Generative artificial intelligence in university mathematics teaching: Theorems-in-action inferred from practicing professors’ discourse
DOI:
https://doi.org/10.59965/ijmsed.v4i2.323Keywords:
Generative artificial intelligence, Theorems-in-action, University mathematics professorsAbstract
This article examines how university professors who teach mathematics conceptualize and use Generative Artificial Intelligence (GenAI) chatbots such as ChatGPT and Gemini, as expressed in their interview discourse. Drawing on the Theory of Conceptual Fields, the study adopts a qualitative, exploratory case-study design bounded to ten practicing professors from the academic units of Mathematics, Physics, Light and Matter Science and Technology (LUMAT), and Engineering at a public university in Mexico. Semi-structured interviews were segmented into episodes, from which theorems-in-action (TA) were inferred by one researcher, reviewed by a second researcher, and agreed upon by the research team; the resulting 68 TA were grouped into seven categories and judged as correct, incorrect, or not yet established in light of current literature on GenAI. The findings reveal the coexistence of contradictory theorems-in-action: some reflect schemes built through experience with search engines (GenAI provides correct results), while others are more appropriate for the use of these technologies (GenAI does not always respond correctly). Furthermore, although most professors report using GenAI for personal or professional tasks, its reported pedagogical integration into the classroom remains limited. These results suggest that professional development for mathematics teachers should go beyond instrumental training and explicitly address the theorems-in-action that guide the use of GenAI, particularly those concerning the verification of its outputs.
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