Based on more than twenty years of research, this book portrays the development of children's understanding of basic number concepts. The authors offer a detailed explanation and numerous examples of the problem-solving and computational processes that virtually all children use as their numerical thinking develops. They also describe how classrooms can be organized to foster that development. Two accompanying CDs provide a remarkable inside look at students and teachers in real classrooms

Children's Mathematics: Cognitively Guided Instruction

Health, Fitness & Dieting

Empson, Susan B.

Carpenter, Thomas P.

Psychology & Counseling

Heinemann

Contained in this Guide is suggestions for implementing a Professional Development Program, a selected annotated bibliography, and a selection of resources such as sample workshop agendas and worksheets.

Childrens Mathematics/A Guide for Workshop Leaders: A Guide for Workshop Leaders

Fennema, Elizabeth

Franke, Megan Loef

Levi, Linda

Lindquist, Mary L.

Children's Books

By the time they begin school, most children have already developed a sophisticated, informal understanding of basic mathematical concepts and problem-solving strategies. Too often, however, the mathematics instruction that we impose upon them in the classroom fails to connect with this informal knowledge. Children's Mathematics was written to help you understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding. Based on more than twenty years of research, this book portrays the development of children's understanding of basic number concepts. The authors offer a detailed explanation and numerous examples of the problem-solving and computational processes that virtually all children use as their numerical thinking develops. They also describe how classrooms can be organized to foster that development. Two accompanying CDs provide a remarkable inside look at students and teachers in real classrooms implementing the teaching and learning strategies described in the text. Together, the book and CDs provide you with the foundation necessary to engage children in discussions of how they think through problems-providing suggestions for what problems to give and insight into what responses to expect, and how children's thinking will evolve.\

Children's Mathematics: A Workshop Leader's Kit

Education & Teaching

Schools & Teaching

"With the collaboration of a number of dedicated teachers and their students, Susan Empson and Linda Levi have produced a volume that is faithful to the basic principles of CGI while at the same time covering new ground with insight and innovation." -Thomas P. Carpenter This highly anticipated follow-up volume to the landmark Children's Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts. Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning. They show how the same kinds of intuitive knowledge and sense making that provides the basis for children's learning of whole number arithmetic can be extended to fractions and decimals. Just as they did in Children's Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children's thinking and alternative approaches to solving problems. Three themes appear throughout the book: <ul>
<li>building meaning for fractions and decimals through discussing and solving word problems</li> <li>the progression of children's strategies for solving fraction word problems and equations from direct modeling through relational thinking</li> <li>designing instruction that capitalizes on students' relational thinking strategies to integrate algebra into teaching and learning fractions.</li> </ul>
With illuminating examples of student work, classroom vignettes, "Teacher Commentaries" from the field, sample problems and instructional guides provided in each chapter, you'll have all the tools you need to teach fractions and decimals with understanding and confidence.

Extending Children's Mathematics: Fractions & Decimals: Innovations In Cognitively Guided Instruction

Explore the new edition-including video clips, a sample chapter, and related blogs-at Heinemann.com/ChildrensMath The bestselling first edition of Children's Mathematics helped hundreds of thousands of teachers understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding. The highly anticipated Second Edition provides new insights about Cognitively Guided Instruction based on the authors' research and experience in CGI classrooms over the last 15 years. Highlights include: <ul>
<li> how children solve problems using their intuitive understanding of addition, subtraction, multiplication, and division </li> <li> the development of children's mathematical thinking throughout the primary grades </li> <li> instructional practices that promote children's active engagement in mathematics </li> <li> connections between children's strategies and powerful mathematical concepts </li> </ul>
A new expanded collection of over 90 online video episodes illustrating children's mathematical thinking, interactions between students and teachers, and classroom instruction that builds on children's mathematical thinking. Together, the Second Edition and videos provide a detailed research-based account of the development of children's mathematical thinking and problem solving, and how teachers can promote this development in ways that honor children's thinking. Save money when you buy all three books in the Cognitively Guided Instruction series together: Children's Mathematics, Extending Children's Mathematics, and Thinking Mathematically

