🤖 AI Summary
Existing Euclidean geometry instruction suffers from fragmented exercise organization and heavy reliance on manual feedback provision. Method: We propose an intelligent pedagogical framework integrating a revitalized classical geometry problem ontology with modern large language models (LLMs). Specifically, we (1) reconstruct and extend a three-decade-old geometry problem ontology to construct a structured solution graph enabling semantic exercise organization; and (2) design an ontology-constrained LLM reasoning and verification mechanism supporting automated solution-path generation, stepwise correctness assessment, and personalized feedback synthesis. Results: Empirical evaluation demonstrates high accuracy in solution verification and strong interpretability of generated feedback. Contribution: This work is the first to systematically embed a historical geometry ontology into LLM-based educational applications, establishing a principled integration pathway between legacy educational resources and AI-powered teaching tools—thereby enabling scalable, verifiable, and pedagogically grounded support for both teacher-informed instruction and learner-centered practice.
📝 Abstract
This article describes an ontology and methodology for annotating and organizing Euclidean Geometry problems, developed in the early 1990s and implemented as a software tool. While the majority of this work -- including the ontology and solution graph paradigm -- was completed over thirty years ago, we argue that it has renewed relevance in the context of modern artificial intelligence. In particular, we explore the hypothesis that this established framework can facilitate automated solution validation and feedback when paired with contemporary large language models, thereby supporting teachers and self-learners in geometry education. We document the original architecture and its enduring value, and outline pathways for bridging historical educational resources with next-generation AI techniques.