Frameworks of children's mathematical thinking have provided a basis for teachers’ practical inquiry into the teaching and learning of mathematics (Franke, Carpenter, Fennema, Ansell, & Behrend, 1996). Due to the paucity of similar frameworks in algebra and because I sought a more concrete link between professional development and classrooms, I relied upon student work to provide examples of students’ algebraic thinking. In this year-long project, I engaged fifteen teachers in workgroups. For each monthly workgroup the teachers brought samples of their own students’ work (generated from pre-selected problems) for discussion. The teachers began to make sense of their students’ algebraic thinking by creating their own frameworks of their students’ strategies. At first the frameworks were simplistic, containing only two categories for “concrete” and “abstract” strategies. However, as the teachers began to discuss the strategies in more detail, the relationships among them, and the mathematics underlying them, the teachers elaborated the frameworks to reflect the complexity of their students’ strategies and of the mathematics involved in utilizing them.
Franke, M. L., Carpenter, T. P., Fennema, E., Ansell, E., & Behrend, J. (1998). Understanding teachers' self-sustaining, generative change in the context of professional development. Teaching and Teacher Education, 14, 67-80.