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.

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.

Creating mathematical community in elementary classrooms to support equitable engagement in deep mathematical content What does a mathematical community look like in an elementary classroom? How do teachers engage young mathematicians in deep and challenging mathematical content? How do we ensure that every student contributes their voice to this community? Interweaving Equitable Participation and Deep Mathematics: Building Community in the Elementary Classroom focuses on a dual commitment: to teaching deep and challenging mathematics and to equitable participation for all students in the classroom community. With practical strategies and real-life examples, Susan Jo Russell and Deborah Schifter offer a design for building community organized around four key aspects: every voice matters; collaboration supports student agency; student-created representations offer anchors, openings, and depth; and students become initiators and advocates for their own learning. Each chapter examines how teachers implement these ideas through video examples from six public elementary-school classrooms. A powerful resource for any educator interested in a mathematics education that fosters a true sense of community, this book Provides a window into a learning community of educators applying their understanding of mathematics to develop a teaching practice that fosters students’ curiosity, meaning-making, and mathematical agency Presents vivid examples of teachers and students in diverse classrooms engaged in rich mathematical tasks and deep collaborative conversations, inviting readers to reflect on their practices and students′ learning Engages readers in math investigations to help them understand student thinking, provides reflection questions about the classroom video, and offers suggestions for taking next steps in one′s own practice Includes commentaries on the videos by a group of "critical friends"—educators with deep experience in mathematics and equity—and by the teachers of the classrooms in the videos Offers free online tools for professional development and book study groups, including a Facilitator’s Guide and a Notes Organizer, and suggests resources for continued learning. This book is a must-read for anyone passionate about creating positive change in the mathematics education system and ensuring that every student has the opportunity to thrive in their mathematical journey.

There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.

Measuring and Visualizing Space in Elementary Mathematics Learning explores the development of elementary students’ understanding of the mathematics of measure, and demonstrates how measurement can serve as an anchor for supporting a deeper understanding of number operations and rational numbers. The concept of measurement is centrally implicated in a number of mathematical operations, yet is not often given the placement it deserves in the elementary mathematics curriculum. By drawing on K-5 classroom research, authors Lehrer and Schauble have been able to articulate a learning progression that describes benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage. Offering a unique, research driven resource for helping students develop a deep understanding of measurement to further enhance mathematical understanding, as well as further learning in other STEM disciplines; the book will be relevant for scholars, teacher educators, and specialists in math education. The book is accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.