| Edition |
Third edition / John A. Van de Walle, late of Virginia Commonwealth University, Karen S. Karp, Johns Hopkins University, LouAnn H. Lovin, James Madison University, Jennifer M. Bay-Williams, University of Louisville. |
| Description |
1 volume (various pagings) : illustrations (chiefly color) ; 28 cm. |
| Series |
Student-centered mathematics series ; volume 2
|
| Bibliography |
Includes bibliographical references and index. |
| Summary |
This book is part of the Student-Centered Mathematics Series, which is designed with three objectives: to illustrate what it means to teach student-centered, problem-based mathematics, to serve as a reference for the mathematics content and research-based instructional strategies suggested for the specific grade levels, and to present a large collection of high quality tasks and activities that can engage students in the mathematics that is important for them to learn. -- Provided by publisher. |
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A practical, comprehensive, developmentally appropriate approach to effective mathematical instruction in grades 3 to 5. Helping students make connections between mathematics and their worlds--and helping them feel empowered to use math in their lives--is the focus of this widely popular guide. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM's teaching practices, and engaging families. The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. -- Provided by publisher. |
| Contents |
Machine generated contents note: pt. 1 Establishing a Student-Centered Environment -- 1. Setting a Vision for Learning High-Quality Mathematics -- Understanding and Doing Mathematics -- How Do Students Learn? -- Constructivism -- Sociocultural Theory -- Teaching for Understanding -- Teaching for Relational Understanding -- Teaching for Instrumental Understanding -- The Importance of Students' Ideas -- Mathematics Classrooms That Promote Understanding -- 2. Teaching Mathematics through Problem Solving -- Teaching through Problem Solving: An Upside-Down Approach -- Mathematics Teaching Practices for Teaching through Problem Solving -- Using Worthwhile Tasks -- Level of Cognitive Demand -- Multiple Entry and Exit Points -- Relevant and Well-Designed Contexts -- Evaluating and Adapting Tasks -- What Do I Do When a Task Doesn't Work? -- Orchestrating Classroom Discourse -- Classroom Discussions -- Aspects of Questioning -- How Much to Tell and Not to Tell -- Leveraging Mistakes and Misconceptions to Enhance Learning -- Representations: Tools for Problem Solving, Reasoning, and Communication -- Build a Web of Representations -- Explore with Tools -- Tips for Using Representations in the Classroom -- Lessons in the Problem-Based Classroom -- A Three-Phase Lesson Format -- Variations of the Three-Phase Lesson -- Life-Long Learning: An Invitation to Learn and Grow -- 3. Creating Assessments for Learning -- Assessment That Informs Instruction -- Observations -- Anecdotal Notes -- Checklists -- Questions -- Interviews -- Tasks -- Problem-Based Tasks -- Translation Tasks -- Writing -- Students' Self-Assessment and Reflection -- Rubrics and Their Uses -- Generic Rubrics -- Task-Specific Rubrics -- 4. Differentiating Instruction -- Differentiation and Teaching Mathematics through Problem Solving -- The Nuts and Bolts of Differentiating Instruction -- Planning Meaningful Content, Grounded in Authenticity -- Recognizing Students as Individuals -- Connecting Content and Learners -- Differentiated Tasks for Whole-Class Instruction -- Parallel Tasks -- Open Questions -- Tiered Lessons -- Flexible Grouping -- 5. Teaching Culturally and Linguistically Diverse Students -- Culturally and Linguistically Diverse Students -- Funds of Knowledge -- Mathematics as a Language -- Culturally Responsive Mathematics Instruction -- Communicate High Expectations -- Make Content Relevant -- Attend to Students' Mathematical Identities -- Ensure Shared Power -- Teaching Strategies That Support Culturally and Linguistically Diverse Students -- Focus on Academic Vocabulary -- Foster Student Participation during Instruction -- Plan Cooperative/Interdependent Groups to Support Language Development -- Assessment Considerations for ELLs -- Select Tasks with Multiple Entry and Exit Points -- Use Diagnostic Interviews -- Limit Linguistic Load -- Provide Accommodations -- 6. Teaching and Assessing Students with Exceptionalities -- Instructional Principles for Diverse Learners -- Prevention Models -- Implementing Interventions -- Explicit Strategy Instruction -- Concrete, Semi-Concrete, Abstract (CSA) -- Peer-Assisted Learning -- Think-Alouds -- Teaching and Assessing Students with Learning Disabilities -- Adapting for Students with Moderate/Severe Disabilities -- Planning for Students Who Are Mathematically Gifted -- Acceleration and Pacing -- Depth -- Complexity -- Creativity -- Strategies to Avoid -- 7. Collaborating with Families and Other Stakeholders -- Sharing the Message with Stakeholders -- Why Change? -- Pedagogy -- Content -- Student Learning and Outcomes -- Administrator Engagement and Support -- Family Engagement -- Family Math Nights -- Classroom Visits -- Involving ALL Families -- Homework Practices and Parent Coaching -- Tips for Helping Parents Help Their Child -- Resources for Families -- Seeing and Doing Mathematics at Home -- pt. |
