Research
Development of a Cross-National Mathematical Reasoning Skills Inventory for Engineers
Principal investigator: | Rehan SHAH |
Co-investigator(s): | Dr. Alexandra Werth (Cornell University, USA) and Ilanthiraiyan Sivagnanamoorthy (SEMS undergraduate) |
This project outlines the development of a mathematical skills inventory for engineers. In education literature, threshold concepts, are discipline-specific concepts that act as learning bottlenecks due to their troublesome and transformative nature. These concepts encompass sets of knowledge, skills, and abilities (KSAs) that often seem unfamiliar, contradictory, or inconsistent, but once grasped, lead to a significant shift in the learner's perspective and understanding. Examples of such threshold concepts within mathematics include the notion of proofs, calculus, limits, and complex numbers. While these threshold concepts have been examined in the context of mathematics students, there is a noticeable gap in literature investigating how engineering students navigate threshold concepts within their curriculum.
Where engineering education research does exist, it typically focuses on electrical and mechanical threshold concepts like frequency responses, equivalent circuits, and Newton's laws, often overlooking the foundational mathematical threshold concepts crucial for engineering education. This gap also extends to concept inventories assessing core mathematical threshold concepts. Existing tools, such as the Calculus Concept Inventory and Function Concept Inventory, are designed for students in mathematics degree programs, focusing on content knowledge rather than skills. These tools lack the engineering perspective and contextual relevance, making them less suitable for use with engineering students.
This creates an opportunity to develop a more skills-based approach that better addresses the specific needs of engineering programs. Such an approach would offer more accurate evaluation of students' KSAs, capturing a deeper level cognitive understanding. In this project, we examine and contextualise the essential mathematical skills needed to master the threshold concepts of functions, drawing from core skills identified in prior literature and insights from teaching experience. This work lays the groundwork for developing a skills inventory—a competency-based mathematical instrument tailored to undergraduate engineering students. This inventory will aim to address the skills-based challenges encountered in the context of mathematics within first- and second-year engineering programs.