In March of this year, NCTM published the Professional Standards for Teaching Mathematics (Professional Teaching Standards) (1991), a companion to the earlier Curriculum and Evaluation Standards for School Mathematics (Curriculum and Evaluation Standards) (1989). Whereas the earlier document focuses on curriculum, the new document addresses teaching. It elaborates the Curriculum and Evaluation Standards's vision of teaching, in which mathematical reasoning, problem solving, communication, and connections are central. It addresses such questions as, What are classrooms like in which students are able to encounter, develop, and use mathematical ideas and skills in the context of genuine problem and situations? What role might a teacher play in helping students learn to use a variety of resources and tools, such as calculators and computers, and concrete and pictorial models? What is meant by engaging students in mathematical reasoning—in making conjectures, presenting arguments, constructing proofs—at various grade levels? How can adequate mathematical skill be developed in concert with mathematical reasoning? The list of questions can be extended indefinitely, for what we are trying to create is quite different from what we experienced when we were in school and even quite different from much of what we are doing now as teachers.