Mary Hynes-Berry is a bestselling author, professional developer, consultant, and a faculty member at Erikson Institute for Early Childhood. Jie-Qi Chen is a professor of early education at the Erikson Institute in Chicago and founder of the Institute's Early Math Collaborative. Barbara Abel is an experienced early childhood leader and clinical lecturer at the University of Illinois Chicago.

• ContentsPreface vAcknowledgments vii1. The WHAT, WHO, and HOW of Mathematical Worlds of Infants and Toddlers 1WHAT: Understanding the Concept and Practice of Precursor Mathematics 2What the Research Says: The Brain Develops Significantly in the First Three Years 5WHO: Infants and Toddlers and Their Conceptual Development 7What the Research Says: The Critical Role of Nurturing 8HOW: Closely Attend and Intentionally Respond—The CAIR Principle 11Looking Back to Look Forward 142. The Precursor Math Concept of Attribute 15WHAT: Where’s the Math in Attribute? 15What the Research Says: Categories of Attribute 18WHO: Infants and Toddlers Developing Understanding of Attribute 19What the Research Says: Sensory Perceptions and Social-Emotional Responses 21HOW: Using CAIR to Develop Understanding of the PMC of Attribute 22Looking Back to Look Forward 27YOUR TURN: Reflective Practice Review 283. The Precursor Math Concept of Comparison 30WHAT: Where’s the Math in Comparison? 30What the Research Says: Infants and Toddlers Are Born Mathematicians/ Statisticians 33WHO: Infants and Toddlers Developing Understanding of Comparison 34What the Research Says: Object Terms and Relational Terms 37HOW: Using CAIR to Develop Understanding of the PMC of Comparison 38Looking Back to Look Forward 44YOUR TURN: Reflective Practice Review 444. The Precursor Math Concept of Change 46WHAT: Where’s the Math in Change? 46What the Research Says: Spatial Sense Is Where Math Begins 50WHO: Infants and Toddlers Developing Understanding of Change 52What the Research Says: It’s Not Surprising That Change Triggers Thinking 54HOW: Using CAIR to Develop Understanding of the PMC of Change 55Looking Back to Look Forward 59YOUR TURN: Reflective Practice Review 605. The Precursor Math Concept of Pattern 62WHAT: Where’s the Math in Pattern? 62What the Research Says: Where Is the Pattern in the Number World? 66WHO: Infants and Toddlers Developing Understanding of Pattern 68What the Research Says: Where’s the Math in Music? 71HOW: Using CAIR to Develop Understanding of the PMC of Pattern 72Looking Back to Look Forward 75YOUR TURN: Reflective Practice Review 766. Bringing It All Together 78Bringing Together the Four Precursor Math Concepts—the WHAT 79Bringing Together WHO and HOW 82Bringing Together the WHAT, WHO, and HOW of Mathematical Thinking in Early Childhood 87YOUR TURN: Bringing It All Together 90References 93Index 100About the Authors 104

Mary Hynes-Berry is a bestselling author, professional developer, consultant, and a faculty member at Erikson Institute for Early Childhood. Jie-Qi Chen is a professor of early education at the Erikson Institute in Chicago and founder of the Institute's Early Math Collaborative. Barbara Abel is an experienced early childhood leader and clinical lecturer at the University of Illinois Chicago.

