An argumentation experience regarding concepts of calculus with ChatGPT

ChatGPT, an artificial intelligence-supported chatbot, has become a resource in the field of education for students across various disciplines. The conversation that unfolds based on the user-generated questions and ChatGPT's responses implies the emergence of an argumentation between the student and ChatGPT. In this study, the argumentation between a university student and ChatGPT, conducted to examine situations where a tangent line cannot be drawn to a function's graph, was analyzed using Toulmin's model enriched with Habermas' construct of rationality. The findings indicate that ChatGPT offers rational support to the warrant in student's reasoning in the of context epistemic rationality regarding the definitions of continuity, derivative, and tangent concepts. However, ChatGPT provides problematic responses in the context of epistemic rationality regarding the relationship between continuity and derivative, as well as in the context of communicative rationality concerning the geometric interpretation of the derivative and the definition of the tangent line. ChatGPT has not provided reliable and stable support to the student in the reasoning process. It can be concluded that ChatGPT, which is considered to have the potential to assist learning processes, requires expertise in calculus concepts for its use in mathematical reasoning processes. Otherwise, it may be confusing and/or misleading.