Background

Preparing Teachers

While the mathematics teacher education sites address different issues of teaching and learning, they share a set of principles about what it means to teach and learn mathematics.

Our shared principles are represented well in Adding it Up (NRC, 2001). We agree that all students need opportunities to develop both concepts and skills, to develop flexibility in their abilities to engage with mathematical ideas and to engage in what some may call higher order or critical thinking. Developing these ideas is about rigor in both depth and breadth and is ultimately how we conceive of understanding. We agree that developing mathematical understanding involves developing knowledge and skill as well as a disposition that orients one as someone capable of doing mathematics well.

Shared Perspectives

While there is growing consensus about the perspective we share about the teaching and learning of mathematics, we also know that it is not a perspective that is widely implemented in schools and classrooms. We know from studies like the Third International Mathematics and Science Study (TIMMS) that in the U.S. most mathematics instruction is not consistent with current reform ideas (Hiebert et al., 2003; Hiebert & Stigler, 2000; Stigler & Hiebert, 1997, 1999). Most U.S. mathematics classrooms maintain a focus on answers rather than strategy. The teacher assumes responsibility for solving the problem while student participation often involves providing the next step in a procedure. TIMMS also reports that U.S. students had little opportunity to discuss connections among mathematical ideas and reason about mathematical concepts. Further we know that often “reform” becomes about using manipulatives, putting students in cooperative groups, and asking higher order questions in ways that in and of themselves do not lead to classrooms that support the development of mathematical understanding (Stigler & Hiebert, 1997, 1999; Webb et at al., 2004). How these approaches play out within the classroom context matters. How the teachers and students engage with the higher order questions or the manipulatives also matters. So, our job as mathematics teacher educators is to find ways to support teacher education students to learn the practices in deep and connected ways that become generative, mathematically meaningful, and make sense for each child in the classroom.

In addition to these principles related to the teaching and learning of mathematics, as teacher educators we have come, through this work, to a better understanding of learning from practice in ways that become generative. A principle driving all of this work is that teacher education students need an opportunity to figure out what it means to learn about practice from practice. To see that teaching practices are not separate from the principles we have laid out and that they are not separate from each other. We want to provide students with the tools, knowledge, skills and dispositions they need to learn as they teach and to do so in a way that is generative. The websites allowed us to focus on learning from practice and we could use that learning to structure opportunities to learn from the practice of teaching.