Teaching Mathematics to All Children: Designing and Adapting Instruction to Meet the Needs of Diverse Learners / Edition 1

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Overview

With the composition of today's classroom in mind, this book approaches teaching and planning elementary mathematics by using methods that accommodate the diverse learning needs of any student having difficulties with basic math concepts. The authors use personal experience and research that supports a complete set of developmental concepts and skills to outline the effective development of mathematical concepts and skills. It stresses lesson planning that will result in learning, understanding, and retaining important concepts and skills.  K-12 Special Education and General Education Teachers.

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Product Details

  • ISBN-13: 9780130270214
  • Publisher: Prentice Hall
  • Publication date: 5/28/2001
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 385
  • Product dimensions: 8.34 (w) x 10.74 (h) x 0.78 (d)

Table of Contents

1 Instructional activities : the building blocks for effective instruction 1
2 Diversity in the classroom : variations of individual needs 11
3 Lesson design : creating lessons that meet the needs of a diverse classroom 29
4 Beginnings : mathematics learning in early childhood 45
5 Whole numbers and numeration : naming and writing quantity 65
6 Adding and subtracting whole numbers : combining and separating quantities 91
7 Multiplying and dividing whole numbers : combining equal-sized groups and separating quantities into equal-sized groups 135
8 Fractions : working with units smaller than one 195
9 Decimals and percents : working with base-ten units smaller than one and using hundredths as a common denominator 241
10 Measurement : assigning a number to a quantity 277
11 Geometry : learning the names and characteristics of shapes 321
12 Data analysis and probability : getting information from data and measuring likelihood 351
13 Effective practice : games and activities for practice and fun 385
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Preface

Why This Book?

Recently, elementary classrooms have become increasingly diverse. This diversity includes differences in gender, race and ethnicity, religion, culture, ability and interest, learning styles, family background and support, and availability of resources such as books and technology. Furthermore, there is a current trend toward inclusion of special needs children in the regular classroom, a trend unlikely to be reversed in the foreseeable future. Typical preparation of special education teachers and regular classroom teachers does not equip either group to operate effectively in the kind of inclusion settings that they are now likely to see. In this text, we provide an approach to the planning and teaching of elementary school mathematics that will better equip teachers to be successful with diverse groups of students and in inclusion classrooms. We hope the teaching suggestions in this text will help teachers be more effective as they attempt to teach mathematics to all children.

Structure of the Book

The text begins with three introductory chapters that provide a basic understanding of instructional activities, diversity, and lesson planning. Then there are eight chapters devoted to teaching the content that most commonly appears in elementary school mathematics textbooks. The final chapter is devoted to practice activities that can be adapted to a wide variety of content.

We have not attempted to provide comprehensive coverage of every mathematics topic that might appear in an elementary school mathematics textbook. Rather, our intent has been to emphasize a way of teaching effectively that will result in learning, understanding,retention of important concepts and skills, and ability to apply those concepts and skills to solve problems. An important part of that way of teaching is effective planning. Therefore, we have made planning for effective teaching an important part of this text.

Emphasis on Concept and Skill Development

Based on findings of educational research that support more complete development of concepts and skills, calls from the National Council of Teachers of Mathematics for more effective development in lessons, and our personal experiences, we have chosen to make more effective development of mathematical concepts and skills a major emphasis. As a result of that emphasis, virtually all activities suggested in the chapters related to specific mathematics content are developmental activities. Since we made a conscious choice not to include practice activities in those chapters, the final chapter is devoted to effective practice. In that chapter, we present a selection of practice activities that can be used after the concepts and skills have been taught.

Basic Philosophy

We believe that successful teaching results in understanding, that understanding provides the most sound basis for skill development, and that understanding results in better retention of what is learned. We believe that the best way to help students understand mathematical ideas is to lead them to connect those ideas to other ideas that they already understand. We believe that, for elementary children, understanding of mathematical concepts and skills depends on the development of appropriate mental imagery for those concepts and skills. And, we believe that all children should be given the opportunity to develop that kind of understanding of mathematics.

