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.

part I|26 pages


chapter 1|26 pages

Early Childhood Mathematics Learning

part II|132 pages

Number and Quantitative Thinking

chapter 2|24 pages

Quantity, Number, and Subitizing

chapter 3|28 pages

Verbal and Object Counting

chapter 4|20 pages

Comparing, Ordering, and Estimating

chapter 5|28 pages


Early Addition and Subtraction and Counting Strategies

chapter 6|30 pages


Composition of Number, Place Value, and Multidigit Addition and Subtraction

part III|112 pages

Geometry and Spatial Thinking

chapter 7|38 pages

Spatial Thinking

chapter 8|48 pages


chapter 9|24 pages

Composition and Decomposition of Shapes

part IV|47 pages

Geometric Measurement

chapter 10|20 pages

Geometric Measurement, Part 1


chapter 11|24 pages

Geometric Measurement, Part 2

Area, Volume, and Angle

part V|30 pages

Other Content Domains and Processes

chapter 12|16 pages

Other Content Domains

chapter 13|12 pages

Mathematical Processes

chapter 14|20 pages

Professional Development and Scaling Up