Learning Mathematics in Elementary and Middle Schools (3rd Edition) - Softcover

How can you create a learning environment that supports and encourages children to build understandings, make connections, reason, and solve problems?

This textbook helps prospective teachers learn how to teach mathematics in a way that is child-centered and focused on developing mathematics concepts aligned with the NCTM Principles and Standards for School Mathematics. Videos that highlight exemplary math teaching, selected from the Annenberg/CPB Teaching Math Series, are free to adopting professors. Key text features identify how the math teachers captured on video weave the teaching of the math process standards—problem solving, representation, communication, reasoning and proof, and connections—into their math lessons.

Features of the third edition include:

• Principles and Standards Links help readers connect the NCTM Principles and Standards for School Mathematics with chapter topics.
• NEW! Additions to chapters 14 and 17 more meaningfully address middle school mathematics concepts.
• Classroom Clips, full-color features integrating the video package, highlight outstanding teachers engaged with children in math classrooms. A NEW video chosen especially for preservice middle school teachers presents an exemplary model for teaching math to adolescents.
• NEW! Technology Links in each chapter look at meaningful website activities for use in the college classroom as well as in elementary and middle school classrooms. Links to each highlighted site can be made directly from our Companion Website at www.prenhall.com/cathcart
• Literature Links throughout chapters connect topics presented in the text to children's books. The Literature Links also include ideas for extension activities readers can use with children to enhance children's understanding of the topic.

This book is about learning mathematics—about children learning mathematics. It is also about teachers creating a learning environment that supports and encourages children to build understandings, make connections, reason, and solve problems.

About the Audience

Preservice teachers will develop an understanding of the content of school mathematics programs and formulate a teaching methodology for the meaningful learning of mathematics. Inservice teachers who wish to explore current thinking about mathematics teaching and learning will find the book a valuable source of theoretical and practical ideas for involving children in meaningful problem-solving tasks and for having children reflect, talk, and write about mathematics.

Teachers will be challenged to reflect on their personal views of mathematics, on how children learn mathematics, and on classroom environments that help children understand mathematics. The more the reader becomes actively involved with the activities, problems, video, and children's literature features in this book, the greater the quality of the reflection will be and, ultimately, the more the reader will learn.

About Our Approach to Mathematics Learning

The vision of mathematics learning presented in this text places the child at the center. Supporting this vision are the following beliefs:

• Children construct for themselves the mathematics they come to know. Therefore, the approach to mathematics learning is an active one, wherein children engage in problem-solving activities that are discovery oriented or open-ended. Chapter 3 describes the importance of teaching problem solving to children, including the problem-solving the strategies. Subsequent chapters reinforce the role that problem solving plays in teaching children to reason and to make mathematical connections.
• Communication is an important part of the learning process. Questions embedded in this text's activities are posed to encourage students to reflect on what they are doing in order to clarify ideas for themselves and to share their thoughts with classmates. Also, students are invited to record their work or findings through various modes such as drawings, diagrams, descriptions, and symbols.
• An active, child-centered approach requires the use of manipulative materials and technology. Within each chapter, appropriate manipulative materials and technology are identified and numerous activities that incorporate their use are described. Look for the calculator logo that identifies math concepts and strategies that allow for appropriate use of calculators.
• The teacher's role is to provide children with opportunities to explore mathematics and help them observe and describe patterns and make generalizations about the mathematics topics and relationships they are exploring. To support teacher development, chapter topics link classroom practice and the NCTM Principles and Standards for 2000, connecting real-world problems, concrete models, language, symbols, and hands-on activities.

We believe the ideas presented in this text support and exemplify the vision of learning and teaching mathematics as encouraged by the Principles and Standards for School Mathematics, published by the National Council of Teachers of Mathematics (NCTM) in 2000, which build on NCTM's recommendations for the Curriculum and Evaluation Standards for School Mathematics (1989), the Professional Standards for Teaching Mathematics (1991), and the Assessment Standards for School Mathematics (1995). These documents recommend teaching mathematics from a problem-solving perspective and making communication, reasoning and proof, connections, and representations the primary foci of mathematics learning. These recommendations are highlighted throughout the text in the Principles and Standards Link features, as well as the Classroom Clips, which help readers connect the recommendations of the new standards to Annenberg video segments and the topics in each chapter.

