Impact of Graphical Reasoning in Elementary Vector Analysis: A Case Study from Statics
- Conference
- Location
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Portland, Oregon
- Publication Date
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June 23, 2024
- Start Date
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June 23, 2024
- End Date
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June 26, 2024
- Conference Session
- Tagged Division
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Mechanics Division (MECHS)
- Page Count
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11
- DOI
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10.18260/1-2--47558
- Permanent URL
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https://peer.asee.org/47558
- Download Count
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166
Paper Authors
Christopher Papadopoulos
University of Puerto Rico, Mayaguez Campus
orcid.org/0000-0002-0259-7264
Christopher Papadopoulos is Professor in the Department of Engineering Sciences and Materials at the University of Puerto Rico, Mayaguez Campus (UPRM). He earned B.S. degrees in Civil Engineering and Mathematics from Carnegie Mellon University (1993) and a PhD in Theoretical and Applied Mechanics from Cornell University (1999). He is active in the Mechanics Division and is also active in the area of Sustainability Engineering, including membership in the Engineering for One Planet Network.
Jean Carlos Batista Abreu
Elizabethtown College
orcid.org/0000-0001-5380-7682
Jean Batista Abreu earned his Ph.D. and M.S.E. at the Johns Hopkins University, M.S. at the University of Puerto Rico, and B.S.E. with Honors at the Pontificia Universidad Católica Madre y Maestra, all in Civil Engineering. Prior to joining Elizabethtown College, he served as a Visiting Assistant Professor of Mechanical and Civil Engineering at Bucknell University, and worked as a Structural Engineer at Acero Estrella.
Abstract
Engineering Statics is a fundamental engineering science course taken by many, if not most, engineering students. A basic skill of Statics is the addition of vectors (also referred to as vector resultants). Typically, textbook and exam questions on this topic are algebraic in nature, with less attention given to graphical interpretation and representation. The authors of this study are interested in investigating the relationship between students’ algebraic and graphical reasoning skills. The following research questions have been posed and are being studied:
R1. Does mastery of vector algebra imply mastery of graphical interpretations of vector addition? R2. Do students adopt the habit of redrawing generic figures to scale when given particular parameter values?
To answer these questions, the authors draw on their common approach to testing students on this and related topics. In particular, test questions on vector addition require students to perform both the algebraic calculations as well as a corresponding sketch, to good scale and proportion. The results demonstrate that in general, a moderate number of students who do not attain the correct calculated values, nevertheless show some ability to achieve a reasonably accurate corresponding diagram. This suggests that use of graphical reasoning is a valid means to develop knowledge and skills with vectors.
Papadopoulos, C., & Batista Abreu, J. C. (2024, June), Impact of Graphical Reasoning in Elementary Vector Analysis: A Case Study from Statics Paper presented at 2024 ASEE Annual Conference & Exposition, Portland, Oregon. 10.18260/1-2--47558
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