This paper presents a semester-long implementation of an AI-integrated pedagogy using ChatGPT in two small undergraduate mathematics courses at Troy University. The instructional design combines a flipped classroom, AI-supported self-study, in-class critical dialogue with AI as a “third voice,” and project-based assessment. Using qualitative student feedback, we examine how generative AI supported conceptual understanding, research skills, and learner confidence, while also highlighting challenges such as misconceptions and over-reliance. Situating this case within recent scholarship on artificial intelligence in education and AI literacy, we propose a three-layer AI-Integrated Pedagogy model—Foundation, Integration, and Innovation—and a conceptual framework of AI as Third Voice in the Mathematics Classroom. We argue that, when carefully balanced with verification and traditional assessment, generative AI can enhance mathematics learning and better prepare students for an AI-enabled future.