The Measuring Space in One, Two, and Three Dimensions Casebook was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation of specific mathematical concepts and teaching strategies.

Teachers and students examine different aspects of size, develop facility in composing and decomposing shapes, and examine different sizes to develop sense of volume.

Teachers and students examine different aspects of size, develop facility in composing and decomposing shapes, and examine different sizes to develope sense of volume.

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.

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.

Now is a time of great interest in mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies on the mathematical knowledge of prospective and practicing U. S. teachers suggest ways to improve their mathematical educations. It is often assumed that because the topics covered in K-12 mathematics are so basic, they should be easy to teach. However, research in mathematics education has shown that to teach well,substantial mathematical understanding is necessary--even to teach whole-number arithmetic. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power. This volume gathers and reports current thinkingon curriculum and policy issues affecting the mathematical education of teachers. It considers two general themes: (1) the intellectual substance in school mathematics; and (2) the special nature of the mathematical knowledge needed for teaching. The underlying study was funded by a grant from the U.S. Department of Education. The mathematical knowledge needed for teaching is quite different from that required by students pursuing other mathematics-related professions. Material here is gearedtoward stimulating efforts on individual campuses to improve programs for prospective teachers. This report contains general recommendations for all grades and extensive discussions of the specific mathematical knowledge required for teaching elementary, middle, and high-school grades, respectively.It is also designed to marshal efforts in the mathematical sciences community to back important national initiatives to improve mathematics education and to expand professional development opportunities. The book will be an important resource for mathematics faculty and other parties involved in the mathematical education of teachers. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.