June 20, 2010
June 20, 2010
June 23, 2010
Educational Research and Methods
15.313.1 - 15.313.14
Constructing Mathematical and Spatial-Reasoning Measures for Engineering Students
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
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