2026 ASEE Annual Conference & Exposition

Engineering students often encounter advanced mathematics and engineering concepts in isolated courses, making it difficult to transfer mathematical reasoning into engineering modeling and design contexts. This research-to-practice paper presents an AI-augmented framework for supporting adaptive learning trajectories by making conceptual relationships across mathematics and engineering courses explicit, interpretable, and responsive to student learning evidence. Building on prior work on Fourier and functional analysis learning trajectories, the framework begins with collaboratively authored concept maps developed by mathematics and engineering faculty. These maps are transformed into adjacency and layered contingency matrices that represent conceptual connections and instructional dependencies across courses such as Calculus II, Differential Equations, Linear Algebra, Control Systems, and Signal Processing. Student work from live computational notebooks (e.g., Jupyter and MATLAB Live Scripts) is analyzed to iteratively refine these representations, allowing instructors to identify conceptual bottlenecks and adjust task sequencing. The framework is operationalized through dual-stance modeling tasks that explicitly link mathematical abstraction with engineering application. Embedded prompts support reflection as students transition between deriving mathematical structures and validating them in engineering contexts. Classroom implementations across coordinated courses suggest that this approach supports clearer instructional sequencing, reveals previously unseen interdisciplinary connections, and helps students articulate relationships between mathematical concepts and engineering practices. By integrating concept mapping, matrix-based representations, and notebook-centered instruction, this work contributes a transparent and adaptable approach to interdisciplinary curriculum design in engineering mathematics. The framework emphasizes faculty interpretability and cross-course alignment, offering a scalable model for adaptive instruction that can be adopted across institutions with diverse curricular structures.