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A newer version of this casebook has been published by NCTM (2016): http://www.nctm.org/Store/Products/Number-and-Operations,-Part-1--Building-A-System-of-Tens-Casebook/What are the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.