1st Edition

Learning and Teaching Early Math The Learning Trajectories Approach

By Douglas H. Clements, Julie Sarama Copyright 2009
    344 Pages
    by Routledge

    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.



    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





    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.

    "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