Preface
Acknowledgements
1. Foundations, Myths and Standards
Equity for Every Child
Serving Children in Inclusive Settings
The Child Who Is Gifted
The Child with Learning Disabilities
The Child Who Is Cognitively Disabled (Children with Mental Retardation)
Where We Are Going
The NCTM Process Standards
The NCTM Focal Points 2006
Models and Modeling Perspectives
Developmentally Appropriate Education: Creating the Best Learning Environment
Piaget, Vygotsky, Bruner, and Dienes
Summary
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Links to Technology
References
2. Planning for Success: A Good Beginning.
How Do I Get Started?
Manipulatives in the Classroom
Your Attitude and Math Anxiety
How Can I Involve Parents in My Program?
What Should I Do if My Students Have Had Only Rote Math Background?
How Can I Meet the Needs of Children from Diverse Backgrounds?
How Can I Use Technology to Enhance Learning?
Planning for Computer-Assisted Instruction
Choosing Appropriate Software
Planning for Calculators
Summary
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Links to Technology
References
3. Assessment
International Results
Boys versus Girls
Formal and Informal Interviews
Assessment and Evaluation Defined
Curriculum Reform and Alignment
Assessment Strategies
Scoring Methods
Alternatives for Students in Inclusive Settings
Record Keeping
Summary
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
References
4. The Language of Math: Communication and Representation
Developing Math and Language Using Song and Verse
Developing Math Language through Children's Literature
Story Telling as Cultural Art Form
Math Language and Older Children
Math Concepts Found in the Early Childhood Curriculum
Representation: The Symbols of Math
The Number Sentence
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Classroom Equipment
Related Children’s Literature
Links to Technology
References
5. Early Math Concepts: Matching, Classification, Comparing, and Ordering or Seriation
Matching
Matching: Informal Learning around Home and School
Assessment of Matching Abilities
Early Classification—Creating Sets
Children and Sets: Informal Learning around Home and School
Pose a Problem to the Whole Class: Sets
Pose a Problem: Complex Classification
Comparing
Comparing: Informal Learning around Home and School
Ordering or Seriation
Ordering or Seriation: Informal Learning around Home and School
Pose a Problem: Assessment of Relationships Involving Ordering
Summary
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Related Children’s Literature
References
6. Developing Number Sense
A Cultural Perspective
Children’s Literature, Art, and Counting
Counting: The Young Child Plays and Learns
Research and Today's Classroom
Piaget's Tests of Conservation
Guided Learning Activities
Counting-On Activities
Counting-Back Activities
From Counting to Part-Part-Whole Activities
Thinking in Groups
Reading and Writing Numerals
Fractions and Number Sense
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Classroom Equipment
Related Children’s Literature
Related Music and CDs
Links to Technology
References
7. Understanding Our Place Value System
A Brief History of Base-Ten
The Unique Features of the Base-Ten System
Multiple Conceptions of Place Value
Children's Unstructured Strategies
Experts Differ on the Use of Manipulatives
Trading Games
Teaching with Bean Sticks or Base-Ten Blocks
Teaching with the Abacus and Money
Estimating and Rounding: When Approximate is Good Enough
Assessing Children's Understanding of Place Value
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Classroom Equipment
Related Children’s Literature
Links to Technology
References
8. Graphing
Topics for Graphing Experiences
The Challenge in Reading Graphs
The Graphing Questions
Early Experiences with Graphing
Choosing Categories That Avoid Hurt Feelings or Wanting to Be on the Winning Side
Probability
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Related Children’s Literature
Links to Technology
References
9. Early Algebra: Pattern and Function
Pattern
Pattern in Music and Art
Functions in the Primary Grade Classroom
Early Algebra
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Related Children’s Literature
References
10. Problem Solving—Addition and Subtraction
Math Is Problem Solving
A Real Problem
Choices of Problems
Problem Posing: Cognitively Guided Instruction
A Positive Environment: Cognitively Guided Instruction
General Strategies
Cognitive Background Information for Teachers: Classes of Problems.
Rules of Operation
Helping Children Write Their Own Problems
Using What Children Know to Learn the Facts
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Classroom Equipment
Related Children’s Literature
Links to Technology
References
11. Problem Solving—Multiplication and Division
Definition
Readiness for Multiplication and Division
Children's Natural Strategies
Cognitive Background for Teachers: Classes of Problems
Remainders
Illustrations
Linking Problem Solving to Symbolic Representation
Rules of Operation
The Role of Zero
Helping Children Write Their Own Problems
Learning the Multiplication Facts
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Related Children’s Literature
Links to Technology
References
12. Geometry: Space and Shape
Space: The Art of Blockbuilding
Assessment of Spatial Relationships
The Art of Block Building
Blocks for Girls as Well as Boys
Shape
Shape: Informal Learning around Home and School
Planning Activities about Shape
Assessment of Shape
Geometric Concepts in the Early Grades
The NCTM 2000 Geometry Standards
The van Hiele Model
Precise Language
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Related Children’s Literature
Links to Technology
References
13. Measurement.
Definition
Principles of Measurement
The General Method
The Young Child Plays and Learns
Two Measurement Systems
Difficulties in the Measurement Process
The Development of Mathematical Thinking About Length
Guided Learning—Physical Quantities
Guided Learning—Non-Physical Quantities
Summary
Ready-Set-Math
Fieldwork – Clinical Log or Math Journal
Activities and Study Questions
Related Children’s Literature
Related Music and CDs
Links to Technology
References
14. Thematic Units
All about Bears (Preschool)
The Circus (Preschool-Kindergarten)
Insects (Preschool-Kindergarten)
Peter Rabbit (First and Second Grade)
Appendix A: The NCTM Focal Points 2006
Appendix B: Classroom Equipment
Appendix C: The More or Less Game
Appendix D: Algebraic Solution
Appendix E: Glyph Clowns
Appendix F: Ten Strips
Appendix G: Dot Cards
Appendix H: The 5 Frame, The 10 Frame and the Double Frame
Appendix I: Bear Pong
Appendix J: First Grade Mathematics Informal Assessment
Appendix K: Bingo Card
Appendix L: One Hundred Chart
Appendix M: A Curriculum Web
Index