This resource emphasizes using effective mathematics to promote understanding-while encouraging understanding to provide a sound basis for skill development. This resource also focuses on the goal of ensuring better learning retention. In a user-friendly format, presenting language consistent with the language used to teach children, the authors of this resource stress that when mathematical information is connected to what students already know about mathematics, it is easier for them to learn and recall. To that end they present the development of mathematical content based on a small number of easy-to-understand and easy-to-teach "big ideas."
Relevant and useful information related to conceptualizing and practicing specific math skills. Beginning teachers often fall 'victim' to using published materials 'as is' and this book provides repeated examples of how teachers can adjust the materials that are provided to them by district-selected curricula. -Rebecca Swanson Gehrke, Professor, Arizona State University, Tempe, AZ
v > About the authors x Preface xi 1 Instructional Activities: T he Building Blocks for Effective Instruction 1 What Are the Students Learning? 1 Developmental Activities 2 Exploratory Developmental Activities 2 Consolidating Developmental Activities 2 Practice Activities 2 Think-Time Practice Activities 3 Speed-Drill Practice Activities 3 Application Activities 3 Classroom Applications 3 Real-World Problems 4 Assessment Activities 4 Varied Assessment Methods 4 Monitoring and Assessment 4 Level of Involvement 6 Flexible Use of Activities and Materials 7 Exercises and Activities 7 References and Related Readings 8 Websites 9 2 Less on Design: C reating Lessons That Meet the Needs of a Diverse Classroom 10 Combining Activities into a Lesson 10 What Is a Lesson? 10 A Traditional Lesson Plan 11 The Nature of Standard Traditional Lessons 13 Adapting Lessons for Diverse Learning Needs 13 A Lesson Adapted for Diverse Learners 16 Adapting Another Lesson 19 The Planning Process and "Official" Lesson Plans 21 contents A01_TUCK7286_01_SE_FM.indd 5 4/9/12 6:54 PM vi C o n t e n t s The Planning Process and Teaching Notes 22 Exercises and Activities 22 References and Related Readings 23 Websites 24 3 Beginnings: M athematics Learning in Early Childhood 25 A Common Misconception 25 About Young Children 25 Teaching Classification 27 Pattern Recognition 28 Teaching Comparison and Seriation 29 Comparison 29 Seriation 32 Matching and Prenumber Comparisons 33 Matching and Prenumber Seriation 33 The Beginning of Geometric Concepts: Relative Position 34 A Revised Lesson 37 Exercises and Activities 40 References and Related Readings 40 Websites 41 4 Whole Nu mbers and Nu meration: N aming and Writing Quantity 42 Number Sense 42 Foundations of Algebra 43 Building on What Children Already Know 43 The Big Picture 45 Development of Numbers and Numeration 45 One-Digit Numbers 46 Two-Digit Numbers 51 Three or More Digits 56 Rounding Numbers 59 Adapting a Lesson 61 Adapting the Lesson for a Diverse Group of Students 61 Exercises and Activities 64 References and Related Readings 64 Websites 64 5 Adding and Subtracting Whole Nu mbers: C ombining and Separating Quantities 65 An Overview of the Development of Computation 65 The Meaning of the Operation 65 The Basic Facts 66 The Algorithm(s) 66 A01_TUCK7286_01_SE_FM.indd 6 4/9/12 6:54 PM C o n t e n t s vii Teaching Addition of Whole Numbers 67 Developing the Meaning of Addition 67 Developing the Easy Basic Addition Facts 69 Activities for Exploring Relationships 73 Developing the Hard Basic Addition Facts 76 Teaching the Addition Algorithm 82 Summary of the Developmental Sequence for Addition 85 Teaching Subtraction of Whole Numbers 86 Developing the Meaning of Subtraction 86 Developing the Easy Basic Subtraction Facts 87 Developing the Hard Basic Subtraction Facts 90 Teaching the Subtraction Algorithm 92 Summary of the Developmental Sequence for Subtraction 93 Adapting a Lesson 94 Teaching Problem Solving Using Addition and Subtraction 96 Exercises and Activities 99 References and Related Readings 100 Websites 100 6 Mu ltiplying and Dividing Whole Nu mbers: C ombining Equal-Sized Groups and Separating Quantities into Equal-Sized Groups 101 Teaching Multiplication of Whole Numbers 101 Developing the Meaning of Multiplication 101 Developing the Easy Basic Multiplication Facts 103 Developing the Hard Basic Multiplication Facts 107 Teaching the Multiplication Algorithm 111 Summary of the Developmental Sequence for Multiplication 121 Adapting a Multiplication Lesson 121 Teaching Division of Whole Numbers 127 Developing the Meaning of Division 127 Developing the Easy Basic Division Facts 129 Developing the Hard Basic Division Facts 131 Teaching the Division Algorithm 133 Adapting a Division Lesson 144 Teaching Problem Solving Using Multiplication and Division 147 Exercises and Activities 147 References and Related Readings 148 Websites 149 7 Fractions: Working with Units Smaller Than One 150 Defining Fractions 150 Three Sides of Fractions 151 A01_TUCK7286_01_SE_FM.indd 7 4/9/12 6:54 PM viii C o n t e n t s Fractional Units 152 Beyond Unit Fractions 154 Fractions of a Set 155 Equivalent Fractions 156 Using the Laboratory Approach 158 Comparison of Fractions 159 Adding Fractions 161 Subtracting Fractions 163 Addition and Subtraction Activities 163 Improper Fractions and Mixed Numbers 165 Adapting a Lesson on Fractions 167 Solving Problems Using Fractions 170 Exercises and Activities 171 References and Related Readings 171 Websites 171 8 Decimals: Working with Base-Ten Units Smaller Than One 172 Decimals 172 Place Value for Decimals 174 Comparing Decimals 178 Adding and Subtracting Decimals 181 Adapting a Lesson on Decimals 184 Using Decimals to Solve Problems 187 Exercises and Activities 187 References and Related Readings 188 Websites 188 9 Measu rement: A ssigning a Number to a Quantity 189 Measurement and Geometry 189 Defining