Learning and Teaching Early Math: The Learning Trajectories Approach, 1st Edition (Hardback) book cover

Learning and Teaching Early Math

The Learning Trajectories Approach, 1st Edition

By Douglas H. Clements, Julie Sarama


330 pages

Purchasing Options:$ = USD
Hardback: 9780415995917
pub: 2009-03-12
eBook (VitalSource) : 9780203883389
pub: 2009-04-01
from $117.00

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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.


"This state-of-the art book makes an invaluable contribution to our understanding of this vital component of early childhood practice and to the children who will benefit from its publication."--Young Children (NAEYC), March 2010

"What math is most important for young learners? What concepts and skills are foundational for their reaching the next level of math understanding? And how can teachers help children grasp each new idea and remain enthusiastic about math? These are the key questions in this incredibly valuable book from Doug Clements and Julie Sarama. For each topic area, they clearly describe the developmental path, or "learning trajectory," along which children move to develop mathematical concepts and skills. And they offer evidence-based guidelines and instructional activities in an engaging, straightforward way that reflects their deep respect for and understanding of what teachers do."--Carol Copple, Director, Publications and Initiatives in Educational Practice National Association for the Education of Young Children

"Learning and Teaching Early Math: The Learning Trajectories Approach is a required text for any early mathematics educator, professional developer, early childhood teacher or researcher. The domain-specific learning trajectories that outline developmental progressions provide information that has been missing from professional development resources. In addition, the instructional tasks aligned with each level provide practical suggestions for the teacher. Clements and Sarama have given us a comprehensive, research-based, rich resource… one that will make a difference to the mathematics learning of the young child!"--Juanita Copley, Professor Emeritus, University of Houston

Table of Contents



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




About the Authors

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.

About the Series

Studies in Mathematical Thinking and Learning Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
EDUCATION / Elementary
EDUCATION / Teaching Methods & Materials / Mathematics