An Ontology-Based Approach to Optimizing Geometry Problem Sets for Skill Development
This work addresses the problem of enhancing geometry education for students and educators by offering a scalable foundation for intelligent tools, but it is incremental as it builds on existing ontology concepts from the 1990s.
The paper tackles the challenge of optimizing geometry problem sets for skill development by presenting an ontology-based framework that classifies problems and solutions, enabling granular tracking of student abilities and curriculum design. It hypothesizes that this approach can lead to adaptive educational tools and automated solution validation, though no concrete results or numbers are provided.
Euclidean geometry has historically played a central role in cultivating logical reasoning and abstract thinking within mathematics education, but has experienced waning emphasis in recent curricula. The resurgence of interest, driven by advances in artificial intelligence and educational technology, has highlighted geometry's potential to develop essential cognitive skills and inspired new approaches to automated problem solving and proof verification. This article presents an ontology-based framework for annotating and optimizing geometry problem sets, originally developed in the 1990s. The ontology systematically classifies geometric problems, solutions, and associated skills into interlinked facts, objects, and methods, supporting granular tracking of student abilities and facilitating curriculum design. The core concept of 'solution graphs'--directed acyclic graphs encoding multiple solution pathways and skill dependencies--enables alignment of problem selection with instructional objectives. We hypothesize that this framework also points toward automated solution validation via semantic parsing. We contend that our approach addresses longstanding challenges in representing dynamic, procedurally complex mathematical knowledge, paving the way for adaptive, feedback-rich educational tools. Our methodology offers a scalable, adaptable foundation for future advances in intelligent geometry education and automated reasoning.