is teacher development. Working directly on improving teaching is their means of becoming better teachers.

Communities of Practice

Learning in ways that continue to be generative over time is best done in a community of fellow practitioners and learners, as illustrated by the Japanese lesson study groups. The foregoing discussion of teacher proficiency focused on individual teachers’ knowledge, but teaching proficiency does not easily develop and is not generally sustained in isolation. Studies of school reform efforts suggest that professional development is most effective when it extends beyond the individual teacher.48 Collaboration among teachers provides support for them to engage in the kinds of inquiry that are needed to develop teaching proficiency. Professional development can create contexts for teacher collaboration, provide a focus for the collaboration, and provide a common frame for interacting with other teachers around common problems. When teachers have opportunities to continue to participate in communities of practice that support their inquiry, instructional practices that foster the development of mathematical proficiency can more easily be sustained.

Professional development can create contexts for teacher collaboration, provide a focus for the collaboration, and provide a common frame for interacting with other teachers around common problems.

The focus of teacher groups matters for what teachers learn from their interactions with others. When sustained work is focused on mathematics, on students’ thinking about specific mathematical topics, or on the detailed work of designing and enacting instruction, the resources generated for teachers’ own practice are greater than when there is less concrete focus. For example, general sharing, or discussion of approaches, ungrounded in the particulars of classroom artifacts, while possibly enjoyable, less often produces usable knowledge that can make a difference for teachers’ work.

Mathematics Specialists

Because of the specialized knowledge required to teach mathematics, there has been increased discussion recently of the use of mathematics specialists, particularly in the upper elementary and middle school grades. The Learning First Alliance, comprising 12 major education groups, recommends that mathematics teachers from grades 5 through 9 have “a solid grounding in the coursework of grades K-12 and the teaching of middle grades mathematics.”49 The Conference Board of the Mathematical Sciences recommends in its draft report that mathematics in middle grades should be taught by mathematics specialists, starting at least in the fifth grade.50 They further recommend that teachers of middle school mathematics have taken 21 semester



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