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Teaching Mathematics to All Children : Designing and Adapting Instruction to Meet the Needs of Diverse Learners,9780130270214

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

by ; ;
Edition:
1st
ISBN13:

9780130270214

ISBN10:
0130270210
Format:
Paperback
Pub. Date:
1/1/2002
Publisher(s):
Prentice Hall
List Price: $72.00

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Summary

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. NCTM's Curriculum and Evaluation Standards for School Mathematics are integrated into every chapter. Other topics include: Diversity in the Classroom; Lesson Design: Creating Lessons That Meet the Needs of a Diverse Classroom; Mathematics Learning in Early Childhood; Whole Numbers and Numeration; Fractions; Decimals and Percents; Measurement; and Geometry.

Table of Contents

Instructional Activities: The Building Blocks for Effective Instruction
3(14)
Basics for the Effective Use of Activities, the Building Blocks for Construction of Effective Lesson
3(6)
What Are the Students Learning?
3(1)
Developmental Activities
4(1)
Practice Activities
5(1)
Application Activities
5(1)
Assessment Activities
6(2)
Level of Involvement
8(1)
Flexibility
9(4)
Webs of Activities
9(2)
Content Flexibility Webs
11(1)
Procedure Flexibility Webs
12(1)
Exercises and Activities
13(1)
References and Related Readings
14(1)
Web Sites
15(2)
Diversity in the Classroom: Variations of Individual Needs
17(16)
Why Diverse Classrooms?
17(2)
Racial, Linguistic, and Cultural Diversity
19(1)
Learning Style Preferences
20(2)
Kinds of Intelligence
22(1)
Low Cognitive Ability
23(2)
Learning Disabilities
25(1)
Visual or Auditory Impairments
25(1)
Physical Impairments
26(1)
Summary
26(1)
Exercises and Activities
26(4)
References and Related Readings
30(1)
Web Sites
31(2)
Lesson Design: Creating Lessons That Meet the Needs of a Diverse Classroom
33(16)
Combining Activities into a Lesson
34(2)
What is a Lesson?
34(1)
A Traditional Lesson Plan
35(1)
The Nature of Standard Traditional Lessons
36(1)
Adapting Lessons for Diverse Learning Needs
36(10)
A Lesson Adapted for Diverse Learners
39(4)
Adapting Another Lesson
43(3)
Exercises and Activities
46(1)
References and Related Readings
47(1)
Web Sites
47(2)
Beginnings: Mathematics Learning in Early Childhood
49(20)
A Common Misconception
50(1)
About Young Children
50(1)
Teaching Classification
51(2)
Teaching Comparison and Seriation
53(6)
Comparison
53(3)
Seriation
56(2)
Matching and Prenumber Comparisons
58(1)
Matching and Prenumber Seriation
58(1)
The Beginning of Geometric Concepts: Relative Position
59(4)
A Revised Lesson
63(2)
Exercises and Activities
65(1)
References and Related Readings
66(1)
Web Sites
67(2)
Whole Numbers and Numeration: Naming and Writing Quantity
69(26)
Building on What Children Already Know
70(2)
The Big Picture
72(1)
Development of Numbers and Numeration
72(1)
One-Digit Numbers
73(5)
Two-Digit Numbers
78(6)
Three or More Digits
84(3)
Rounding Numbers
87(2)
Adapting a Lesson
89(4)
Adapting the Lesson for a Diverse Group of Students
90(3)
Exercises and Activities
93(1)
References and Related Readings
94(1)
Web Sites
94(1)
Adding and Subtracting Whole Numbers: Combining and Separating Quantities
95(44)
Teaching Addition of Whole Numbers
96(22)
An Overview of the Development of Computation
96(1)
Developmental Sequence for the Addition of Whole Numbers
97(3)
Developing the Easy Basic Addition Facts
100(6)
Memorization of the Easy Basic Addition Facts
106(2)
Thinking Strategies for Hard Basic Addition Facts
108(3)
Teaching the Hard Basic Addition Facts
111(2)
Teaching the Addition Algorithm
113(5)
Summary of the Development Sequence for Addition
118(1)
Teaching Substration
118(11)
Developing the Meaning of Substraction
118(2)
Developing the Easy Basic Subtraction Facts
120(5)
Thinking Strategies for Hard Basic Substraction Facts
125(2)
Teaching the Subtraction Algorithm
