Elementary and Middle School Mathematics: Teaching Developmentally, Global Edition
Höfundar: John A. Van de Walle, Karen S. Karp
4.790 kr.
Lýsing:
Elementary and Middle School Mathematics illustrates how children in PreK to 8th grade learn math, and then shows the most effective methods of teaching math using problem-based activities. Examples of real student work and common challenges help you visualize developmentally appropriate mathematics instruction and assessment that supports and challenges all learners. Clear discussions detail how to teach each topic, what a learning progression for that topic might be, and what worthwhile tasks look like.
Hundreds of classroom-ready activities show how you can engage students with the concepts. A valuable reference to consult throughout your teaching career, Elementary and Middle School Mathematics helps you develop pedagogical strategies now, and in your future teaching. The 11th Edition, Global Edition, reflects the Common Core State Standards and NCTM's Principles to Actions, as well as current research and the latest teaching technology.
Annað
- Höfundar: John Van de Walle, Jennifer M. Bay-Williams, Karen S. Karp
- Útgáfa:11
- Útgáfudagur: 2023-06-14
- Hægt að prenta út 2 bls.
- Hægt að afrita 2 bls.
- Format:Page Fidelity
- ISBN 13: 9781292460048
- Print ISBN: 9781292460079
- ISBN 10: 1292460040
Efnisyfirlit
- Title Page
- Copyright
- Pearson’s Commitment to Diversity, Equity, and Inclusion
- About the Authors
- About the Contributor
- Preface
- Brief Contents
- Contents
- Part I: Teaching Mathematics Developmentally: Big Ideas and Research-Based Practices
- Chapter 1. Developing Confident and Competent Mathematics Learners
- Learning How to Teach Mathematics Developmentally
- Math Is Important
- Mathematics Is about Effort, Not Genetics and Other Myths
- Strengths-Based Approach
- Teaching Developmentally
- What Influences the Mathematics We Teach?
- The World Is Changing
- International Comparisons
- Research on Learning and Teaching
- How Do We Use the Standards to Teach?
- Mathematics Content Standards
- Mathematical Practices
- How to Teach the Standards Effectively
- An Invitation to Learn and Grow
- Becoming a Teacher of Mathematics
- Resources for Chapter 1
- Learning How to Teach Mathematics Developmentally
- Chapter 2. Exploring What It Means to Know and Do Mathematics
- What Is Mathematical Proficiency?
- Conceptual Understanding
- Procedural Fluency
- Strategic Competence
- Adaptive Reasoning
- Productive Disposition
- An Invitation to Do Mathematics
- Task 1. One Up, One Down
- Task 2. Solving the Mystery
- Task 3. Two Machines, One Job
- Reflecting on the Three Tasks
- How Do Students Learn Mathematics?
- Constructivism
- Sociocultural Theory
- Implications for Teaching Mathematics
- Connecting the Dots
- Resources for Chapter 2
- What Is Mathematical Proficiency?
- Chapter 3. Teaching Problem-Based Mathematics
- Effective Mathematics Teaching
- Success for Every Student
- The Mathematics Teaching Practices
- Establishing Goals to Focus Learning
- Problem-Based Mathematics Teaching
- Learning Progressions
- Tasks That Promote Problem Solving
- Worthwhile Tasks
- Evaluating and Adapting Tasks
- Procedural Fluency from Conceptual Understanding
- Tasks That Build Procedural Fluency from Conceptual Understanding
- What about Drill and Practice?
- Facilitating Mathematical Discourse
- Elicit and Use Evidence of Student Thinking
- Posing Purposeful Questions
- Using and Connecting Mathematical Representations
- Supporting Productive Struggle
- Teaching Practices At-a-Glance
- Resources for Chapter 3
- Effective Mathematics Teaching
- Chapter 4. Planning in the Problem-Based Classroom
- A Three-Phase Lesson Format
- The Before Lesson Phase
- The During Lesson Phase
- The After Lesson Phase
- The Planning Process
- Step 1: Determine the Learning Goals
- Step 2: Consider Your Students’ Needs
- Step 3: Select, Design, or Adapt a Worthwhile Task
- Step 4: Design Lesson Assessments
- Step 5: Plan the Before Phase
- Step 6: Plan the During Phase
- Step 7: Plan the After Phase
- Step 8: Reflect and Refine
- Routines and Other Worthwhile Learning Experiences
- Language-Focused Routines
- Number Talks
- Number Strings
- Splat!
