Learning Mathematics in Elementary and Middle School (2nd Edition) - Softcover

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

This book is for preservice and inservice elementary and middle school mathematics teachers. 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, and Video Links features in this book, the greater the quality of that reflection will be and, ultimately, the greater his or her learning will be. About the 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, where children engage in problem-solving activities that are discovery-oriented or open-ended. Chapter 3 in this text describes for readers the importance of teaching problem solving to children, including the problem-solving process and problem-solving 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. Readers will find questions embedded in activities included in the text that are posed to encourage children to reflect on what they are doing in order to clarify ideas for themselves and to share their thoughts with classmates. Also, frequent invitations are offered for children to record their work or findings through various modes such as drawings, diagrams, descriptions, and symbols. NEW! 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. NEW! 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 new 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 built on NCTM's recommendations of 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, which help readers connect the recommendations of the new standards to the topics in each chapter. About the Text Features

This book has several unique 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 to 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. 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. The Principles and Standards Link feature helps the reader understand the importance of chapter content. Video Links, throughout each chapter, connect topics presented in the textbook to videos of outstanding teachers teaching the same topics to children in classrooms. The Video Links feature also includes questions on which readers are asked to reflect, to strengthen their understanding of the topic and its link to practice. NEW! Classroom Clips are four-color inserts that highlight outstanding video segments focused on exemplary teachers engaged with children in math classrooms. 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. NEW! Literature Links, throughout each chapter, connect topics presented in the text of this book to children's books. The Literature Links feature also includes ideas for extension activities readers can use with children to enhance children's 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 children to respond to one or more of these questions as part of a course assignment. 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. Links to the Internet, located at the end of each chapter, lead readers to helpful Web destinations, where they can find valuable resources to assist their development of teaching strategies. Blackline Masters, which can be found at the end of the text, 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 prenhall/cathcart. The Companion Website is designed to guide readers in their study of the text content and includes access to self-assessment quizzes and resources that allow users to link directly to Web destinations identified in Links to the Internet. Students who use the self-quizzes will get immediate feedback and clues for finding correct answers as appropriate. Test results can be e-mailed to course instructors. With the Companion Website, students will also have an opportunity to engage in interactive peer discussions to answer the beginning-of-the-chapter Focus Questions using the threaded Message Board. In addition, professors who complete the Syllabus Manager feature of the Companion Website can make the course syllabus, course assignments, and due dates available to students online.

An instructor's manual for course instructors includes chapter objectives, strategies for developing major concepts presented in each chapter, transparency masters, and additional projects and discussion questions. The manual is free to adopters of this textbook.

Five videos, free to adopting professors, accompany this text. These videos are part of the Annenberg/CPB Math and Science Collection and include the following titles:

—Communication: Teaching Math: A Video Library, K-l; Tape 21
—Whole Number Computation: Teaching Math: A Video Library, K-l; Tape 7
—Concepts of Whole Number Operations: Teaching Math: A Video Library, K-4; Tape 4
—Geometry and Spatial Sense: Teaching Math: A Video Library, K-l; Tape 8
—Fraction Tracks: Teaching Math: A Video Library, 5-8; Tape 1 Acknowledgments

We appreciate the thoughtful comments and suggestions made by the reviewers: Anna O. Graeber, University of Maryland; Anne Madsen, University of New Mexico; and Ann S. Massey, Indiana University of Pennsylvania. Further, we are grateful for the insights of the reviewers of the Canadian version: Catherine Ebbs, University of Windsor; Douglas Edge, University of Western Ontario; John Grant McLoughlin, Okanagan College; Helen Horsman, University of Saskatchewan; Wilfred L. Innerd, University of Windsor; Werner Liedtke, University of Victoria; Joan McDuff, Queen's University; Howard Riggs, McGill University; Daiyo Sawada, University of Alberta; Thomas Schroeder, State University of New York at Buffalo; Frances M. Butler, Weber State University; Arnold R. Davis, University of Tennessee-Knoxville; Lorel Preston Huhnke, Westminster College; Annette Ricks Leitze, Ball State University; Walter F. Ryan, Indiana University Southeast; Pearl Solomon, St. Thomas Aquinas College; Marilyn E. Strutchens, University of Maryland; and Judith A. Wells, University of Southern Indiana. Their insightful comments became the guidelines used to improve the organization of this text and the applications included.

We would also like to thank Dr. Patricia S. Moyer of George Mason University for her contributions to this edition in developing the children's Literature Links. We are also grateful to Lisa L. Clemente of San Diego State University for her help in developing the section on integrating standards that appears in chapter 1.

In addition, the suggestions and encouragement received from colleagues and students at San Diego State University, numerous teachers in San Diego City Schools, and the children, teachers, and administrators at Rosa Parks Elementary School were invaluable. Thank you, all.

G. Cathcart
Y Pothier
J. Vance
N. Bezuk

FEATURES/BENEFITS

* NEW Principles and Standards Links
Teacher development supported by text features that identify the various grade bands and concepts outlined by the 2000 NCTM Standards document.
* NEW Classroom Clips
These new 4-color video inserts features a video library selected from the Annenberg/CPB Teaching Math Series, which is free to adopters.

* Provides a high-quality window into classrooms, with a special focus on process standards.

* NEW Children's Literature Links

* Provides specific ideas for connecting children's literature with the mathematical concepts discussed in each chapter.

* NEW Icons that Identify Calculator Use

* Indicates strategies and concepts appropriate for calculators to support responsible technology use.

* Emphasis on Problem Solving

* Describes the problem-solving process, problem-solving strategies, sources for involving students in real-world problems, and the teacher's role in guiding students in problem-solving tasks.

* Support of Portfolio and Journal Use

* Chapters end with activities that encourage preservice teachers to record their understandings in math journals and create teaching portfolios.

* A Companion Website
Features self-assessment tests with immediate feedback, weblinks, an interactive Message Board, and real-time chat. Syllabus Manager is available to professors so they can provide the syllabus and assignments online.

* The text is fully supported with technology.