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Teaching student-centered mathematics. Grades 3-5
Teaching student-centered mathematics. Developmentally appropriate instruction for grades 3-5.
Bibliographic Record Display
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Title:[Teaching student-centered mathematics. Grades 3-5]
Teaching student-centered mathematics. Developmentally appropriate instruction for grades 3-5.
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Author/Creator:Van de Walle, John A.
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Other Contributors/Collections:Karp, Karen S.
Lovin, LouAnn H.
Bay-Williams, Jennifer M.
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Published/Created:New York : Pearson Education, [2018]
©2018
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Holdings
Holdings Record Display
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Location:EDUCATION LIBRARY stacksWhere is this?
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Call Number: QA13 .V34 2018
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Number of Items:1
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Status:Available
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Location:EDUCATION LIBRARY stacksWhere is this?
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Library of Congress Subjects:Mathematics--Study and teaching (Elementary)
Individualized instruction.
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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.
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Description:1 volume (various pagings) : illustrations (chiefly color) ; 28 cm
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Series:Van de Walle, John A. Student-centered mathematics series ; volume 2.
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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.
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.
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Notes:Includes bibliographical references and index.
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ISBN:9780134556420
0134556429
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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
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
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
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. 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
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
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
Meaning of Variables
Contents note continued: 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
Meaning and Process of Measuring
Concepts and Skills
Introducing Nonstandard Units
Introducing Standard Units
Important Standard Units and Relationships
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
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
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?
Shape of Data
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.