Several studies have shown that when teachers teach for conceptual and procedural understanding, rather than focusing solely on computational fluency, student achievement improves (Haycock, 2001; Knapp, 1995; Newmann & Associates, 1996). But because teachers themselves learned mathematics through a system that emphasized procedural fluency, many teachers currently lack the conceptual basis to teach in this manner. There is thus a need for high-quality professional development that gives teachers both the knowledge and the pedagogical tools to teach for deep mathematical understanding. This chapter describes one successful effort to develop and implement a professional development framework that models what teaching for understanding looks like while deepening teachers’ own conceptual content knowledge.
In order to build a model for teaching mathematics with understanding and conducting professional development to promote this type of teaching in mathematics, we researched and identified instructional practices we wanted to observe in teachers’ classrooms. From this theoretical framework for developing mathematical thinking, we proceeded to build a professional development model that helps teachers put these instructional structures into practice.