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2 Teaching Student-Centered Mathematics -- 8. Exploring Number and Operation Sense -- Developing Addition and Subtraction Operation Sense -- Addition and Subtraction Problem Structures -- Teaching Addition and Subtraction -- Developing Multiplication and Division Operation Sense -- Multiplication and Division Problem Structures -- Equal-Group Problems -- Comparison Problems -- Array and Area Problems -- Combination Problems -- Teaching Multiplication and Division -- Contextual Problems -- Symbolism for Multiplication and Division -- Choosing Numbers for Problems -- Remainders -- Model-Based Problems -- Properties of Multiplication and Division -- Commutative and Associative Properties of Multiplication -- Zero and Identity Properties -- Distributive Property -- Why Not Division by Zero? -- Strategies for Solving Contextual Problems -- Analyzing Context Problems -- Multistep Word Problems -- 9. Developing Basic Fact Fluency -- Developmental Phases for Learning the Basic Fact Combinations -- Teaching and Assessing the Basic Fact Combinations -- Different Approaches to Teaching the Basic Facts -- Teaching Basic Facts Effectively -- Assessing Basic Facts Effectively -- Reasoning Strategies for Addition Facts -- One More Than and Two More Than -- Combinations of 10 -- Making 10 -- Doubles and Near-Doubles -- Reasoning Strategies for Subtraction Facts -- Think-Addition -- Down Under 10 -- Take from 10 -- Reasoning Strategies for Multiplication and Division Facts -- Twos -- Fives -- Zeros and Ones -- Nines -- Derived Multiplication Fact Strategies -- Division Facts -- Reinforcing Basic Fact Mastery -- Games to Support Basic Fact Mastery -- About Drill -- Fact Remediation -- What to Do When Teaching Basic Facts -- What Not to Do When Teaching Basic Facts -- 10. Developing Whole-Number Place-Value Concepts -- Extending Number Relationships to Larger Numbers -- Part -- Part -- Whole Relationships -- Relative Magnitude -- Connections to Real-World Ideas -- Approximate Numbers and Rounding -- Important Place-Value Concepts -- Integration of Base-Ten Grouping with Counting by Ones -- Integration of Base-Ten Groupings with Words -- Integration of Base-Ten Grouping with Place-Value Notation -- Base-Ten Models -- Extending Base-Ten Concepts -- Grouping Hundreds to Make 1000 -- Equivalent Representations -- Oral and Written Names for Numbers -- Three-Digit Number Names -- Written Symbols -- Patterns and Relationships with Multidigit Numbers -- The Hundreds Chart -- Relationships with Benchmark Numbers -- Numbers beyond 1000 -- Extending the Place-Value System -- Conceptualizing Large Numbers -- 11. Building Strategies for Whole-Number Computation -- Toward Computational Fluency -- Direct Modeling -- Invented Strategies -- Standard Algorithms -- Development of Invented Strategies in Addition and Subtraction -- Models to Support Invented Strategies -- Adding Multidigit Numbers -- Subtraction as "Think Addition" -- Take-Away Subtraction -- Standard Algorithms for Addition and Subtraction -- Invented Strategies for Multiplication -- Useful Representations -- Multiplication by a One-Digit Multiplier -- Multiplication of Multidigit Numbers -- Standard Algorithms for Multiplication -- Begin with Models -- Invented Strategies for Division -- Missing-Factor Strategies -- Cluster Problems -- Standard Algorithms for Division -- Begin with Models -- Two-Digit Divisors -- Computational Estimation -- Teaching Computational Estimation -- Computational Estimation Strategies -- 12. Exploring Fraction Concepts -- Meanings of Fractions -- Fraction Interpretations -- Why Fractions Are Difficult -- Models for Fractions -- Area Models -- Length Models -- Set Models -- Fractional Parts of a Whole -- Fraction Size Is Relative -- Partitioning -- Iterating -- Fraction Notation -- Magnitude of Fractions -- Equivalent Fractions -- Conceptual Focus on Equivalence -- Equivalent-Fraction Models -- Developing an Equivalent-Fraction Algorithm -- Comparing Fractions -- Using Number Sense -- Using Equivalent Fractions -- Teaching Considerations