About the Revision

Besides updating all materials with new research, streamlining prose and activities alike, in this edition we have looked closely at the changing needs of middle-school mathematics teachers. You'll find strengthened treatment of middle-school issues, particularly in chapter 14, "Developing Geometric Thinking and Spatial Sense," and chapter 17, "Developing Integers and Algebraic Thinking." We have also chosen a new video, "Polygons and Angles: Discovery," which emphasizes excellent teaching and learning in middle-school classrooms. This video is contextualized throughout chapters in new Video Link features, as well as an entirely new Classroom Clip feature, which integrates video footage, chapter content, and NCTM's Process Standards.

In keeping with our constant effort to integrate appropriate technology into the text and classroom, we have added a new feature to this edition. Technology Links, found in every chapter, highlight and explore specific mathematics-related Internet sites that can be used in the college classroom as well as in elementary and middle-school classrooms.

About the Text Features

We have updated and strengthened the many unique text features aimed at helping readers learn how to teach children mathematics. Readers are encouraged to use all of these features to maximize their own learning.

• Key Concepts, at the beginning of each chapter, list the most important topics included in the chapter and serve as an advance organizer for the reader.
• Focus Questions, at the beginning of each chapter, include questions based on the key concepts to help focus the reader's attention while studying each chapter. Link to our Companion Web site at www.prenhall.com/cathcart to discuss these questions with a global audience by means of our threaded message board.
• Principles and Standards Links, throughout each chapter, connect the content of each chapter with the NCTM Curriculum and Evaluation Standards for 2000, the Professional Standards for Teaching Mathematics, and the Assessment Standards.
• Technology Links, new in each chapter, look at meaningful website activities for use in the college classroom as well as in elementary and middle-school classrooms. Link to each high-lighted site directly from our Companion Website at www.prenhall.com/cathcart.
• Video Links throughout chapters connect topics presented in the textbook to videos of outstanding teachers in their own classrooms, including a new video, "Polygons and Angles: Discovery," emphasizing the middle-school mathematics classroom. This feature includes reflection questions to strengthen readers' understanding of each topic and its link to practice.
• Classroom Clips are full-color features that highlight outstanding video segments focused on exemplary teachers engaged with children in math classrooms, including a new Classroom Clip highlighting the new middle-school video. Each of these Classroom Clips provides readers with an opportunity to closely consider lessons designed to develop children's understanding of mathematics topics and to consider how each lesson exemplifies the recommendations of the NCTM Process Standards. In addition, these video inserts include ideas for extensions and connections for each math lesson.
• Literature Links throughout chapters connect topics presented in the text to children's books. The Literature Links also include ideas for extension activities that readers can use with children to enhance their understanding of the topic.
• Activities, prolific throughout each chapter, provide practical applications related to chapter topics. These activities are appropriate for the college classroom as well as the elementary and middle-school classrooms.
• For Your Journal, at the end of each chapter, asks readers to respond to specific questions in a math journal to strengthen and help them to reflect on their understanding of chapter topics. Instructors may choose to require students to respond to one or more of these questions as part of a course assignment. Use these questions to create an online journal by linking to the Online Journal module of our Companion Website at www.prenhall.com/cathcart.
• For Your Portfolio, at the end of each chapter, describes activities or assignments that readers may complete to help them connect the chapter's key concepts to classroom practice. Instructors may choose to include one or more of these items as course assignments. Compile these pieces for a mathematics teaching portfolio online by clicking on the Online Portfolio module of our Companion Website at www.prenhall.com/cathcart.
• Links to the Internet, located at the end of each chapter, lead readers to helpful Internet destinations where they can find valuable resources to assist their development of teaching strategies. Link to all highlighted websites directly from our Companion Website at www.prenhall.com/cathcart.
• Blackline Masters, which can be found in the Appendix, are formatted so they may be copied and used as manipulatives. Readers can handle them to help develop their own understandings of mathematical concepts and then copy them for children in their K-8 classrooms.

About Text Supplements

A Companion Website is available for professors and students who adopt this text. It can be accessed via the Internet at www.prenhall.com/cathcart. This truly text-integrated Companion Website is designed to guide readers in their study of the text content and includes access to self-assessments ...