AI-assisted Socratic Questioning for Formal Proof Competence in Plane Geometry: A Literature Review

Abstract

Formal proof is at the heart of university-level plane geometry because it requires students to build deductively valid arguments based on definitions, theorems, and known results, rather than visual observation or intuition. However, students often struggle to justify inferential steps, while generative artificial intelligence can provide fluent proofs before learners examine diagrams, check theorem conditions, or construct their own reasoning. This conceptual article proposes a Warrant-Seeking Socratic AI Framework for supporting formal proof learning in plane geometry. Literature was searched in Scopus, Web of Science, ERIC, and Google Scholar from March 15 to May 21, 2026, using terms related to formal proof, geometry, Socratic questioning, and artificial intelligence. Of 72 records identified, 14 duplicates were removed, leaving 58 sources for screening, full-text assessment, and narrative synthesis. Sources were synthesized by identifying recurring pedagogical and epistemic functions related to proof construction, questioning, AI interaction, and validation. Based on the synthesis: problem orientation, conjecture articulation, theorem-condition analysis, inferential construction, proof validation, and metacognitive reflection, a six-phase recursive model is proposed. The framework positions AI as an epistemic interviewer rather than a proof generator, prompting students to distinguish visual conjectures from warranted claims, examine theorem conditions, justify inferential steps, and retain ownership of their proofs. The synthesis distinguishes evidence directly related to geometry and mathematical proving from findings extrapolated from broader educational contexts. The framework is therefore a theoretically grounded proposition rather than an empirically validated model, and its effectiveness remains to be established through future empirical research.