Interactive, Intelligent Tutoring for Auxiliary Constructions in Geometry Proofs
Ke Wang, Zhendong Su

TL;DR
This paper introduces AGPT, an interactive geometry tutoring system that combines automated theorem proving with student interaction to teach auxiliary constructions, showing effectiveness comparable to human tutors.
Contribution
The paper presents AGPT, a novel interactive geometry tutor that integrates automated proof capabilities with student training on auxiliary constructions, addressing limitations of prior systems.
Findings
AGPT performs comparably to human tutors in training students.
AGPT outperforms existing geometry solvers in effectiveness.
Pilot study with 78 students validates AGPT's educational benefits.
Abstract
Geometry theorem proving forms a major and challenging component in the K-12 mathematics curriculum. A particular difficult task is to add auxiliary constructions (i.e, additional lines or points) to aid proof discovery. Although there exist many intelligent tutoring systems proposed for geometry proofs, few teach students how to find auxiliary constructions. And the few exceptions are all limited by their underlying reasoning processes for supporting auxiliary constructions. This paper tackles these weaknesses of prior systems by introducing an interactive geometry tutor, the Advanced Geometry Proof Tutor (AGPT). It leverages a recent automated geometry prover to provide combined benefits that any geometry theorem prover or intelligent tutoring system alone cannot accomplish. In particular, AGPT not only can automatically process images of geometry problems directly, but also can…
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Taxonomy
TopicsIntelligent Tutoring Systems and Adaptive Learning · Teaching and Learning Programming · Educational Games and Gamification
