Number and Operations: Making Meaning for Operations is a set of materials that builds upon Part 1 of the DMI curriculum, Number and Operations: Building a System of Tens. The eight modules or sessions address counting models, addition/subtraction and multiplication/division of whole numbers, and operations on rational numbers. The final module highlights research literature related to operations on whole and rational numbers. The materials include a Casebook of classroom-based cases written by elementary teachers about their own classroom situations. A Facilitator's Guide references the Casebook and supports the session leader with a detailed agenda and a composite journal kept by a fictitious facilitator reflecting on each session. The videotape illustrates many of the ideas encountered in the Casebook and is accurate in its portrayal of real students and classrooms.
Both the disciplinary and pedagogical content of these materials is very strong. While the activities focus on elementary-level mathematics, they all provide teachers with meaningful and challenging problems to contemplate and solve, problems that are well-suited for teachers to explore the type of thinking in which their students are likely to engage. The pedagogical rigor is at the highest level. Teachers are expected to think deeply and reflect on important and complicated issues related to mathematics teaching and learning.
The materials consistently stress the importance of listening to and giving careful consideration to the thinking of all students, clearly reflecting an emphasis on equitable practice. Efforts were also made to involve teachers from rural, urban, and suburban settings in the piloting and preparation of materials. Children on the videotaped segments and in the cases represent several ethnic groups and there is equal gender representation.
In summary, this set of professional development materials for elementary teachers is an exemplary program that promotes deep reflection about the teaching and learning of mathematics.