AI-Assisted Mathematical Problem Solving: Epistemic Configuration and Prompt Design

Abstract

This workshop explored the pedagogical use of generative artificial intelligence tools, such as ChatGPT and Gemini, for mathematical problem solving from a critical and didactic perspective. It focused on two key concepts: epistemic configuration, understood as the set of knowledge, procedures, representations, and rules that determine the validity of a mathematical answer in an institutional context, and prompts, as the instruction given to AI to guide the form and content of its response. The proposal, aimed at secondary school teachers and university professors, combined presentations with two practical activities: (i) free exploration of AI responses to typical problems of the level, evaluated using epistemic criteria, and (ii) redesign guided by prompts to improve the didactic relevance of the solutions generated. Criteria for evaluating AI responses (correctness, justification, representations, language, and rules) were also presented, along with a practical guide for integrating these tools into the classroom, encouraging critical and metamathematical thinking beyond the mere results obtained. Participants verified that well-designed prompts encourage more complete, justified responses that are aligned with school mathematics practice. The workshop concluded with a reflection on the role of teachers in relation to AI, highlighting the importance of using it consciously and with mediation to enhance meaningful learning.