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.

"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

Mathematics Teacher Noticing is the first book to examine research on the particular type of noticing done by teachers---how teachers pay attention to and make sense of what happens in the complexity of instructional situations. In the midst of all that is happening in a classroom, where do mathematics teachers look, what do they see, and what sense do they make of it? This groundbreaking collection begins with an overview of the construct of noticing and the various historical, theoretical, and methodological perspectives on teacher noticing. It then focuses on studies of mathematics teacher noticing in the context of teaching and learning and concludes by suggesting links to other constructs integral to teaching. By collecting the work of leaders in the field in one volume, the editors present the current state of research and provide ideas for how future work could further the field.

This volume contains papers from the Second International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The intended audience includes policy makers, curriculum developers, researchers, teachers, teacher trainers, and anyone else interested in school mathematics curricula.

A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM) In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics education of students at all grade levels. This important new collection provides that much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. Such a story includes understanding how the forms of proof, including the nature of argumentation and justification as well as what counts as proof, evolve chronologically and cognitively and how curricula and instruction can support the development of students’ understanding of proof. Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. By building and extending on existing research and by allowing a variety of voices from the field to be heard, Teaching and Learning Proof Across the Grades not only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.

(Orginally published in 2008) The goal of AMTE Monograph 4, "Cases in Mathematics Teacher Education: Tools for Developing Knowledge Needed for Teaching", is to provide detailed accounts of case use that will inform the mathematics teacher education community on the range of ways in which cases can be used to foster teacher learning and the capacity to reflect on and learn from teaching. The chapters in this monograph describe the use of cases with preservice and practicing teachers at all levels K - 12, in content and methods courses as well as professional development settings, and focus on developing various aspects of teachers' knowledge base (i.e., content, pedagogy, and students as learners). Hence, Monograph 4 should prove to be a superb resource for mathematics teacher educators.