International Group for the Psychology of Mathematics Education (PME)

Proceedings of the International Group for the Psychology of Mathematics Education · Volume 1

Interplay Between External and Internal Factors in the Use of Genai for the Construction of Proofs: Shorts in the Essential Algebraic Cycle

Francesco Contel, Annalisa Cusi

Sapienza University of Rome

49th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2026Helsinki27 July 2026 - 1 August 2026pp. 291–298ISSN 2790-36482026Scopus conference code 336559
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Abstract

In this paper, we explore secondary students’ interaction with GPT-4o in the context of activities of proof construction through algebraic language with the aim of investigating how the interplay between internal and external factors affects the represent-manipulate-interpret essential algebraic cycle. A qualitative micro-analysis of chats, students’ interviews and their written work was conducted. The findings show that bias and hallucinations in the GenAI tool interact with students’ epistemic beliefs, producing different forms of short circuits of the algebraic cycle. Implications are raised for the design of GenAI systems that support algebraic reasoning as meaning-making rather than procedural execution.

Keywords

human-GenAI interactionalgebraic proofChatGPTinstrumental genesisinternal and external factors

Recommended citation

Contel, F., & Cusi, A. (2026). Interplay Between External and Internal Factors in the Use of Genai for the Construction of Proofs: Shorts in the Essential Algebraic Cycle. In Krzywacki H., Hähkiöniemi M., Haataja E., Hannula M.S., Hästö P. (Eds.), Proceedings of the International Group for the Psychology of Mathematics Education, Volume 1 (pp. 291–298). Psychology of Mathematics Education (PME). ISSN 2790-3648.
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