Learning Mathematics in Elementary and Middle Schools

by Cathcart, W. George; Pothier, Yvonne M.; Vance, James H.; Bezuk, Nadine S.

• ISBN13: 9780130483430
• ISBN10: 0130483435
• Edition: 3rd
• Format: Paperback
• Copyright: 2003-01-01
• Publisher: Prentice Hall

Summary

For Mathematics Methods in Elementary School courses. This K8 methods text clearly links the teaching theories and techniques it proscribes to the most current NCTM Principles and Standards for School Mathematics. Based on the premise that mathematics teaching should be child-centered and constructivist, this text explains what children's math thinking might be developmentally and then models typical problems for concept building. Beginning with the problem solving chapter and followed up in subsequent content chapters, this edition provides over 200 activities that can serve future teachers as classroom resources.

Table of Contents

1. Teaching Mathematics: Influences and Directions.
2. Learning and Teaching Mathematics.
3. Developing Mathematical Thinking and Problem-Solving Ability.
4. Assessing Mathematics Understanding.
5. Developing Number Concepts.
6. Developing Understanding of Numeration.
7. Developing Whole-Number Operations: Meaning of Operations.
8. Developing Whole-Number Operations: Mastering the Basic Facts.
9. Estimation and Computational Procedures for Whole Numbers.
10. Developing Fraction Concepts.
11. Developing Fraction Computation.
12. Developing Decimal Concepts and Computation.
13. Understanding Ratio, Proportion, and Percent.
14. Developing Geometric Thinking and Spatial Sense.
15. Developing Measurement Concepts and Skills.
16. Collecting, Organizing, and Interpreting Data.
17. Developing Integers and Algebraic Thinking.
Appendix: Blackline Masters.
References.
Index.

Excerpts

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 thePrinciples and Standards for School Mathematics,published by the National Council of Teachers of Mathematics (NCTM) in 2000, which build on NCTM's recommendations for theCurriculum and Evaluation Standards for School Mathematics(1989), theProfessional Standards for Teaching Mathematics(1991), and theAssessment 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 hel