127(1)
Summary of the Developmental Sequence for Subtraction
128(1)
Adapting a Lesson
129(2)
Teaching Problem Solving Using Addition and Substraction
131(3)
Exercises and Activities
134(3)
References and Related Readings
137(1)
Web Sites
137(2)
Multiplying and Dividing Whole Numbers: Combining Equal-Sized Groups and Separating Quantities into Equal-Sized Groups
139(60)
Teaching Multiplication of Whole Numbers
140(32)
Developmental Sequence for Teaching Multiplication
140(1)
Developing the Meaning of Multiplication
140(4)
Teaching the Easy Basic Multiplication Facts
144(5)
Thinking Strategies for Hard Basic Multiplication Facts
149(5)
Teaching the Multiplication Algorithm
154(12)
Summary of Developmental Sequence for Multiplication
166(1)
Adapting a Multiplication Lesson
167(5)
Teaching Division of Whole Numbers
172(23)
Developmental Sequence for Teaching Division
172(20)
Adapting a Division Lesson
192(3)
Using Multiplication and Division to Solve Problems
195(1)
Exercises and Activities
195(2)
References and Related Readings
197(1)
Web Sites
197(2)
Fractions: Working with Units Smaller Than One
199(46)
Defining Fractions
200(1)
Three Sides of Fractions
200(1)
Fractional Units
201(2)
Beyond Unit Fractions
203(2)
Fractions of a Set
205(1)
Equivalent Fractions
206(2)
Using the Laboratory Approach
208(3)
Comparison of Fractions
211(3)
Adding Fractions
214(2)
Subtracting Fractions
216(1)
Least Common Denominators
216(5)
Improper Fractions and Mixed Numbers
221(2)
Multiplying Fractions
223(4)
Dividing Fractions
227(8)
Adapting a Lesson on Fractions
235(3)
Solving Problems Using Fractions
238(3)
Problem-Solving Strategies
239(2)
Exercises and Activities
241(1)
References and Related Readings
242(1)
Web Sites
243(2)
Decimals and Percents: Working with Base-Ten Units Smaller Than One and Using Hundredths as a Common Denominator
245(36)
Defining Decimals
246(1)
Place Value for Decimals
247(6)
Comparison of Decimals
253(3)
Addition and Substraction of Decimals
256(3)
Multiplying Decimals
259(5)
Division of Decimals
264(7)
Fraction Comparison Revisited
271(1)
Defining Percent
272(1)
Adapting a Lesson on Decimals
272(4)
Using Decimals to Solve Problems
276(2)
Exercises and Activities
278(1)
References and Related Readings
279(1)
Web Sites
279(2)
Measurement: Assigning a Number to a Quantity
281(46)
Measurement and Geometry
281(1)
Defining Measurement
281(1)
Measuring Length
281(14)
Teaching Area Measurement
295(9)
The Big Idea for Developing Area Formulas
299(5)
Teaching Volume Measurement
304(9)
Measuring Angles
313(3)
Measuring with Indirect Units
316(1)
Measuring Time
317(1)
Measuring Weight
318(1)
Measuring Temperature
319(1)
Measuring Value
319(1)
Adapting a Lesson on Volume
319(3)
Using Measurement to Solve Problems
322(2)
Exercises and Activities
324(2)
References and Related Readings
326(1)
Web Sites
326(1)
Geometry: Learning the Names and Characteristics of Shapes
327(30)
The Big Ideas of Elementary School Geometry
328(4)
Straightness
328(1)
Congruence
328(1)
Similarity
329(2)
Parallelism
331(1)
Perpendicularity
332(1)
Symmetry
332(1)
Using the Big Ideas to Study Geometric Shapes
332(16)
Rectangles in Elementary School
333(7)
Circles in Elementary School
340(3)
Angles in Elementary School
343(3)
Prisms in Elementary School
346(2)
Adapting a Geometry Lesson
348(5)
Using Geometry to Solve Problems
353(2)
Exercises and Activities
355(1)
References and Related Readings
356(1)
Web Sites
356(1)
Effective Practice: Games and Activities for Practice and Fun
357(22)
Matching Activities
358(10)
Ordering Activities
368(5)
Answer/Example Construction Activities
373(5)
Summary
378(1)
References and Related Readings
378(1)
Index 379

Excerpts

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 toteach 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 thatall childrenshould 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 dire


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