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.

Julie Sarama is Distinguished University Professor, Kennedy Endowed Chair in Innovative Learning Technologies, Co-Executive Director of the Marsico Institute of Early Learning at the University of Denver, Denver, CO, USA.

Douglas H. Clements is Distinguished University Professor; Kennedy Endowed Chair in Early Childhood Learning; Executive Director, Marsico Institute of Early Learning at the University of Denver, Denver, CO, USA.

Preface

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

8. Shape

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

Notes

References

Index