Measurement 189 Measuring Length 190 Teaching Area Measurement 199 Teaching Volume Measurement 204 Measuring Time 208 Measuring Weight 210 Measuring Temperature 210 Measuring Value 210 Adapting a Lesson on Volume 211 Using Measurement to Solve Problems 214 Exercises and Activities 214 References and Related Readings 215 Websites 215 A01_TUCK7286_01_SE_FM.indd 8 4/9/12 6:54 PM C o n t e n t s ix 10 Geometry: L earning the Names and Characteristics of Shapes 216 The Big Ideas of Elementary School Geometry 216 Straightness 217 Congruence 217 Similarity 218 Parallelism 218 Perpendicularity 219 Symmetry 220 Using the Big Ideas to Study Geometric Shapes 220 Rectangles in Elementary School 220 Circles in Elementary School 225 Angles in Elementary School 228 Prisms in Elementary School 230 Adapting a Geometry Lesson 231 Exercises and Activities 235 References and Related Readings 236 Websites 236 11 Data Analysis and Probability: G etting Information from Data and Measuring Likelihood 237 Data Analysis and Probability-Two Distinct but Related Areas of Mathematics 237 Data Analysis 238 Emphasizing the Big Ideas of Data Analysis 238 From Exploratory Experiences toward Conceptual Understanding: A Typical K-4 Development of Data Analysis 238 Adapting a Data Analysis Lesson 245 Using Data Analysis to Solve Problems 250 Probability 250 Emphasizing the Big Ideas of Probability 250 From Exploratory Experiences toward Conceptual Understanding: A Typical K-4 Development of Probability 251 Using Probability to Solve Problems 256 Exercises and Activities 256 References and Related Readings 257 Websites 257 A ctivities to Take to Your Class room 258 I ndex 260 A01_TUCK7286_01_SE_FM.indd 9 4/9/12 6:54 PM about the authors Benny F. Tucker earned his Ph.D. at the University of Illinois in 1975. He has authored or co-authored more than 50 books, on topics ranging from teaching methods for elementary school mathematics to the use of instructional activities in the mathematics classroom. He has authored or co-authored more than 20 articles in professional journals and has made more than 30 presentations at professional conferences. Ann Haltom Singleton is Associate Dean of the School of Education at Union University in Jackson Tennessee. She earned her Ed.D. in Special Education from the University of Memphis. Her research areas include leadership development and mathematics instruction, especially in inclusive settings. She has contributed to numerous articles and has made over 30 national presentations. She was recognized as the Union University 2003 Faculty of the Year. Terry L. Weaver honed his teaching skills in the Miami-Dade County School System. He received his Ph.D. in Special Education from George Peabody College for Teachers at Vanderbilt University. Dr. Weaver then shared his teaching skills at Carson-Newman College and Union University where he continues to teach. Dr. Weaver has served as an item writer for and participated in the revalidation of the Praxis II Specialty Area Test in SE (Core Knowledge). He is a co-author of Teaching Mathematics to All Children: Designing and Adapting Instruction to Meet the Needs of Diverse Learners, has presented on differentiated instruction and assessment, universal design, inclusion, and adapting instruction for diverse learners, and recently lead the revision of a chapter on mathematics in Vaughn's and Bos's Strategies for Teaching Students with Learning and Behavior Problems. x A01_TUCK7286_01_SE_FM.indd 10 4/9/12 6:54 PM xi Why This Book? The diversity of students in K-4 classrooms is extensive. The children in a typical classroom are diverse in gender, diverse in race and ethnicity, and diverse in religion and culture. They are diverse in ability, diverse in interests, and diverse in preferred learning styles. And they are diverse in family background, and diverse with respect to resources in the home such as books and technology. In the face of such diversity, how can the teacher expect to plan for effective instruction? Although teachers must certainly be aware of student diversity and the need to accommodate that diversity, it is perhaps more important for K-4 teachers to be aware of the ways in which their students are alike. For example, almost universally, children are kinesthetic learners. It is natural for them to be active and move around. They love classroom activities that allow (even require) them to be energetic and animated. Children are also naturally inquisitive. They are interested in what, why, and how. It is the nature of children to be curious about things. They like to talk to one another, to exchange ideas, and to discuss the things that they are experiencing and learning. Children are concrete learners. They enjoy handling things, seeing how things are related. They like to understand. In this text, we provide an approach to the planning and teaching of K-4 mathematics that is based on the nature of children. We believe that the teaching suggestions in this text will help teachers be more effective as they plan and teach mathematics in diverse classrooms, grades K-4. Structure of the Book The book begins with two introductory chapters that provide a basic understanding of instructional activities and lesson planning. Then there are nine chapters devoted to teaching the content that most commonly appears in K-4 mathematics textbooks. We do not attempt to provide comprehensive coverage of every topic that might appear in a K-4 textbook. Rather, our intent is to emphasize a way of teaching effectively that will result in learning, understanding, retention of important concepts and skills, and an ability to apply those concepts and skills to solve problems. Important to that way of teaching is effective planning. Therefore, we have made planning for effective teaching an important part of this text. preface
Number Of Pages: 288
Published: 23rd May 2012
Publisher: ALLYN & BACON
Dimensions (cm): 27.5 x 21.8
Weight (kg): 0.679