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

by Tucker, Benny F.; Singleton, Ann H; Weaver, Terry L

• ISBN13: 9780130270214
• ISBN10: 0130270210
• Edition: 1st
• Format: Paperback
• Copyright: 2002-01-01
• Publisher: Prentice Hall

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