- Which One Doesn’t Belong (WODB)
- Worked Examples
- Three-Act Math
- Estimation 180
- Learning Centers
- Differentiating Instruction
- Opening Closed Questions
- Differentiating Tasks
- Incorporating Choice
- Planning for Family Engagement
- Connecting with Families
- Homework Tips
- Resources for Chapter 4
- A Three-Phase Lesson Format
- Chapter 5. Creating Assessments for Learning
- Integrating Assessment into Instruction
- What Are the Main Assessment Types?
- What Should Be Assessed?
- Assessment Methods
- Observations
- Interviews
- Tasks for Assessment
- Rubrics and Their Uses
- Generic Rubrics
- Task-Specific Rubrics
- Student Self-Assessment
- Tests
- Expanding the Usefulness of Tests
- Improving Performance on Large-Scale Assessments
- Communicating Grades and Shaping Instruction
- Grading
- Shaping Instruction
- Resources for Chapter 5
- Integrating Assessment into Instruction
- Chapter 6. Teaching Mathematics Equitably to All Students
- Equitable Mathematics Instruction
- Deep Understanding of Mathematics
- Mathematics Identity
- Mathematical Agency
- Implicit Bias and Structural Barriers in Mathematics Learning
- Addressing the Needs of Specific Learners
- Multitiered System of Support (MTSS)
- Supporting Students Who Struggle and Those with Special Needs in Math
- Implementing Interventions
- Teaching Strategies and Support in the Tier 1 Classroom
- Adapting Instruction for Students Who Need Extensive Support in Math
- Multilingual Learners
- Mathematics Language Considerations
- Strategies to Support Multilingual Learners
- Promoting Advanced Education and Talent Development
- Spot and Foster Students’ Strengths
- Resources for Chapter 6
- Equitable Mathematics Instruction
- Chapter 1. Developing Confident and Competent Mathematics Learners
- Chapter 7. Developing Early Number Concepts and Number Sense
- Developmentally Appropriate Early Learning
- Learning Progressions in Early Childhood
- The Number Core: Quantity, Counting, and Cardinality
- Quantity and the Ability to Subitize
- Counting
- Cardinality
- Thinking about Zero
- Numeral Writing and Recognition
- Counting On and Counting Back
- The Relations Core: More Than, Less Than, and Equal To
- Developing Number Sense by Building Number Relationships
- Relationships between Numbers 1 through 10
- Relationships for Numbers 10 through 20 and Beyond
- Number Sense in Their World
- Estimation and Measurement
- Represent and Interpret Data
- Common Challenges Related to Early Number Concepts from Research
- Resources for Chapter 7
- Developmentally Appropriate Early Learning
- Chapter 8. Developing Meanings for the Operations
- Developing Addition and Subtraction Problem Structures
- Teaching Addition and Subtraction
- Contextual Problems
- Representing Addition and Subtraction: Concrete Representations
- Representing Addition and Subtraction: Semi-Concrete Representations
- Representing Addition and Subtraction: Abstract Representations
- Developing Multiplication and Division Problem Structures
- Equal-Group Problems
- Comparison Problems
- Array and Area Problems
- Combination Problems
- Teaching Multiplication and Division
- Representing Multiplication and Division: Concrete Representations
- Representing Multiplication and Division: Semi-concrete Representations
- Representing Multiplication and Division: Abstract Representations
- Strategies for Solving Word Problems
- Analyzing Word Problems
- Think about the Answer before Solving the Problem
- Work a Simpler Problem
- Caution: Avoid the Key-Word Strategy!
