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Do They Understand Your Language? Assess Their Fluency with Vector Representations

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Conference

2019 ASEE Annual Conference & Exposition

Location

Tampa, Florida

Publication Date

June 15, 2019

Start Date

June 15, 2019

End Date

June 19, 2019

Conference Session

Mechanics Division Technical Session 4

Tagged Division

Mechanics

Page Count

17

Permanent URL

https://peer.asee.org/32675

Download Count

9

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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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Jill Davishahl Western Washington University

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Jill Davishahl is the Director of Pre-Engineering Program Development and faculty member at Western Washington University. She spends her time teaching, developing and implementing innovative curriculum, and managing National Science Foundation grants. She is passionate about inspiring the next generation of engineering students to think outside of the box, especially those that are walking along a non-traditional pathway.

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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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Wade H. Goodridge Utah State University

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Wade Goodridge is an Assistant Professor in the Department of Engineering Education at Utah State University. He holds dual B.S. degrees in Industrial Technology Education and Civil and Environmental Engineering. His M.S. and Ph.D. are in Civil Engineering. Wade has over 18 years of teaching experience primarily focused at the University level but also including 2+ years of teaching in high schools. Dr. Goodridge’s current research interests include spatial thinking and spatial visualization in engineering education, creativity, and effective pedagogy/andragogy in engineering education. His research revolves around developing and validating curricular methods to improve engineering education in informal, traditional, distance, and professional environments. Dr. Goodridge currently teaches courses in “Teaching, Learning, and Assessment in Engineering Education” and “Engineering Mechanics: Statics.” Dr. Goodridge is an engineering councilor for the Council on Undergraduate Research (CUR) and serves on ASEE’s project board. Dr. Goodridge actively consults for projects both in engineering and engineering education.

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Abstract

In teaching mechanics, we use multiple representations of vectors to develop concepts and analysis techniques. These representations include pictorials, diagrams, symbols, numbers and narrative language. Through years of study as students, researchers, and teachers, we develop a fluency 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. The term representational competence refers to the ability to interpret, switch between, and use multiple representations of a concept as appropriate for learning, communication and analysis. In engineering statics, an understanding of what each vector representation communicates and how to use different representations in problem solving is important to the development of both conceptual and procedural knowledge. Science education literature identifies representational competence as a marker of true conceptual understanding.

This paper presents development work for a new assessment instrument designed to measure representational competence with vectors in an engineering mechanics context. We developed the assessment over two successive terms in statics courses at a community college, a medium-sized regional university, and a large state university. We started with twelve multiple-choice questions that survey the vector representations commonly employed in statics. Each question requires the student to interpret and/or use two or more different representations of vectors and requires no calculation beyond single digit integer arithmetic. Distractor answer choices include common student mistakes and misconceptions drawn from the literature and from our teaching experience. We piloted these twelve questions as a timed section of the first exam in fall 2018 statics courses at both Whatcom Community College (WCC) and Western Washington University. Analysis of students’ unprompted use of vector representations on the open-ended problem-solving section of the same exam provides evidence of the assessment’s validity as a measurement instrument for representational competence. We found a positive correlation between students’ accurate and effective use of representations and their score on the multiple choice test. We gathered additional validity evidence by reviewing student responses on an exam wrapper reflection. We used item difficulty and item discrimination scores (point-biserial correlation) to eliminate two questions and revised the remaining questions to improve clarity and discriminatory power. We administered the revised version in two contexts: (1) again as part of the first exam in the winter 2019 Statics course at WCC, and (2) as an extra credit opportunity for statics students at Utah State University. This paper includes sample questions from the assessment to illustrate the approach. The full assessment is available to interested instructors and researchers through an online tool.

Davishahl, E., & Haskell, T. R., & Davishahl, J., & Singleton, L., & Goodridge, W. H. (2019, June), Do They Understand Your Language? Assess Their Fluency with Vector Representations Paper presented at 2019 ASEE Annual Conference & Exposition , Tampa, Florida. https://peer.asee.org/32675

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2019 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015