This paper explains the method and value of critical aesthetic inquiry when researching the teaching of art. The paper contends that teaching is an art, and the only appropriate way to research art practice is through an artistic approach to critical inquiry. The paper explains how art education research is distinctive from scientific research. It then explains the framework of critical aesthetic inquiry, including the basic theory, data gathering instruments, and methods of analysis. It addresses the methodology's limitations and realms of effective application. (Contains 27 references.) (BT)