Leveraging AI in Mathematics Tutoring: Designing for Reasoning, Not Replacement

Large language models have made answers more accessible than ever. For education, this creates a central tension: the same systems that can help students understand difficult material can also make it easier to bypass the learning process entirely. This is especially visible in mathematics, where the value often lies not in the final answer, but in the reasoning that leads to it. In this talk, we use Ratatoskur, an iPad-based AI tutor for handwritten mathematics in Icelandic, as a case study for exploring how LLMs can be used more productively in tutoring. Rather than treating the model as an answer engine, Ratatoskur is designed around a student’s own work: it reads handwritten solutions, checks intermediate reasoning, gives hints, asks for clarification when input is ambiguous, and only reveals full solutions as one possible mode of interaction. We will discuss how this changes the design problem from “can the model solve the task?” to “how should the system guide the student?” That shift raises practical questions about user interface design, feedback modes, uncertainty, evaluation, observability, and responsible use of student data. More broadly, the talk considers how educational AI systems can be designed so that the easiest and most natural way to use them still encourages active thinking.