This set of materials, part of the "Developing Mathematical Ideas" (DMI) professional development curriculum for grades K-6 teachers, deals with base ten and place value concepts. The materials consist of a 184-page Facilitator's Guide (FG), a 117-page Casebook (CB), and a 55-minute videotape of classroom clips and interviews with children and teachers.

The purpose of these materials, as well as the overall DMI project, is to "...help teachers think through the major ideas of K-6 mathematics and examine how children develop those ideas" (FG, p. 5). This set is designed specifically to help participants explore the development of mathematical ideas related to the base ten number system. A comprehensive professional development package, these materials can be used by professional development providers who work with practicing teachers, prospective teachers, administrators, and/or parents.

Number and Operations: Building a System of Tens is a set of materials that provides a powerful combination of tools to build a rich learning environment for teachers. The program is designed for a workshop format, which includes a variety of activities for the participating teachers:

• reading/viewing and discussing cases of classroom interactions of and with students;
• viewing and discussing interviews with children regarding their mathematical thinking;
• exploring mathematical ideas as adult learners; sharing student mathematical thinking and behavior from their own classrooms;
• interviewing their own students and analyzing their responses;
• writing classroom episodes;
• analyzing lessons from innovative elementary mathematics curricula; and
• reading overviews of related research, which are provided in the Casebook.

This set of materials is well grounded in the pedagogy and content of standards-based mathematical learning opportunities, both for children and adult learners. It provides a rigorous model for teachers to follow in their own mathematical instruction. The Facilitator's Guide is extensive, well organized, and readable, with several sections that discuss flexible use of the materials. The topics included in the Casebook and videotape segments allow for teachers from grades 1-6 to read about and see students in action.

The DMI curriculum emphasizes equitable practice in a variety of ways. The videotaped segments show highly diverse populations of students engaged in mathematical thinking as they solve problems. The video segments also depict interviews with a diverse group of students and teachers. The variety of materials and activities used in the professional growth sessions accommodate multiple learning styles. The professional growth model that is encouraged-to create a community of learners among teachers and to promote their mathematical knowledge and abilities to talk about mathematics-models the development of mathematical power among all learners. As such, it emphasizes respect for the individual learner as part of the larger learning community and, therefore, models equitable practice.

These materials provide professional developers with a comprehensive and detailed program of study for teachers.

Reviewers noted that these materials would be excellent for use in pre-service or in-service studies of mathematical thinking and discourse at the building, district or university level. The program could also be used with groups of parents who are interested in constructivist learning and student mathematical discourse. These materials are designed to be used in a multi-session, sustained, in-depth professional development setting and are finely tuned to this purpose.

While the Facilitator's Guide provides thorough directions and the Casebook and videotape provide participants with excellent examples of classroom activities for discussion, effective use of the materials requires a skilled facilitator who is familiar with constructivist learning and mathematical discourse.