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Learning and Teaching Early Math: The Learning Trajectories Approach,9780415995924
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Learning and Teaching Early Math: The Learning Trajectories Approach



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Most everyone agrees that effective mathematics teaching involves "meeting the students where they are" and helping them build on what they know. But that is often easier said than done. In this important new book for pre-and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose what mathematics a child knows. 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. Book jacket.

Author Biography

Douglas H. Clements is SUNY Distinguished Professor of Early Childhood, Mathematics, and Computer Education at the University at Buffalo, State University of New York. Julie Sarama is an Associate Professor of Mathematics Education at the University at Buffalo, State University of New York.

Table of Contents

Prefacep. ix
Acknowledgmentsp. xiii
Young Children and Mathematics Learningp. 1
Quantity, Number, and Subitizingp. 9
Verbal and Object Countingp. 19
Comparing, Ordering, and Estimatingp. 43
Arithmetic: Early Addition and Subtraction and Counting Strategiesp. 59
Arithmetic: Composition of Number, Place Value, and Multidigit Addition and Subtractionp. 81
Spatial Thinkingp. 107
Shapep. 123
Composition and Decomposition of Shapesp. 149
Geometric Measurement: Lengthp. 163
Geometric Measurement: Area, Volume, and Anglep. 173
Other Content Domainsp. 189
Mathematical Processesp. 203
Cognition, Affect, and Equityp. 209
Early Childhood Mathematics Education: Contexts and Curriculap. 233
Instructional Practices and Pedagogical Issuesp. 255
Notesp. 293
Referencesp. 295
Indexp. 317
Table of Contents provided by Ingram. All Rights Reserved.

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