Learning and Teaching Early Math: The Learning Trajectories Approach » (New Edition)

Douglas H. Clements is SUNY Distinguished Professor of Early Childhood, Mathematics, and Computer Education at the University at Buffalo, State University of New York.

Julie Sarama is an Associate Professor of Mathematics Education at the University at Buffalo, State University of New York.

In this important new book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help teachers become more effective professionals. By opening up new windows to seeing young children and the inherent delight and curiosity behind their mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying level of knowledge and thinking of their classes and the individuals within them as key in serving the needs of all children. In straightforward, no-nonsense language, this book summarizes what is known about how children learn mathematics, and how to build on what they know to realize more effective teaching practice. It will help teachers understand the learning trajectories of early mathematics and become quintessential professionals.

Preface ix

Acknowledgments xiii

1 Young Children and Mathematics Learning 1

2 Quantity, Number, and Subitizing 9

3 Verbal and Object Counting 19

4 Comparing, Ordering, and Estimating 43

5 Arithmetic: Early Addition and Subtraction and Counting Strategies 59

6 Arithmetic: Composition of Number, Place Value, and Multidigit Addition and Subtraction 81

7 Spatial Thinking 107

8 Shape 123

9 Composition and Decomposition of Shapes 149

10 Geometric Measurement: Length 163

11 Geometric Measurement: Area, Volume, and Angle 173

12 Other Content Domains 189

13 Mathematical Processes 203

14 Cognition, Affect, and Equity 209

15 Early Childhood Mathematics Education: Contexts and Curricula 233

16 Instructional Practices and Pedagogical Issues 255

Notes 293

References 295

Index 317