2025 ASEE Annual Conference & Exposition

Towards a Cross-National Mathematical Skills Inventory for Engineers

Presented at MATH - Pedogogical Reflections in Mathematics Education

This Work-in-Progress (WiP) paper outlines the development of a mathematical skills inventory tailored for undergraduate engineering students. While traditional concept inventories (CIs) primarily assess students' conceptual understanding, the proposed skills inventory focuses on evaluating the practical competencies and cognitive abilities essential for mastering fundamental mathematical concepts. By adopting this skill-oriented approach, the inventory aims to offer a more accurate and comprehensive evaluation of students’ knowledge, skills, and abilities (KSAs), capturing deeper levels of cognitive understanding. The broader implication of this work lies in equipping educators with actionable insights that guide targeted interventions and address skill deficits effectively.

Using the concept of functions as an exemplar, this paper lays the foundation for a competency-based framework in engineering mathematics. While the concept of functions has been extensively studied within the context of mathematics students and supported by a dedicated CI, existing instruments often lack an engineering perspective. Their limited contextual relevance renders them less suitable for use with broader engineering cohorts, where foundational mathematics is embedded within practical engineering contexts and applications. Moreover, where engineering research does exist, they tend to focus on discipline-specific concepts, such as frequency responses within control theory, equivalent circuits, and Newton’s laws, often overlooking the underlying mathematical concepts that support engineering learning and problem-solving.

Authors

Mr. Ilanthiraiyan Sivagnanamoorthy Queen Mary University of London [biography]

Ilanthiraiyan Sivagnanamoorthy is a third-year undergraduate student pursuing an MEng in Aerospace Engineering at Queen Mary University of London (QMUL). His research interests centre on the role of mathematics in engineering education, with a particular emphasis on threshold concepts and the development of skill inventories.
Alexandra Werth http://orcid.org/0000-0003-0310-2654 Cornell University [biography]

Alexandra Werth is an assistant professor at the Meinig School of Biomedical Engineering, specializing in Engineering Education Research (EER). She focuses on developing evidence-based teaching methodologies to foster authentic learning environments and developing novel educational assessment instruments. Dr. Werth holds a Ph.D. in Electrical and Computer Engineering from Princeton University, where she developed a non-invasive mid-infrared glucose sensor. She later conducted postdoctoral research in physics education at the University of Colorado Boulder, where she helped develop the first large-enrollment introductory physics course-based research experience (CURE).
Dr. Rehan Shah http://orcid.org/0000-0002-5025-3503 Queen Mary University of London [biography]

Dr. Shah is a Lecturer (Assistant Professor) in Mathematics and Engineering Education at Queen Mary University of London (QMUL) with research interests in applied mathematics (nonlinear dynamics, analytical mechanics and mathematical modelling) as well as mathematics and engineering education pedagogy (diversification of STEM curricula, threshold concepts and concept inventories in mathematics courses, university-industry and community partnerships, embedding ethics and sustainability in mathematics, history of mathematics and physics).

He completed his PhD in Applied Mathematics (Nonlinear Dynamics) at University College London (UCL), an MSc in Mathematical Modelling and Scientific Computing from the University of Oxford (St. Anne's College) and a BEng in Mechanical Engineering with Business Finance from UCL.

Note

The full paper will be available to logged in and registered conference attendees once the conference starts on June 22, 2025, and to all visitors after the conference ends on June 25, 2025

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