Learning and Teaching Early Math: The Learning Trajectories Approach

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.

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.

Preface
Acknowledgments
1. Young Children and Mathematics Learning
2. Quantity, Number, and Subitizing
3. Verbal and Object Counting
4. Comparing, Ordering, and Estimating
5. Arithmetic: Early Addition and Subtraction and Counting Strategies
6. Arithmetic: Composition of Number, Place Value, and Multidigit Addition and Subtraction
7. Spatial Thinking
8. Shape
9. Composition and Decomposition of Shapes
10. Geometric Measurement: Length
11. Geometric Measurement: Area, Volume, and Angle
12. Other Content Domains
13. Mathematical Processes
14. Cognition, Affect, and Equity
15. Early Childhood Mathematics Education: Contexts and Curricula
16. Instructional Practices and Pedagogical Issues
Notes
References
Index