Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume One is rational numbers and proportionality. Using materials that were developed under the NSF-funded COMET (Cases of Mathematics to Enhance Teaching) program, each volume in the set features cases from urban, middle school classrooms with ethnically, racially, and linguistically diverse student populations. Each case illustrates an instructional episode in the classroom of a teacher who is implementing standards-based instruction, the teachers' perspective, including their thoughts and actions as they interact with students and with key aspects of mathematical content, cognitively challenging mathematics activities that are built around samples of authentic classroom practice., and facilitation chapters to help professional developers "teach" the cases, including specific guidelines for facilitating discussions and suggestions for connecting the ideas presented in the cases to a teacher's own practice. As a complete set, this resource provides a basis on which to build a comprehensive professional development program to improve mathematics instruction and student learning.

Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume One is rational numbers and proportionality. Using materials that were developed under the NSF-funded COMET (Cases of Mathematics to Enhance Teaching) program, each volume in the set features cases from urban, middle school classrooms with ethnically, racially, and linguistically diverse student populations. Each case illustrates an instructional episode in the classroom of a teacher who is implementing standards-based instruction, the teachers' perspective, including their thoughts and actions as they interact with students and with key aspects of mathematical content, cognitively challenging mathematics activities that are built around samples of authentic classroom practice., and facilitation chapters to help professional developers "teach" the cases, including specific guidelines for facilitating discussions and suggestions for connecting the ideas presented in the cases to a teacher's own practice. As a complete set, this resource provides a basis on which to build a comprehensive professional development program to improve mathematics instruction and student learning.

An eyeopening look at how teachers can use literacy strategies to help students better understand mathematics.

Offers a practical guide for improving schools dramatically that will enable all students from all backgrounds to achieve at high levels. Includes assessment forms, an index, and a DVD.

Provides educators with instructions on applying response-to-intervention (RTI) while teaching and planning curriculum for students with learning disabilities.

Teachers and teacher educators interested in synthesizing their current practice with new mathematics standards will welcome this highly useful volume. Author Mary Kay Stein and her colleagues at the QUASAR Project at the University of Pittsburgh present prevalent cases of mathematics instruction drawn from their research of nearly 500 classroom lessons. The Mathematical Tasks Framework, developed by the authors and explained thoroughly in the book, offers teachers and teacher educators the means to evaluate instructional decisions, the choice of materials, and learning outcomes, and the case studies afford readers the opportunity to ground these ideas in actual classroom practice. Readers will gain insight about how to foster a challenging, cognitively rich, and exciting classroom climate that propels students toward a richer understanding of mathematics. “If every teacher and teacher educator took the opportunity to study and discuss these cases, students everywhere would know and value mathematics as the national standards have envisioned.” —Susan Loucks-Horsley, Director of Professional Development for the National Institute for Science Education “The power of case discussions can be fully realized using this book as a tool. Equally important, teachers will be highly motivated because they see their own practice mirrored in the cases.” —Carne Barnett, WestEd, San Francisco, CA

ECERS-E is designed to be used with the Early Childhood Rating Scale-Revised (ECERS-R), an internationally recognized measure of quality in education and care written by Thelma Harms, Richard M. Clifford, and Debby Cryer. It not only complements the ECERS-R but extends the scales to provide additional insights into important aspects of literacy, mathematics, science and environment, as well as practices related to issues of diversity. Given the current focus on emerging literacy and numeracy skills, the ECERS-E provides unique guidance on the kinds of environments that enhance learning in preschool settings. The curriculum domains within the scales bear important relationships to children’s (age 3–5) cognitive and social/behavioral developmental outcomes. Using the ECERS-E alongside the ECERS-R gives users a more complete picture of what a high-quality early childhood education program can look like. It can be used by program directors, teaching staff, agency staff, and in teacher training programs. Convenient organization: Literacy Items: Print in the environment Book and literacy areas Adults reading with children Sounds in words Emergent writing/mark making Talking and listening Mathematics Items: Counting and application of counting Reading and representing simple numbers Activities: Shape Activities: Sorting, matching and comparing Science and Environment Items: Natural materials Areas featuring science/science materials Activities: Non living Activities: Living processes Activities: Food preparation Diversity Items: Planning for individual learning needs Gender equality and awareness Race equality and awareness