"Participants examine generalizations at the heart of the study of operations in the elementary grades. They express these generalizations in common language and in algebraic notation, develop arguments based on representations of the operations, study what it means to prove a generalization, and extend their generalizations and arguments when the domain under consideration expands from whole numbers to integers"--DMI website

What are the "big ideas" in elementary school mathematics? How do students understand them? How can teachers best offer help and support as their students grapple with these ideas? These and other questions about the practice of teaching K-8 mathematics are the focus of Developing Mathematical Ideas (DMI), a powerful, engaging professional development curriculum for current and future teachers. At the heart of a DMI seminar is the casebook, sets of classroom episodes (cases) illustrating student thinking as described by their teachers. In addition to case discussions, the curriculum offers teachers opportunities: to explore mathematics in lessons led by facilitators; to share and discuss the work of their own students; to view and discuss DVD clips of mathematics classrooms; to write their own classroom cases; and to read overviews of related research.

This module is intended to help teachers explore methods by which students work with numbers to formulate generalizations about operations. By expanding students understanding of the properties that underlie the number systems introduced in the elementary grades, they will be prepared to think algebraically for success in middle school and beyond.

Developing mathematical ideas : part 1, building a system of tens : DS21961.