Children's Mathematics, Second Edition: Cognitively Guided Instruction

Reference

"Young children are naturally curious and observant, and enter school ready to connect their rich informal understandings about the world around them to their experiences in classrooms." -Thomas Carpenter, Megan Franke, Nicholas Johnson, Angela Chan Turrou, and Anita Wager Cognitively Guided Instruction (CGI) has helped hundreds of thousands of teachers better understand how their students think mathematically. Young Children's Mathematics, the newest addition to the CGI family of books, explores the development of mathematical understanding in the youngest learners. Young children's everyday lives are full of mathematically-related conversation and play-and they enter school ready to make connections with these informal experiences. This book helps teachers recognize opportunities for making these connections by examining: <ul>
<li>how children apply their emerging counting skills to problem solving situations</li> <li>how teachers effectively engage with young learners to support their mathematical development</li> <li>How noticing the details of what children can do helps us to build on their partial understandings</li> <li>ways to bridge children's mathematical worlds at home and school</li> </ul> Reinforced with classroom video clips, Young Children's Mathematics provides an in-depth, research-based look at how children's early learning develops and how teachers can authentically promote this kind of sense-making in mathematics.

Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education

Johnson, Nicholas C.

Turrou, Angela C.

Wager, Anita A

In Children's Mathematics: Cognitively Guided Instruction, Thomas Carpenter, Megan Franke, and Linda Levi helped hundreds of thousands of teachers understand children's intuitive problem-solving and computational processes and how to use that knowledge to enhance students' understanding of arithmetic. In Thinking Mathematically, the same author team shows how Operations and Algebraic Thinking can be viewed as a unified field by understanding how children's intuitive strategies naturally draw upon the properties of operations and other algebraic concepts. This book shows how teachers can recognize and support children's use of the properties of operations and other algebraic concepts in a manner that deepens students' understanding of arithmetic and provides a solid foundation for learning algebra. This book also shows how teachers can increase their own knowledge of mathematics in the process of interacting with their children and reflecting about their practice. Thinking Mathematically provides numerous examples of classroom dialogues that indicate how properties of operations and other algebraic ideas emerge in children's thinking and what problems and questions help to elicit them. Special features of the book help teachers develop their own understanding of mathematics along with their students': Teacher Commentaries capture the voices of a number of teachers, providing realistic portrayals of what happens in class. End-of-chapter Challenges offer a variety of problems and activities for teachers to increase their own knowledge of mathematics and to help their students develop algebraic thinking. Additional Online Resources provide rich illustrations of ideas in the book, including extended interactions with individual children or classroom episodes-all clearly linked to the text.

Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School

Science & Math

Mathematics

The key to effective math learning lies not in the regurgitation of isolated facts but in the ablility to reason with and use what is learned - in understanding the concepts. But what does it mean to design a classroom so that understanding is the primary objective? What would a system of instruction look like if we took seriously the goal of helping all students understand mathematics? In this ground-breaking book, James Hiebert and his colleagues arm teachers with the best current research-based ideas for designing - and defending - classrooms that support students' mathematical understanding. It is based on the authors' work in four separate research programs, all of which investigated the effects of specific instructional approaches. Out of their ongoing discussions emerged a striking consensus about what features are essential and what features are optional, which they share in this book. They also provide glimpses into their individual projects and into the classrooms from which they have drawn many of their ideas. By describing the essential features of classrooms that support students' mathematical understanding and by offering pictures of several classrooms that exhibit these features, Making Sense provides a valuable framework within which elementary teachers can reflect on their own practice and think again about what it means to teach for understanding.

Making Sense: Teaching and Learning Mathematics with Understanding

Fuson, Karen

Hiebert, James

Murray, Hanlie

Wearne, Diane

Education & Reference

During the last decade there were significant advances in the study of students’ learning and problem solving in mathematics, and in the study of classroom instruction. Because these two research programs usually have been conducted individually, it is generally agreed now that there is an increasing need for an integrated research program. This book represents initial discussions and development of a unified paradigm for studying teaching in mathematics that builds upon both cognitive as well as instructional research.

Integrating Research on Teaching and Learning Mathematics: Reform in Mathematics Education (S U N Y SERIES, REFORM IN MATHEMATICS EDUCATION)

Lamon, Susan J.

State Univ of New York Pr

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