In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child's level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind young children's mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying levels of knowledge exhibited by individual students, which in turn allows them to better meet the learning needs of all children. Using straightforward, no-nonsense language, this book summarizes the current research about how children learn mathematics, and how to build on what children already know to realize more effective teaching.
This second edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics and become quintessential professionals.
Updates to the new edition include:
* Explicit connections between Learning Trajectories and the new Common Core State Standards.
* New coverage of patterns and patterning.
* Incorporation of hundreds of recent research studies.
Douglas H. Clements is the Kennedy Endowed Chair in Early Childhood Learning, Executive Director of the Marsico Institute of Early Learning and Literacy, and Professor at the University of Denver, USA. Julie Sarama is the Kennedy Endowed Chair in Innovative Learning Technologies and Professor at the University of Denver, USA.
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 Processs and Practices 14. Cognition, Affect, and Equity 15. Early Childhood Mathematics Education: Contexts and Curricula 16. Instructional Practices and Pedagogical Issues