Acknowledgments

This book evolved over several years from informal conversations with many colleagues about how teachers could plan to teach more effectively, from preservice and inservice teachers who responded to our ideas before they were fully formed, and from reactions of children who demonstrated that the more fully evolved teaching methods really worked. And, of course, invaluable assistance was provided by these professionals, whose reviews of the preliminary manuscript helped to direct the text into its final form: Bruce F. Godsave, SUNY Genesco; Dennis Munk, Northern Illinois University; Ann L. Lee, Bloomsburg University of PA; Thomasenia Lott Adams, University of Florida; and Dorothy Spethman, Dakota State University.

Benny F. Tucker
Ann H. Singleton
Terry L. Weaver

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Introduction

Why This Book?

Recently, elementary classrooms have become increasingly diverse. This diversity includes differences in gender, race and ethnicity, religion, culture, ability and interest, learning styles, family background and support, and availability of resources such as books and technology. Furthermore, there is a current trend toward inclusion of special needs children in the regular classroom, a trend unlikely to be reversed in the foreseeable future. Typical preparation of special education teachers and regular classroom teachers does not equip either group to operate effectively in the kind of inclusion settings that they are now likely to see. In this text, we provide an approach to the planning and teaching of elementary school mathematics that will better equip teachers to be successful with diverse groups of students and in inclusion classrooms. We hope the teaching suggestions in this text will help teachers be more effective as they attempt to teach mathematics to all children.

Structure of the Book

The text begins with three introductory chapters that provide a basic understanding of instructional activities, diversity, and lesson planning. Then there are eight chapters devoted to teaching the content that most commonly appears in elementary school mathematics textbooks. The final chapter is devoted to practice activities that can be adapted to a wide variety of content.

We have not attempted to provide comprehensive coverage of every mathematics topic that might appear in an elementary school mathematics textbook. Rather, our intent has been to emphasize a way of teaching effectively that will result in learning,understanding, retention of important concepts and skills, and ability to apply those concepts and skills to solve problems. An important part of that way of teaching is effective planning. Therefore, we have made planning for effective teaching an important part of this text.

Emphasis on Concept and Skill Development

Based on findings of educational research that support more complete development of concepts and skills, calls from the National Council of Teachers of Mathematics for more effective development in lessons, and our personal experiences, we have chosen to make more effective development of mathematical concepts and skills a major emphasis. As a result of that emphasis, virtually all activities suggested in the chapters related to specific mathematics content are developmental activities. Since we made a conscious choice not to include practice activities in those chapters, the final chapter is devoted to effective practice. In that chapter, we present a selection of practice activities that can be used after the concepts and skills have been taught.

Basic Philosophy

We believe that successful teaching results in understanding, that understanding provides the most sound basis for skill development, and that understanding results in better retention of what is learned. We believe that the best way to help students understand mathematical ideas is to lead them to connect those ideas to other ideas that they already understand. We believe that, for elementary children, understanding of mathematical concepts and skills depends on the development of appropriate mental imagery for those concepts and skills. And, we believe that all children should be given the opportunity to develop that kind of understanding of mathematics.

Acknowledgments

This book evolved over several years from informal conversations with many colleagues about how teachers could plan to teach more effectively, from preservice and inservice teachers who responded to our ideas before they were fully formed, and from reactions of children who demonstrated that the more fully evolved teaching methods really worked. And, of course, invaluable assistance was provided by these professionals, whose reviews of the preliminary manuscript helped to direct the text into its final form: Bruce F. Godsave, SUNY Genesco; Dennis Munk, Northern Illinois University; Ann L. Lee, Bloomsburg University of PA; Thomasenia Lott Adams, University of Florida; and Dorothy Spethman, Dakota State University.

Benny F. Tucker
Ann H. Singleton
Terry L. Weaver

Read More Show Less

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