Learning Through Problems: Number Sense and Computational Strategies/A Resource for Primary Teachers

Read a sample chapter from Learning Through Problems (requires Adobe Acrobat Reader)!

Learning Through Problems describes a powerful approach to mathematics instruction that honors children's thinking and sense-making ability. Too often, the strands of mathematics (addition, subtraction, place value, and problem solving) are viewed as isolated topics. Paul Trafton and Diane Thiessen weave these strands together and offer a wide variety of contexts for genuine mathematical exploration.

While grounded in solid theory, Learning Through Problems is above all a practical resource, based on many years of field testing. The book takes you into classrooms where students value challenges, reflect on their work, and participate in thoughtful discussions with their classmates. Throughout the book, classroom teachers reflect on their experiences and offer suggestions on a comprehensive range of issues, including how to get started, where to find good problems, when to provide help, when to step back, where manipulatives fit in, how to integrate problem solving into the curriculum, and how to assess students' learning.

The book also shows how number sense and computation can be learned within a problem-centered framework. Thus, understanding and skills develop as mutually supporting aspects through a single approach. They do not have to be dichotomous. Numerous classroom examples and teacher observations provide guidance in developing both invented and familiar computational approaches.

In addition to providing valuable information about the development of children's mathematical thinking, this book is an inspiring look at what students can accomplish when they are given the opportunity, time, and freedom to solve problems in ways that make sense to them.

Diane Thiessen is a professor in the mathematics department at the University of Northern Iowa. She has designed undergraduate and graduate mathematics education programs, authored elementary math methods textbooks, and worked as a member of the Evaluation of Mathematics Teaching group for the Professional Teaching Standards (NCTM, 1991). Paul Trafton was a professor in the mathematics department and Fellow in the Regent's Center for Early Developmental Education at the University of Northern Iowa. His long-term interest was in primary mathematics and led to his chairing the K-4 writing team of the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989).