• ContentsPreface vAcknowledgments vii1. The WHAT, WHO, and HOW of Mathematical Worlds of Infants and Toddlers 1WHAT: Understanding the Concept and Practice of Precursor Mathematics 2What the Research Says: The Brain Develops Significantly in the First Three Years 5WHO: Infants and Toddlers and Their Conceptual Development 7What the Research Says: The Critical Role of Nurturing 8HOW: Closely Attend and Intentionally Respond—The CAIR Principle 11Looking Back to Look Forward 142. The Precursor Math Concept of Attribute 15WHAT: Where’s the Math in Attribute? 15What the Research Says: Categories of Attribute 18WHO: Infants and Toddlers Developing Understanding of Attribute 19What the Research Says: Sensory Perceptions and Social-Emotional Responses 21HOW: Using CAIR to Develop Understanding of the PMC of Attribute 22Looking Back to Look Forward 27YOUR TURN: Reflective Practice Review 283. The Precursor Math Concept of Comparison 30WHAT: Where’s the Math in Comparison? 30What the Research Says: Infants and Toddlers Are Born Mathematicians/ Statisticians 33WHO: Infants and Toddlers Developing Understanding of Comparison 34What the Research Says: Object Terms and Relational Terms 37HOW: Using CAIR to Develop Understanding of the PMC of Comparison 38Looking Back to Look Forward 44YOUR TURN: Reflective Practice Review 444. The Precursor Math Concept of Change 46WHAT: Where’s the Math in Change? 46What the Research Says: Spatial Sense Is Where Math Begins 50WHO: Infants and Toddlers Developing Understanding of Change 52What the Research Says: It’s Not Surprising That Change Triggers Thinking 54HOW: Using CAIR to Develop Understanding of the PMC of Change 55Looking Back to Look Forward 59YOUR TURN: Reflective Practice Review 605. The Precursor Math Concept of Pattern 62WHAT: Where’s the Math in Pattern? 62What the Research Says: Where Is the Pattern in the Number World? 66WHO: Infants and Toddlers Developing Understanding of Pattern 68What the Research Says: Where’s the Math in Music? 71HOW: Using CAIR to Develop Understanding of the PMC of Pattern 72Looking Back to Look Forward 75YOUR TURN: Reflective Practice Review 766. Bringing It All Together 78Bringing Together the Four Precursor Math Concepts—the WHAT 79Bringing Together WHO and HOW 82Bringing Together the WHAT, WHO, and HOW of Mathematical Thinking in Early Childhood 87YOUR TURN: Bringing It All Together 90References 93Index 100About the Authors 104

Mary Hynes-Berry is a bestselling author, professional developer, consultant, and a faculty member at Erikson Institute for Early Childhood. Jie-Qi Chen is a professor of early education at the Erikson Institute in Chicago and founder of the Institute's Early Math Collaborative. Barbara Abel is an experienced early childhood leader and clinical lecturer at the University of Illinois Chicago.

• ContentsPreface vAcknowledgments vii1. The WHAT, WHO, and HOW of Mathematical Worlds of Infants and Toddlers 1WHAT: Understanding the Concept and Practice of Precursor Mathematics 2What the Research Says: The Brain Develops Significantly in the First Three Years 5WHO: Infants and Toddlers and Their Conceptual Development 7What the Research Says: The Critical Role of Nurturing 8HOW: Closely Attend and Intentionally Respond—The CAIR Principle 11Looking Back to Look Forward 142. The Precursor Math Concept of Attribute 15WHAT: Where’s the Math in Attribute? 15What the Research Says: Categories of Attribute 18WHO: Infants and Toddlers Developing Understanding of Attribute 19What the Research Says: Sensory Perceptions and Social-Emotional Responses 21HOW: Using CAIR to Develop Understanding of the PMC of Attribute 22Looking Back to Look Forward 27YOUR TURN: Reflective Practice Review 283. The Precursor Math Concept of Comparison 30WHAT: Where’s the Math in Comparison? 30What the Research Says: Infants and Toddlers Are Born Mathematicians/ Statisticians 33WHO: Infants and Toddlers Developing Understanding of Comparison 34What the Research Says: Object Terms and Relational Terms 37HOW: Using CAIR to Develop Understanding of the PMC of Comparison 38Looking Back to Look Forward 44YOUR TURN: Reflective Practice Review 444. The Precursor Math Concept of Change 46WHAT: Where’s the Math in Change? 46What the Research Says: Spatial Sense Is Where Math Begins 50WHO: Infants and Toddlers Developing Understanding of Change 52What the Research Says: It’s Not Surprising That Change Triggers Thinking 54HOW: Using CAIR to Develop Understanding of the PMC of Change 55Looking Back to Look Forward 59YOUR TURN: Reflective Practice Review 605. The Precursor Math Concept of Pattern 62WHAT: Where’s the Math in Pattern? 62What the Research Says: Where Is the Pattern in the Number World? 66WHO: Infants and Toddlers Developing Understanding of Pattern 68What the Research Says: Where’s the Math in Music? 71HOW: Using CAIR to Develop Understanding of the PMC of Pattern 72Looking Back to Look Forward 75YOUR TURN: Reflective Practice Review 766. Bringing It All Together 78Bringing Together the Four Precursor Math Concepts—the WHAT 79Bringing Together WHO and HOW 82Bringing Together the WHAT, WHO, and HOW of Mathematical Thinking in Early Childhood 87YOUR TURN: Bringing It All Together 90References 93Index 100About the Authors 104