Computer Science Department PhD Proposal Defense: Ethan Croteau, "Representation-Ready and Tutor-Ready Visual Mathematics for Educational AI"
2:00 p.m. to 3:00 p.m.
Ethan Croteau
PhD Candidate
WPI - Computer Science Department
Wednesday, September 9, 2026
Time: 2:00 p.m. – 3:00 p.m.
Zoom Link: https://tiny.cc/zoomwithethan
Committee members:
Prof. Neil Heffernan, Advisor - WPI - Computer Science Department
Prof. Emmanuel Agu - WPI - Computer Science Department
Prof. Ethan Prihar - WPI - Computer Science Department
Dr. Vincent Ybarra – MITRE
Abstract:
Many educational uses of artificial intelligence assume that a mathematics problem can be represented as text, an image, and an answer key. This assumption breaks down for curriculum-authentic visual mathematics, where diagrams, graphs, tables, number lines, and geometric figures often contain information that is required for solving the problem. In these settings, reliable tutoring, feedback, accessibility support, learner modeling, and model evaluation require more than a stronger vision model. They require auditable representations of what must be seen, what must be inferred, what must be calculated, and how a learner response relates to the visual and mathematical structure of the task.
This proposal describes a dissertation organized around papers on representation-ready and tutor-ready visual mathematics for educational AI. The completed and current papers move from chatbot support for students in ASSISTments, to multimodal model evaluation on image-required mathematics, to alternative representation studies, audits of residual failures, representation-ready artifact corpus, and tutor-ready knowledge graph infrastructure. Adjacent knowledge tracing work is included as broader educational data mining context. The proposed remaining work is a focused graph-grounded tutoring study with three connected aims: diagnose common wrong answers, generate visually and mathematically grounded tutoring support, and create structurally similar practice problems from explicit graph constraints. Together, these aims test whether problem knowledge graphs can serve as reproducible infrastructure for more diagnostic, faithful, and instructionally useful visual mathematics tutoring.