- Multistep Word Problems
- Common Challenges Related to the Meaning of the Operations
- Resources for Chapter 8
- Chapter 9. Developing Basic Fact Fluency
- Teaching Basic Facts Developmentally
- Developmental Phases for Learning Basic Facts
- Approaches to Teaching Basic Facts
- Build on Conceptual Understanding
- Addition and Subtraction Facts
- Addition Foundational Fact Sets
- Doubles
- Reasoning Strategies for Addition
- Reasoning Strategies for Subtraction
- Games to Practice Addition and Subtraction Strategies
- Multiplication and Division Facts
- Multiplication Foundational Facts: 2, 10, 5, 0, 1, and Squares
- Reasoning Strategies for Multiplication and Division
- Games to Practice Multiplication and Division Facts and Strategies
- Mixed Facts and More Games
- Assessing Basic Fact Fluency
- The Problem with Timed Tests
- Observing Basic Fact Fluency
- Interviews and Journals
- Addressing Challenges Related to Basic Fact Fluency
- Ongoing Support for Fact Fluency
- Common Challenges and How to Help
- Resources for Chapter 9
- Teaching Basic Facts Developmentally
- Chapter 10. Developing Whole-Number Place-Value Concepts
- Developing Whole-Number Place-Value
- Unitary: Counting by Ones
- Base-Ten Grouping
- Equivalent Grouping
- Integrating Base-Ten Groupings with Words
- Integrating Base-Ten Groupings with Place-Value Notation
- Base-Ten Models for Place Value
- Groupable Models
- Pregrouped Models
- Non-proportional Models
- Activities to Develop Base-Ten Concepts
- Grouping Activities
- Grouping Tens to Make 100
- Equivalent Representations
- Reading and Writing Numbers
- Two-Digit Number Names
- Three-Digit Number Names
- Written Symbols
- Place Value Patterns and Relationships—A Foundation for Computation
- The Hundred Chart
- Relative Magnitude, Using Benchmark Numbers
- Approximate Numbers and Rounding
- Connections to Real-World Ideas
- Numbers Beyond 1000
- Extending the Place-Value System
- Conceptualizing Large Numbers
- Common Challenges Related to Place Value
- Resources for Chapter 10
- Developing Whole-Number Place-Value
- Chapter 11. Developing Strategies for Addition and Subtraction Computation
- Connecting Addition and Subtraction to Place Value
- Progression for Computational Fluency
- Reasoning Strategies in Addition and Subtraction
- Creating a Supportive Environment for Reasoning Strategies
- Jump Strategies
- Think-Addition
- Count Back – Take-Away
- Decomposition Strategies
- Compensation Strategies
- Adding or Subtracting a Single-Digit Number
- Adding Tens and Hundreds
- Adding Multi-Digit Numbers
- Selecting Problems
- Algorithms for Addition and Subtraction
- Partial Sums and Differences
- Standard Algorithm for Addition
- Standard Algorithm for Subtraction
- Computational Estimation
- Understanding Computational Estimation
- Suggestions for Teaching Computational Estimation
- Computational Estimation Strategies
- Front End
- Rounding
- Compatible Numbers
- Common Challenges Related to Addition and Subtraction Computation
- Resources for Chapter 11
- Connecting Addition and Subtraction to Place Value
- Chapter 12. Developing Strategies for Multiplication and Division Computation
- Reasoning Strategies for Multiplication
- Direct Modeling
- Decomposition Strategies
- Compensation Strategies
- Teaching Reasoning Strategies
- Multiplication of Larger Numbers
- Algorithms for Multiplication
- Concrete: Contexts and Manipulatives
- Semi-Concrete
- Moving to the Abstract
- Reasoning Strategies for Division
- Direct Modeling
- Teaching Reasoning Strategies
