teacher must master in order to reach that end and the levels of mastery needed. What mathematics must a teacher know, and what pedagogical knowledge does she or he need to make and implement appropriate decisions about the next best instructional steps to develop student thinking about gravity, for example? Although these questions are central to effective practice, little research has been done to provide answers.

Moreover, learning is as complex an undertaking when the teacher is the target as it is when the student is the target. A teacher’s existing conceptions of teaching and learning, of student thinking, and of the subject matter must be understood and engaged. And experiences that bring about conceptual change for the teacher must be designed and effectively deployed for learning to occur.

The task is challenging; conceptual change is difficult to achieve when everyday experiences reinforce a misconception. In many everyday experiences one can simply tell people what they want or need to know. This is likely to influence a teacher’s view about learning and instruction. When the frame of reference is common, simply telling works just fine. But when conceptions differ, telling is unlikely to be enough. “Elephants are bigger than pigs” may be completely adequate to communicate intended meaning, while “the orientation of the earth’s axis relative to the sun determines the seasons” may be entirely inadequate. If the conception of teaching as telling is to be replaced by a more variegated model, powerful experiences that facilitate conceptual change on the part of the teacher about how students learn will be required.

The typical learning trajectory for teachers, and how it changes with learning opportunities, also requires empirical investigation. Much that teachers need to know cannot be learned apart from practice. This raises several questions for inquiry: Under what conditions can teachers best learn while engaged in practice? What knowledge and skill must teachers acquire at the beginning of their careers? What knowledge and skill is best acquired once they enter the profession? What organizational, material, and human resources are necessary to support and sustain teacher learning over time?

Widespread adoption and use of improved instructional methods are often hampered by institutional barriers that prevent or frustrate efforts to change: these may include problems of organizational structure, incentive structures, organizational



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