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Constructing Mathematical And Spatial Reasoning Measures For Engineering Students

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Conference

2010 Annual Conference & Exposition

Location

Louisville, Kentucky

Publication Date

June 20, 2010

Start Date

June 20, 2010

End Date

June 23, 2010

ISSN

2153-5965

Conference Session

Measurement Tools

Tagged Division

Educational Research and Methods

Page Count

14

Page Numbers

15.313.1 - 15.313.14

DOI

10.18260/1-2--16401

Permanent URL

https://strategy.asee.org/16401

Download Count

93

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Paper Authors

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Laura L. Pauley Pennsylvania State University

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Laura L. Pauley, Arthur L. Glenn Professor of Engineering Education and professor of mechanical engineering, joined the The Pennsylvania State University faculty in 1988. From 2000 to 2007, she served as the Professor-in-Charge of Undergraduate Programs in Mechanical and Nuclear Engineering. In 2003, Laura received the Penn State Undergraduate Program Leadership Award. Dr. Pauley teaches courses in the thermal sciences and conducts research in computational fluid mechanics and engineering education. She received degrees in mechanical engineering from University of Illinois (B.S. in 1984) and Stanford University (M.S. in 1985 and Ph.D. in 1988). She can be contacted at LPauley@psu.edu .

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Jonna M. Kulikowich Pennsylvania State University

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Jonna M. Kulikowich, Professor of Education, joined The Pennsylvania State University faculty in 2003. Dr. Kulikowich teaches courses in applied psychometrics and statistics for the Department of Educational and School Psychology and Special Education. Currently, Dr. Kulikowich is an Associate Editor of the Journal of Educational Psychology. She is also Chair of the Faculty Senate Subcomittee on Undergraduate Education at Penn State. She received a psychology/philosophy degree from the University of Scranton in 1985 and degrees in educational psychology: research, measurement and statistics from Texas A&M University (M.S. in 1986 and Ph.D. in 1990). She can be contacted at jmk35@psu.edu.

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Nell Sedransk National Institute of Statistical Sciences

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Dr. Nell Sedransk, Co-Pi, is the Associate Director of the National Institute of Statistical Sciences (NISS) and Professor of Statistics at North Carolina State University. She is an Elected Fellow of the International Statistical Institute, also Elected Fellow of the American Statistical Association. She has served as Associate Editor for the Journal of the American Statistical Association, the Journal of Statistical Planning and Inference, and has been Vice-Chair of the Publication Board of the American Statistical Association. The areas of her technical expertise and current research include design of complex experiments, Bayesian inference, spatial statistics and topological foundations for statistical theory. She received her Ph.D. in Statistics in 1969 from Iowa State University. She can be contacted at sedransk@niss.org

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Renata Engel Pennsylvania State University

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Renata S. Engel is Associate Dean for Academic Programs and Professor of Engineering Design and Engineering Science & Mechanics. A member of the Penn State faculty since 1990, she served from 2000-2006 as the Executive Director of the Schreyer Institute for Teaching Excellence. Through various collaborative efforts, she has affected changes in the engineering curriculum at Penn State, primarily to incorporate elements of design in fundamental engineering courses. Engel earned a BS in engineering science at Penn State and PhD in engineering mechanics at the University of South Florida. She can be contacted at rse1@psu.edu.

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Abstract
NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Constructing Mathematical and Spatial-Reasoning Measures for Engineering Students

Abstract

Engineering students sometimes encounter difficulties in classes due to their ability to understand and interpret mathematical and visual representations of a problem. This paper describes tools to assess students’ abilities in four different constructs. The two mathematical constructs are: M1. Compare and contrast mathematical operations and M2. Express engineering- and physics- based principles mathematically. The two spatial-reasoning constructs are: S1. Rotate and transform geometric objects in three-dimensional space and S2. Translate two-dimensional images to three-dimensional images and vice-versa when representing visually engineering- or physics-based principles. Examples are provided for each construct and assessment methods are also presented.

Background and Motivation

The purpose of this paper is to introduce mathematical and spatial-reasoning constructs that are keys to academic success in engineering. The term, “construct”, is defined as a latent, unobservable trait, such as an ability or skill that directs how students select or generate answers to test items.1 Several constructs or latent traits have been identified as important in engineering education. The authors illustrate how test items can be designed given various classroom assessment goals (e.g., course examinations, homework assignments) for two sets of constructs that can result in reliable and valid scores. Specifically, two mathematical constructs and two spatial-reasoning constructs are the focus of this paper. The mathematical constructs represent students’ abilities to: (M1) compare and contrast mathematical operations (e.g., differentiation, integration, interpolation); and (M2) express engineering- and physics-based principles mathematically.

Likewise, two spatial-reasoning constructs are of interest. These constructs represent students’ strategies to: (S1) rotate and transform geometric objects in three-dimensional space; and (S2) translate two-dimensional images to three-dimensional images and vice versa when representing visually engineering- or physics-based principles (e.g., acceleration, equilibrium, force).

Each mathematical and spatial-reasoning measure individually has received attention in the literature because of its importance in defining academic success in engineering. Devon, Engel, and Turner2 determined that the students’ ability to rotate and transform geometric objects in three- dimensional space is predictive of graduation and retention in engineering programs. Similarly, knowing how forces are represented visually in diagrams commonly employed in statics and

Pauley, L. L., & Kulikowich, J. M., & Sedransk, N., & Engel, R. (2010, June), Constructing Mathematical And Spatial Reasoning Measures For Engineering Students Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--16401

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: © 2010 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