- Instructional Routines
- Algorithms for Division
- Concrete: Contexts and Manipulatives
- Semi-Concrete
- Moving to the Abstract
- Two-Digit Divisors
- Computational Estimation
- Teaching Computational Estimation
- Computational Estimation Strategies
- Common Challenges Related to Multiplication and Division Computation
- Resources for Chapter 12
- Reasoning Strategies for Multiplication
- Chapter 13. Algebraic Thinking
- Equivalence, Expressions, Equations, and Inequalities
- The Meaning of the Equal Sign
- The Meaning of Inequalities
- Developing the Concept of Equivalence
- Generalized Arithmetic and Properties of the Operations
- Number Combinations
- Algorithms
- Properties of the Operations
- Conjectures
- Variables
- Variable Expressions
- Variables as Unknown Values
- Variables That Vary
- Patterns and Functional Thinking
- Repeating Patterns
- Growing Patterns
- Functional Thinking
- Graphs of Functions
- Linear Functions
- Mathematical Modeling
- Algebraic Thinking across the Curriculum
- Measurement and Algebra
- Data and Algebra
- Common Challenges Related to Algebraic Thinking
- Resources for Chapter 13
- Equivalence, Expressions, Equations, and Inequalities
- Chapter 14. Developing Fraction Concepts
- Meanings of Fractions
- Fraction Constructs
- Fraction Language and Notation
- Fraction Size Is Relative
- Fraction Representations
- Area Models
- Length Models
- Set Models
- Fractions as Numbers
- Equal Sharing Problems
- Partitioning
- Iterating
- Magnitude of Fractions
- Equivalent Fractions
- Conceptual Focus on Equivalence
- Equivalent Fraction Activities across Models
- Fractions Greater than 1
- Developing an Equivalent-Fraction Algorithm
- Comparing and Ordering Fractions
- Comparing Fractions, Using Number Sense
- Using Equivalent Fractions to Compare
- Addressing Challenges Related to Fraction Concepts
- Teaching Recommendations
- Challenges and How to Help
- Resources for Chapter 14
- Meanings of Fractions
- Chapter 15. Developing Fraction Operations
- Understanding Fraction Operations
- Effective Teaching Process
- Addition and Subtraction
- Contextual Examples
- Models
- Estimating Sums and Differences
- Developing Strategies and Algorithms
- Challenges with Adding and Subtracting Fractions
- Multiplication
- Contextual Examples and Models
- Estimating Products
- Developing Strategies and Algorithms
- Challenges with Multiplying Fractions
- Division
- Contextual Examples and Models
- Answers That Are Not Whole Numbers
- Estimating Division
- Developing the Algorithms
- Challenges with Dividing Fractions
- Resources for Chapter 15
- Understanding Fraction Operations
- Chapter 16. Developing Decimal and Percent Concepts and Decimal Computation
- Extending the Place-Value System
- The 10-to-1 Relationship—Now in Two Directions!
- Units and the Decimal Point
- Measurement and Monetary Units
- Precision and Equivalence
- Connecting Fractions and Decimals
- Say Decimals Correctly
- Representations for Decimals
- Connecting Visuals to Symbols
- Developing Decimal Number Sense
- Familiar Fractions Connected to Decimals
- Comparing and Ordering Decimals
- Computation with Decimals
- Addition and Subtraction
- Multiplication
- Division
- Introducing Percents
- Models and Terminology
- Percent Problems in Context
- Estimation
- Common Challenges in Decimals and Percents
- Resources for Chapter 16
- Extending the Place-Value System
- Chapter 17. Ratios and Proportional Reasoning
- Ratios
- Types of Ratios
- How Do Ratios Relate to Fractions?
