Chatting with Chatters: A Case Study on a Personal AI Assistant for Linear Algebra
MSc Thesis of Martijn Elands, defended on Monday, August 11, 2025 at DACS/FSE, Maastricht University, The Netherlands
Abstract: "The rapid advancement of Large Language Models (LLMs) has unlocked new opportunities for personalized education through AI-driven dialogue systems. This thesis presents a case study on the design, implementation, and evaluation of a Virtual Teaching Assistant (VTA) tailored for university-level Linear Algebra (LA) courses at Maastricht University (UM). We address key challenges such as LLM hallucinations, outdated knowledge, and inadequate pedagogical feedback by using an advanced system design that uses 2 LLMs with code verification and Retrieval-Augmented Generation (RAG). The system integrates OpenAI’s o4-mini with code execution for mathematical verification, and Google’s LearnLM to facilitate pedagogically guided interaction. Both are supported by RAG based on an LA textbook to give up-to-date and contextually relevant information. Our evaluations were done using real-user testing and analysis of their interactions, revealing that the system effectively aids student understanding. Students were overall positive about their experience with the VTA. It was helpful, the amount of work was right, and they think they learned more than using traditional learning methods. Our evaluations also suggest that we could reduce teacher workload by generating a concrete, helpful, and logically organized report that addresses struggles that students had during their interactions with the VTA, which hindered their understanding. Our findings suggest that such a VTA can enhance co-directed learning and serve as a scalable, adaptive supplement to traditional instruction."
Cite: Martijn Elands, Chatting with Chatters: A Case Study on a Personal AI Assistant for Linear Algebra, DACS/FSE, Maastrhicht University, The Netherlands, August 2025.