Praise from Reviewers "I consistently get positive and constructive suggestions [from my students] on how the chapters will impact their future teaching." -Kathleen Cramer, University of Minnesota "Anchoring the text on NCTM standards and drawing from NAEYC and NCATE will place the text at an advantage over many other texts. The approach will work with my students." -Benjamin Ngwudike, Jackson State University Standards-based, practical guidance for teaching math in the early years Aligned to the NCTM Standards, this new edition of a trusted text encourages teacher candidates to create an active learning environment that fosters curiosity, confidence, and persistence in children learning mathematics. Author Susan Sperry Smith presents the three key ingredients for the successful acquisition of math in the early years: knowledge of important mathematical relationships, number sense, and the ability to solve problems. Through practical knowledge and applications, this book gives special attention to helping teachers foster these skills and ways of thinking to build student success from year to year.A collection of lesson ideas, blackline masters, and fieldwork and assessment activities provide resources for the classroom, and close ties to NCTM standards ensure that teachers are ready to facilitate young children's math learning in today's educational climate. New to this edition: *A completely reordered table of contents more closely follows the way professors use the book, with concepts such as planning and assessment in the opening chapters, explanation of math concepts such as number sense and place value in the middle, classroom applications and best practices in the later chapters, and discussions of thematic unit development in the final chapter. *Extensive coverage of the NCTM Focal Points-including a valuable reprint of the PreK-third grade focal points-guides teachers to implement appropriate curricula.*Expanded use of NCTM Process Standards deepens the book's presentation of effective instructional techniques.*Numerous children's work examples in sample lessons and discussion provide insight into students' mathematical thought processes.

Table of Contents

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