This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.
Table of Contents
Appreciation the Funding Agencies
Part I: Introduction
1. Early Childhood Mathematics Learning
Part II: Number and Quantitative Thinking
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
Part III: Geometry and Spatial Thinking
7. Spatial Thinking
9. Composition and Decomposition of Shapes
Part IV: Geometric Measurement
10. Geometric Measurement, Part 1: Length
11. Geometric Measurement, Part 2: Area, Volume, and Angle
Part V: Other Content Domains and Processes
12. Other Content Domains
13. Mathematical Processes
14. Professional Development and Scaling Up
Julie A. Sarama is an Associate Professor of Mathematics Education at the University at Buffalo, State University of New York.
Douglas H. Clements is Distinguished Professor of Early Childhood, Mathematics, and Computer Education at the University at Buffalo, State University of New York.
"Sarama and Clements’ landmark book provides a comprehensive review of psychological and educational research leading to new insights into young children’s mathematical learning and how it can be fostered. The authors’ "learning trajectories" approach blends a research-based appreciation of the developing child’s mathematical mind with practical educational goals and methods. The book is essential reading for all those with a deep interest in promoting an effective and enriched approach to early childhood mathematics education."
-- Herbert P. Ginsburg, Jacob H. Schiff Foundation Professor of Psychology and Education, Department of Human Development, Teachers College Columbia University