ABSTRACT

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.

chapter 1|8 pages

Young Children and Mathematics Learning

chapter 2|10 pages

Quantity, Number, and Subitizing

chapter 3|24 pages

Verbal and Object Counting

chapter 4|16 pages

Comparing, Ordering, and Estimating

chapter 5|22 pages

Arithmetic

Early Addition and Subtraction and Counting Strategies

chapter 6|26 pages

Arithmetic

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

chapter 7|16 pages

Spatial Thinking

chapter 8|26 pages

Shape

chapter 9|14 pages

Composition and Decomposition of Shapes

chapter 10|10 pages

Geometric Measurement

Length

chapter 11|16 pages

Geometric Measurement

Area, Volume, and Angle

chapter 12|14 pages

Other Content Domains

chapter 13|6 pages

Mathematical Processes

chapter 14|24 pages

Cognition, Affect, and Equity

chapter 15|22 pages

Early Childhood Mathematics Education

Contexts and Curricula