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Abstract
This article reports about our efforts to determine engineering students' competence in mathematics. Our research is embedded in a larger project, KoM@ING–Modeling and developing competence: Integrated IRT based and qualitative studies with a focus on mathematics and its usage in engineering studies, within the program Modeling and Measuring Competencies in Higher Education (KoKoHS). KoKoHS provides the umbrella organization of several research projects addressing the modeling and measuring of competences at the college level. KoM@ING aims to model the role of engineering students' mathematical competences for their studies from both a quantitative and a qualitative perspective.
Here, we report the development of a large-scale instrument assessing engineering freshmen's competence in mathematics by applying Rasch analysis to determine measures for item difficulties and student abilities. Several analyses were performed to provide insights into the measures' reliability and validity. In particular, to examine cognitive validity, we scrutinized students' think-aloud protocols when solving the items to investigate their problem solving abilities as a proxy for item difficulty. Overall, we found first evidence that our instrument is suitable to assess engineering freshmen's competence in mathematics. This instrument may be helpful to conduct further research and to inform those concerned with college organization and policy.
Notes
We also performed a three-dimensional analysis with each content area (algebra and mathematical basics, analysis, and geometry) forming a single trait. From a mere statistical perspective, the three-dimensional model showed a better fit than the unidimensional one, based on a comparison of deviance and information criteria. However, the measures of the three traits were less reliable than the unidimensional trait. Also, the single measures would then rely on only 14 (resp. 12 or 9) items, which impairs their content validity.