for Fraction Concepts -- 13. Building Strategies for Fraction Computation -- Understanding Fraction Operations -- A Problem-Based, Number Sense Approach -- Addition and Subtraction -- Contextual Examples and Models -- Estimation and Invented Strategies -- Developing the Algorithms -- Fractions Greater Than One -- Addressing Common Errors and Misconceptions -- Multiplication -- Contextual Examples and Models -- Estimating and Invented Strategies -- Developing the Algorithms -- Factors Greater Than One -- Addressing Common Errors and Misconceptions -- Division -- Contextual Examples and Models -- Estimating and Invented Strategies -- Developing the Algorithms -- Addressing Common Errors and Misconceptions -- 14. Developing Decimal and Percent Concepts and Decimal Computation -- Developing Concepts of Decimals -- Extending the Place-Value System -- Connecting Fractions and Decimals -- Say Decimal Fractions Correctly -- Use Visual Models for Decimal Fractions -- Multiple Names and Formats -- Developing Decimal Number Sense -- Familiar Fractions Connected to Decimals -- Comparing and Ordering Decimal Fractions -- Computation with Decimals -- Addition and Subtraction -- Multiplication -- Division -- Introducing Percents -- Models and Terminology -- Percent Problems in Context -- Estimation -- 15. Promoting Algebraic Thinking -- Strands of Algebraic Thinking -- Generalized Arithmetic -- Generalization with Number and Operations -- Meaningful Use of Symbols. |
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Note continued: The Meaning of Variables -- Making Structure in the Number System Explicit -- Making Sense of Properties -- Making Conjectures Based on Properties -- Patterns and Functional Thinking -- Growing Patterns -- Functional Thinking -- 16. Building Measurement Concepts -- The Meaning and Process of Measuring -- Concepts and Skills -- Introducing Nonstandard Units -- Introducing Standard Units -- Important Standard Units and Relationships -- The Role of Estimation and Approximation -- Strategies for Estimating Measurements -- Measurement Estimation Activities -- Length -- Conversion -- Fractional Parts of Units -- Area -- Comparison Activities -- Using Physical Models of Area Units -- The Relationship between Area and Perimeter -- Developing Formulas for Perimeter and Area -- Volume -- Comparison Activities -- Using Physical Models of Volume Units -- Developing Formulas for Volumes of Common Solid Shapes -- Weight and Mass -- Comparison Activities -- Using Physical Models of Weight or Mass Units -- Angles -- Comparison Activities -- Using Physical Models of Angular Measure Units -- Using Protractors -- Time -- Comparison Activities -- Reading Clocks -- Elapsed Time -- Money -- 17. Developing Geometric Thinking and Concepts -- Geometry Goals for Your Students -- Spatial Sense -- Geometric Content -- Developing Geometric Thinking -- The van Hiele Levels of Geometric Thought -- Implications for Instruction -- Shapes and Properties -- Sorting and Classifying -- Composing and Decomposing Shapes -- Categories of Two-Dimensional Shapes -- Categories of Three-Dimensional Shapes -- Construction Activities -- Investigations, Conjectures, and the Development of Proof -- Learning about Transformations -- Learning about Location -- Learning about Visualizations -- Three-Dimensional Imagery -- 18. Representing and Interpreting Data -- What Does It Mean to Do Statistics? -- Is It Statistics or Is It Mathematics? -- The Shape of Data -- The Process of Doing Statistics -- Formulating Questions -- Classroom Questions -- Beyond One Classroom -- Data Collection -- Using Existing Data Sources -- Data Analysis: Classification -- Data Analysis: Graphical Representations -- Creating Graphs -- Bar Graphs -- Circle Graphs -- Continuous Data Graphs -- Line Graphs -- Interpreting Results. |
| Subject |
Mathematics -- Study and teaching (Elementary)
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Individualized instruction.
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Individualized instruction. (OCoLC)fst00970355
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Mathematics -- Study and teaching (Elementary)
(OCoLC)fst01012272
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| Added Author |
Karp, Karen S.
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Lovin, LouAnn H.
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Bay-Williams, Jennifer M.
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| Added Title |
Teaching student-centered mathematics. Grades 3-5
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| ISBN |
9780134556420 |
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0134556429 |
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