Teaching Student-Centered Mathematics Grades 3-5

by Van de Walle, John; Lovin, Lou Ann H.

• ISBN13: 9780205408443
• ISBN10: 0205408443
• Edition: 1st
• Format: Paperback
• Copyright: 2005-06-01
• Publisher: Pearson

Summary

The resource math teachers have been waiting for is finally here! #xA0; Volume Two of the Van de Walle Professional Mathematics Series provides practical guidance along with proven strategies for practicing teachers of grades 3 through 5. In addition to many of the popular topics and features from John Van de Walle#x19;s market-leading textbook, Elementary and Middle School Mathematics, this volume offers brand-new material specifically written for these grades. The expanded grade-specific coverage and unique page design allow readers to quickly and easily locate information to implement in the classroom. Nearly 200 grade-appropriate activities are included. The student-centered, problem-based approach will help students develop real understanding and confidence in mathematics, making this series indispensable for teachers! Big Ideas provide clear and succinct explanations of the most critical concepts in 3#x13;5 mathematics. Problem-based activities in Chapters 2#x13;12 provide numerous engaging tasks to help students develop understanding. Assessment Notes illustrate how assessment can be an integral part of instruction and suggest practical assessment strategies. Expanded Lessons elaborate on one activity in each chapter, providing examples for creating step-by-step lesson plans for classroom implementation. A Companion Website (http://www.ablongman.com/vandewalletscm1e) provides access to more than 50 reproducible blackline masters to utilize in the classroom. Theare provided in the appendix for teachers#x19; reference. Collect all three volumes in the Van de Walle Professional Mathematics Series! Each volume provides in-depth coverage at specific grade levels. Teaching Student-Centered Mathematics: Volume One, Grades K#x13;3, ISBN: 0-205-40843-5 Teaching Student-Centered Mathematics: Volume Two, Grades 3#x13;5, ISBN: 0-205-40844-3 Teaching Student-Centered Mathematics: Volume Three, Grades 5#x13;8, ISBN: 0-205-41797-3

Author Biography

John Van de Walle is Professor Emeritus at Virginia Commonwealth University LouAnn Lovin is a former classroom teacher and is currently an assistant professor in mathematics education at James Madison University, where she teaches mathematics methods and mathematics content courses for Pre-K-8 prospective teachers and is involved in the mathematical professional development of teachers in grades 4-8

Table of Contents

Preface	p. ix
Activities at a Glance	p. xv
About the Authors	p. xxi
Foundations of Student-Centered Instruction	p. 1
How Children Learn and Understand Mathematics	p. 1
Constructing Ideas	p. 2
Understanding	p. 2
Classroom Influences on Learning	p. 4
Using Models in the Classroom	p. 8
Teaching with Problems	p. 11
Problem-Based Tasks	p. 11
The Value of Teaching with Problems	p. 15
A Three-Part Format for Problem-Based Lessons	p. 16
Teachers' Questions About Problem-Based Teaching	p. 21
Planning in a Problem-Based Classroom	p. 24
Planning Problem-Based Lessons	p. 24
Variations of the Three-Part Lesson	p. 27
Diversity in the Classroom	p. 28
Assessment in a Problem-Based Classroom	p. 30
Appropriate Assessment	p. 30
Rubrics and Their Uses	p. 32
Diagnostic Interviews	p. 34
Grading	p. 36
Get Started	p. 37
Number and Operation Sense	p. 39
Developing Number Relationships	p. 40
Numbers Beyond 1000	p. 47
Activities for Flexible Thinking with Whole Numbers	p. 51
Developing Multiplication and Division Operation Sense	p. 56
Solving Contextual Problems	p. 67
Expanded Lesson	p. 72
Helping Children Master the Basic Facts	p. 74
From Concepts and Strategies to Fact Mastery	p. 74
Strategies for Additional Facts	p. 79
Strategies for Subtraction Facts	p. 84
Strategies for Multiplication Facts	p. 88
Division Facts and "Near Facts"	p. 93
Effective Drill	p. 94
Fact Remediation with Upper-Grade Students	p. 96
Facts: No Barrier to Good Mathematics	p. 97
Expanded Lesson	p. 98
Strategies for Whole-Number Computation	p. 100
Toward Computational Fluency	p. 100
Development of Invented Strategies: A General Approach	p. 106
Invented Strategies for Addition and Subtraction	p. 108
Traditional Algorithms for Addition and Subtraction	p. 112
Invented Strategies for Multiplication	p. 113
The Traditional Algorithm for Multiplication	p. 118
Invented Strategies for Division	p. 121
The Traditional Algorithm for Division	p. 124
Expanded Lesson	p. 129
Developing Fraction Concepts	p. 131
Sharing and the Concept of Fractional Parts	p. 131
Models for Fractions	p. 133
From Fractional Parts to Fraction Symbols	p. 136
Fraction Number Sense	p. 144
Equivalent-Fraction Concepts	p. 151
Expanded Lesson	p. 158
Fraction Computation	p. 160
Number Sense and Fraction Algorithms	p. 160
Addition and Subtraction	p. 162
Multiplication	p. 167
Division	p. 172
Expanded Lesson	p. 179
Decimal and Percent Concepts and Decimal Computation	p. 181
Connecting Two Different Representational Systems	p. 181
Developing Decimal Number Sense	p. 187
Introducing Percents	p. 192
Computation with Decimals	p. 196
Expanded Lesson	p. 202
Geometric Thinking and Geometric Concepts	p. 204
Geometry Goals for Your Students	p. 204
Geometric Thought: Reasoning About Shapes and Relationships	p. 206
Shapes and Properties Activities	p. 211
Transformation Activities	p. 233
Location Activities	p. 239
Visualization Activities	p. 243
Expanded Lesson	p. 250
Developing Measurement Concepts	p. 252
The Meaning and Process of Measuring	p. 252
Developing Measurement Concepts and Skills	p. 254
Measuring Length	p. 257
Measuring Area	p. 261
Measuring Volume and Capacity	p. 265
Measuring Weight and Mass	p. 268
Measuring Time	p. 269
Measuring Angles	p. 272
Introducing Standard Units	p. 274
Estimating Measures	p. 278
Developing Formulas for Area and Volume	p. 281
Expanded Lesson	p. 288
Algebraic Reasoning	p. 290
Repeating Patterns	p. 291
Growing Patterns	p. 293
Patterns with Numbers	p. 299
Representing Ideas	p. 303
Variables and Equations	p. 306
Functions	p. 313
Expanded Lesson	p. 318
Exploring Data Analysis	p. 320
Gathering Data to Answer Questions	p. 320
Descriptive Statistics	p. 323
Understanding the Mean: Two Concepts	p. 325
Graphical Representations	p. 329
Expanded Lesson	p. 337
Exploring Concepts of Probability	p. 339
Probability on a Continuum	p. 340
Sample Spaces and Probability	p. 344
Short-Run Versus Long-Run Results	p. 351
Expanded Lesson	p. 356
Principles and Standards for School Mathematics	p. 358
A Guide to the Blackline Masters	p. 369
References	p. 376
Index	p. 379
Table of Contents provided by Ingram. All Rights Reserved.