Teaching Student-Centered Mathematics : Grades K-3

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

• ISBN13: 9780205408436
• ISBN10: 0205408435
• Edition: 1st
• Format: Paperback
• Copyright: 2005-05-27
• Publisher: Pearson

Summary

The resource math teachers have been waiting for is finally here! #xA0; Volume One of the Van de Walle Professional Mathematics Series provides practical guidance along with proven strategies for practicing teachers of kindergarten through grade 3.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 the early 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 Ideasprovide clear and succinct explanations of the most critical concepts in K-3 mathematics. Problem-based activitiesin every chapter provide numerous engaging tasks to help students develop understanding. Assessment Notesillustrate how assessment can be an integral part of instruction and suggest practical assessment strategies. Expanded Lessonselaborate on one activity from each chapter, providing examples for creating step-by-step lesson plans for classroom implementation. A Companion Website(http://www.ablongman.com/vandewalleseries/) provides access to more than 50 reproducible blackline mastersto utilize in the classroom. The NCTM Content Standardsare provided for teachers#x19; reference in the appendix. 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-3,#xA0;ISBN: 0-205-40843-5 Teaching Student-Centered Mathematics: Volume Two, Grades 3-5,#xA0;ISBN: 0-205-40844-3 Teaching Student-Centered Mathematics: Volume Three, Grades 5-8, ISBN: 0-205-41797-3

Author Biography

John Van de Walle is Professor Emeritus at Virginia Commonwealth University.

Table of Contents

Preface	ix
Activities at a Glance	xiv
About the Authors	xxii
Foundations of Student-Centered Instruction	1	(36)
How Children Learn and Understand Mathematics	1	(9)
Constructing Ideas	2	(1)
Understanding	2	(2)
Classroom Influences on Learning	4	(4)
Using Models in the Classroom	8	(2)
Teaching with Problems	10	(12)
Problem-Based Tasks	11	(3)
The Value of Teaching with Problems	14	(1)
A Three-Part Format for Problem-Based Lessons	15	(4)
Teachers' Questions about Problem-Based Teaching	19	(3)
Planning in a Problem-Based Classroom	22	(6)
Planning Problem-Based Lessons	22	(3)
Variations of the Three-Part Lesson	25	(1)
Diversity in the Classroom	26	(2)
Assessment in a Problem-Based Classroom	28	(8)
Appropriate Assessment	29	(1)
Rubrics and Their Uses	30	(3)
Diagnostic Interviews	33	(1)
Grading	34	(2)
Get Started	36	(1)
Developing Early Number Concepts and Number Sense	37	(28)
Early Counting and Number	37	(5)
Early Number Sense	42	(1)
Relationships Among Numbers 1 Through 10	42	(12)
Relationships for Numbers 10 to 20	54	(2)
Numbers to 100: Early Introductions	56	(2)
Number Sense and the Real World	58	(5)
Expanded Lesson	63	(2)
Developing Meaning for the Operations and Solving Story Problems	65	(29)
Addition and Subtraction	65	(5)
Teaching Addition and Subtraction	70	(7)
Problem Structures for Multiplication and Division	77	(3)
Teaching Multiplication and Division	80	(6)
More Thoughts About Children Solving Story Problems	86	(6)
Expanded Lesson	92	(2)
Helping Children Master the Basic Facts	94	(26)
From Concepts and Strategies to Fact Mastery	94	(5)
Strategies for Addition Facts	99	(7)
Strategies for Subtraction Facts	106	(5)
Strategies for Multiplication Facts	111	(5)
Division Facts and ``Near Facts''	116	(1)
Effective Drill	117	(3)
Expanded Lesson	120	(37)
Base-Ten Concepts and Place Value	122	(1)
Children's Pre-Base-Ten Concepts	123	(1)
Goals of Place Value Development	124	(3)
Models for Place Value	127	(2)
Developing Place-Value Concepts and Procedures	129	(13)
Number Sense Development	142	(3)
Activities for Flexible Thinking	145	(5)
Helping Children Work with Money	150	(5)
Expanded Lesson	155	(2)
Strategies for Whole-Number Computation	157	(29)
Toward Computational Fluency	157	(6)
Development of Invented Strategies: A General Approach	163	(2)
Invented Strategies for Addition and Subtraction	165	(4)
Traditional Algorithms for Addition and Subtraction	169	(4)
Invented Strategies for Multiplication	173	(2)
The Traditional Algorithm for Multiplication	175	(3)
Invented Strategies for Division	178	(2)
The Traditional Algorithm for Division	180	(4)
Expanded Lesson	184	(2)
Geometric Thinking and Geometric Concepts	186	(37)
Geometry Goals for Your Students	186	(2)
Geometric Thought: Reasoning about Shapes and Relationships	188	(5)
Shapes and Properties Activities	193	(16)
Transformation Activities	209	(4)
Location Activities	213	(3)
Visualization Activities	216	(5)
Expanded Lesson	221	(2)
Developing Measurement Concepts	223	(28)
The Meaning and Process of Measuring	223	(2)
Developing Measurement Concepts and Skills	225	(3)
Measuring Length	228	(6)
Measuring Area	234	(4)
Measuring Volume and Capacity	238	(3)
Measuring Weight and Mass	241	(1)
Measuring Time	242	(3)
Introducing Standard Units	245	(4)
Expanded Lesson	249	(2)
Early Fraction Concepts	251	(24)
Sharing and the Concept of Fractional Parts	252	(2)
Models for Fractions	254	(2)
From Fractional Parts to Fraction Symbols	256	(6)
Fraction Number Sense	262	(6)
Equivalent-Fraction Concepts	268	(5)
Expanded Lesson	273	(2)
Algebraic Reasoning	275	(35)
Repeating Patterns	276	(5)
Growing Patterns	281	(3)
Patterns with Numbers	284	(9)
Representing Ideas	293	(4)
Variables and Equations	297	(5)
Relations and Functions	302	(6)
Expanded Lesson	308	(2)
Helping Children Use Data	310	(21)
Gathering Data to Answer Questions	310	(3)
Classification and Data Analysis	313	(4)
Graphical Representations	317	(7)
Describing a Set of Data	324	(5)
Expanded Lesson	329	(2)
Early Experiences with Probability Concepts	331	(19)
Probability on a Continuum	332	(5)
Sample Spaces and Probability	337	(6)
Short-Run versus Long-Run Results	343	(5)
Expanded Lesson	348	(2)
Appendix A. Principles and Standards for School Mathematics	350	(11)
Appendix B. A Guide to the Blackline Masters	361	(7)
References	368	(3)
Index	371