AI Responses to Challenging Problems and Educator Responses to AI Availability

This article considers the rise of generative Artificial Intelligence (GenAI) in the context of secondary mathematics education, focusing on its responses to cognitively demanding tasks and the pedagogical implications of these interactions. Using tools such as ChatGPT (OpenAI) and Gemini (Google), we investigate how GenAI engages in complex mathematical reasoning and problem-solving beyond the capabilities of traditional digital tools. Our analysis reveals that, although GenAI thus far tends to typically produce tasks of low cognitive demand, it clearly exhibits an ability to respond to cognitively-demanding mathematical tasks. We share examples of GenAI responses to three tasks from secondary mathematics, and, although the GenAI made substantial errors, it also demonstrated an ability to revise and refine its work with prompting. For educators faced with GenAI, we argue against banning its use and instead propose two instructional strategies to promote student learning in this new AI era: (1) fostering student interaction with GenAI to explore and expand on mathematical concepts and (2) encouraging students to critically evaluate and discuss GenAI-generated solutions to mathematical problems. These instructional strategies aim to enhance students’ mathematical understanding and critical thinking skills by using GenAI as a tool that can promote substantive student involvement and meaningful learning. (An initial draft of this abstract was produced by ChatGPT 4.0, but GenAI was not used in any other way for this article, other than as an interactive partner within the excerpts as clearly marked.)