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The current mathematics reform movement has recognized that new forms of mathematics teaching will be needed to support the proposed curricular changes. These new forms extend beyond the acquisition of new teaching techniques and strategies to the reconstitution of fundamental notions of teaching, learning, and the nature of mathematics as a discipline, and also to the creation of different classroom opportunities for learning. The means by which teachers effect this kind of transformation are, as yet, little understood. This paper describes a set of components of developmental models that can be used to guide efforts to build models of the process of teachers' development in mathematics practice. Drawing from theories of cognitive development, the paper focuses on three components of the change process: (1) qualitative reorganizations of understanding; (2) orderly progression of changes; and (3) the contexts and mechanisms by which transitions are effected; and suggests a fourth component-individual motivational and dispositional factors.