Abstract
Background The rise of artificial intelligence systems that can make their own goals plan several steps and take initiative in tasks that involve people is changing how students learn math. Earlier technology was mostly a tool thatwaited for instructions. Currently, agentic AI systems are becoming increasingly popular. They share the initiative to negotiate goals and help manage parts of learning with the student. This change raises several questions. How is agency shared? What does this mean for thinking? How good is the math understanding that comes from the long-term collaboration between humans and AI? Methods This article introduces an idea called the agency-cognition–mathematics (ACM) model. The model blends theories on agency, ideas on distributed and situated thinking, and research on how people learn math. It also examines research on agentic AI in education. Results This study shows how agency can be seen in a spectrum. On one end AI is a tool for this purpose. Finally, AI is a delegate who helps make decisions. It also explains how using AI to think and regulate learning changes how students practice metacognition. This article discusses how a student’s math identity and the power to know what they can do are either strengthened or weakened in environments where humans and AI work together. Conclusion This article offers design rules for teachers, thoughts on ethics, and ideas, for studies. These suggestions aim to carefully and responsibly bring AI into math classrooms.