MCA: Supporting Equation Navigation and Sensemaking in Engineering with AI

This project aims to serve the national interest by helping engineering students connect equations to physical reality. This Mid-Career Advancement (MCA) project addresses an important challenge in engineering education: students often set up equations that resemble legitimate formulas but do not understand what those equations mean physically. These students treat equations as templates for calculation instead of mathematical descriptions of physical behavior. Conventional assessments have largely overlooked this challenge. As AI tools become increasingly able to carry out routine computation, the reasoning that distinguishes genuine understanding from pattern-matching becomes even more important, and AI itself can help reveal that reasoning. The project plans to develop AI-supported learning and assessment methods that make students' reasoning during equation setup visible, teachable, and assessable. Its significance lies in improving students' ability to connect equations with physical systems, lowering barriers in introductory engineering courses while maintaining high expectations for conceptual understanding. Developing this capacity in engineering students supports NSF's mission to advance the nation's STEM workforce and ensure graduates are equipped for the demands of technical careers. What distinguishes this project from conventional approaches is its focus on the formulation stage of problem solving, the step before computation where students must decide what equations mean and whether they apply, and its use of AI to reveal students’ equation reasoning rather than to automate computation. Expected outcomes include improved student preparation for reasoning about equations, reusable instructional tools that make that reasoning visible and teachable, and practical guidance for engineering instructors on supporting conceptual understanding in the AI era. Critically, the project also builds the PI’s skills in qualitative research methods that will enable her to expand her expertise to study AI-supported undergraduate learning. The goals of the project are to advance understanding of how engineering students coordinate two types of reasoning: semantic reasoning and syntactic reasoning. Semantic reasoning connects mathematical symbols and equations to physical quantities and behavior; syntactic reasoning relies on equation patterns and algebraic routines. The scope includes problem-solving tasks in sophomore-level Dynamics and Thermodynamics courses that require students to set up and interpret equations in symbolic rather than numerical form. The project plans to collect written student work and conduct think-aloud and retrospective recall interviews to capture students' reasoning during equation setup. From this evidence, the project intends to develop and validate a coding framework for semantic, syntactic, and blended reasoning, and identify critical junctures where students must connect notation with physical meaning. Building on these findings, the project also intends to design AI-supported prompts that ask students to articulate their equation reasoning in writing or through conversation, and to compare traditional computation-heavy assessments with symbolic-only and AI-integrated formats. Planned methodologies include qualitative coding, response-process analysis, conceptual measurement, and psychometric validation of reliability and construct validity. Project results are expected to include a construct framework, annotated task banks, prompt designs, and comparative assessment data. The project plans to disseminate findings through peer-reviewed publications, conference presentations, faculty workshops, and openly available materials for instructors. This project is supported by the Mid-Career Advancement program that offers opportunities for scientists and engineers to substantively enhance and advance their research program through synergistic and mutually beneficial partnerships and the IUSE: EDU Program, which supports research and development projects to improve the effectiveness of STEM education for all students. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.