In recent years, the use of intelligent technologies in education has grown significantly, transforming the way students access knowledge. However, teaching mathematics in junior high school remains a challenge, as current teaching methods in Mexico continue to prioritize memorization of formulas or procedures, affecting student development.

The present paper introduces Smart Math AI, an educational instrument that integrates a virtual tutor based on artificial intelligence with the Problem-Based Learning (PBL) methodology. The application's primary objective is to facilitate the mastery of the Pythagorean theorem through a personalized learning experience. This is achieved by offering students interactive exercises, immediate feedback, and progress tracking. The application contains exercises that allow the learner to practice while interacting with a virtual tutor. The tutor provides feedback tailored to the learner's individual needs and progress, thereby guiding the learner in their learning process.

To evaluate its effectiveness, a study was conducted with junior high school students using pre- and post-tests, as well as perception surveys. The results showed a significant improvement in learning, accompanied by high motivation and acceptance of the use of such technologies in the classroom. It is concluded that the integration of generative language models into educational platforms has the potential to strengthen the understanding of mathematical concepts, encourage critical thinking, and increase student motivation, validating the use of AI-supported PBL in school contexts.

Keywords: Problem-Based Learning (PBL), Large Language Model (LLM), Virtual Tutor, Feedback with AI.