- Two Ways to Think about Ratio
- Proportional Reasoning
- Types of Comparing Situations
- Covariation
- Strategies for Comparing Ratios
- Proportional Reasoning Strategies and Representations
- Early and Transitional Reasoning with Ratio Tables
- Early and Transitional Reasoning with Tape Diagrams
- Transitional Reasoning with Double Number Lines
- Proportional Strategies
- Percent Problems
- Proportional Reasoning across the Curriculum
- Measurement and Geometry
- Algebra
- Addressing Challenges Related to Ratios and Proportions
- Tips for Supporting Ratio and Proportional Reasoning
- Addressing Challenges Related to Ratio and Proportional Reasoning
- Resources for Chapter 17
- Ratios
- Chapter 18. Developing Measurement Concepts
- The Meaning and Process of Measuring
- Decide on the Attribute
- Select a Unit
- Make Comparisons
- Use Concrete Representations of Measuring Units
- Introduce Nonstandard Units
- Introduce Standard Units
- Use Measuring Tools
- Use Formulas
- Estimation and Approximation
- Strategies for Estimating Measurements
- Measurement Estimation Activities
- Length
- Comparison Activities
- Use Concrete Representations
- Make and Use Rulers
- Conversion
- Area
- Comparison Activities
- Use Concrete Representations
- The Relationship between Area and Perimeter
- Develop Formulas for Perimeter and Area
- Volume and Capacity
- Comparison Activities
- Use Concrete Representations
- Developing Formulas for Volume
- The Relationship between Volume and Surface Area
- Weight and Mass
- Comparison Activities
- Use Concrete Representations
- Angles
- Comparison Activities
- Use Concrete Representations
- Use Protractors
- Time
- Comparison Activities
- Reading Clocks
- Elapsed Time
- Money
- Common Challenges in Measurement
- Resources for Chapter 18
- The Meaning and Process of Measuring
- Chapter 19. Developing Geometric Thinking and Geometric Concepts
- A Progression for Developing Geometric Thinking
- The van Hiele Levels of Geometric Thought
- Implications for Instruction
- Shapes and Properties
- Concrete and Virtual Tools
- Sorting and Classifying
- Composing and Decomposing Shapes
- Categories of Two- and Three-Dimensional Shapes
- Construction Activities
- Applying Definitions and Categories
- Exploring Triangles
- Exploring Quadrilaterals
- Exploring Circles
- Conjectures and Proofs
- Transformations
- Symmetry
- Composition of Transformations
- Congruence
- Similarity
- Dilation
- Location
- Coordinate Plane
- Measuring Distance on the Coordinate Plane
- Visualization
- Two-Dimensional Imagery
- Three-Dimensional Imagery
- Common Challenges in Geometry
- Resources for Chapter 19
- A Progression for Developing Geometric Thinking
- Chapter 20. Developing Concepts of Data and Statistics
- What Does It Mean to Do Statistics?
- Is It Statistics or Is It Mathematics?
- The Process of Doing Statistics
- Anticipating Student Statistical Thinking
- Formulating Statistical Investigative Questions
- Classroom Questions
- Questions beyond Self and Classmates
- Data Collection
- Sampling
- Using Existing Data Sources
- Data Analysis: Classification
- Attribute Materials
- Data Analysis: Graphical Representations
- Graphs for Categorical Data
- Graphs for Numerical Data
- Bivariate Data
- Data Analysis: Center, Variability, and Shape
- Shape of Data
- Measures of Center
- Understanding the Mean
- Choosing a Measure of Center
- Variability
- Interpreting Results
- Resources for Chapter 20
- What Does It Mean to Do Statistics?
- Chapter 21. Exploring Concepts of Probability
- Introducing Probability
- Likely or Not Likely
- The Probability Continuum
- Theoretical Probability and Experiments
- Process for Teaching Probability
- Theoretical Probability
- Experiments
- Use of Technology in Experiments
- Probability of Compound Events
- Independent Events
- Dependent Events
- Simulations
- Student Assumptions Related to Probability
- Resources for Chapter 21
- Introducing Probability
- Chapter 22. Exploring Exponents, Negative Numbers, and Real Numbers
- Exponents
- Exponents in Expressions and Equations
- Order of Operations
- Exploring Exponents on the Calculator
- Integer Exponents
- Scientific Notation
- Positive and Negative Numbers
- Contexts for Exploring Positive and Negative Numbers
- Meaning of Negative Numbers
- Tools for Illustrating Positive and Negative Numbers
- Operations with Positive and Negative Numbers
- Addition and Subtraction
- Multiplication
- Division
- Real Numbers
- Rational Numbers
- Irrational Numbers
- Common Challenges Related to Exponents, Negative Numbers, and Real Numbers
- Resources for Chapter 22
- Exponents
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- X
- Y
- Z
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- Gerð : 208
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