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.
Author(s): Douglas H. Clements, Julie A. Sarama
Series: Studies in Mathematical Thinking and Learning
Edition: 1
Publisher: Routledge
Year: 2009
Language: English
Pages: 344
Cover......Page 1
Learning and teaching early math : the learning trajectories approach......Page 6
Contents......Page 8
Preface......Page 10
Acknowledgments......Page 14
1 Young Children and Mathematics Learning......Page 16
2 Quantity, Number, and Subitizing......Page 24
3 Verbal and Object Counting......Page 34
4 Comparing, Ordering, and Estimating......Page 58
5 Arithmetic: Early Addition and Subtraction and Counting Strategies......Page 74
6 Arithmetic: Composition of Number, Place Value, and Multidigit Addition and Subtraction......Page 96
7 Spatial Thinking......Page 122
8 Shape......Page 138
9 Composition and Decomposition of Shapes......Page 164
10 Geometric Measurement: Length......Page 178
11 Geometric Measurement: Area, Volume, and Angle......Page 188
12 Other Content Domains......Page 204
13 Mathematical Processes......Page 218
14 Cognition, Affect, and Equity......Page 224
15 Early Childhood Mathematics Education......Page 248
16 Instructional Practices and Pedagogical Issues......Page 270
Notes......Page 308
References......Page 310
Index......Page 332
