body of research indicates well-developed spatial skills are important to student success in many STEM majors, and that students can improve these skills through targeted training.

Davishahl, E., & Haskell, T. R., & Singleton, L. (2019, March), Targeting Representational Competence and Spatial Skills Development with Hands-on Models in Calculus and Statics Paper presented at 2019 ASEE PNW Section Conference, Corvallis, Oregon. https://peer.asee.org/31896

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