This 249-page book is a resource on problem-solving strategies for secondary mathematics teachers. It contains example problems with solutions based on ten problem-solving strategies.

The purpose of this book is to "examine 10 strategies that are widely used in problem-solving, both in mathematics and real-life situations" that "provide an alternate plan for resolving many problem situations that arise within the curriculum" (p. xv). The authors wrote this book "for the [secondary] classroom teacher who has a sincere desire to help students succeed as problem solvers both in mathematics and beyond" (p. xv).

Problem-Solving Strategies for Efficient and Elegant Solutions emphasizes the premise that problem solving is of paramount importance at all levels of mathematics instruction and focuses specifically on the secondary mathematics classroom. The authors hope to convince teachers that algebraic procedures are only one way to solve problems and that it is worthwhile to promote multiple problem-solving strategies with their students. Specifically, the book examines ten particular problem-solving strategies: working backwards; finding a pattern; adopting a different point of view; solving a simpler analogous problem; considering extreme cases; making a drawing or visual representation; intelligent guessing and testing; accounting for all possibilities; organizing data; and logical reasoning.

The book includes about 200 problems distributed evenly to illustrate these ten problem-solving strategies. Each of the problems is analyzed in a clear manner and solved in at least one way; many offer several solution approaches. The content of the problems is primarily number, algebra, or geometry. Many of the problems are considered classics and will be familiar to readers. Although the text has no large problem sets to share with students, there are reference lists with about 200 sources of problems together with 80 recommended readings on various facets of problem solving.

Each section of the book begins with a brief introduction to the particular strategy under consideration and then offers some real life applications of the strategy to illustrate the pervasiveness and usefulness of the technique. By offering several solutions for most of the problems, flexible thinking about problem solving is promoted and students with different learning styles may benefit. Although some of the problems may be too challenging for some students, a judicious choice of examples could be a valuable supplement to the curriculum and contribute much to the development of students' problem-solving skills.

This book has potential for both pre-service and in-service teacher development. It could be used as a supplementary text in a secondary mathematics methods course to promote discussion of problem solving or as a text in a formal course on problem solving. Reviewers recommended it as a useful adjunct not only for the development of the ten strategies it features, but also because it contains several problems with which future teachers should be familiar. The book could also be useful in seminars built around the practicum experience for pre-service secondary mathematics teachers, and offers a ready supply of problems that student teachers can include in their lesson plans. It is also a viable way to build in-service teachers' understanding of problem solving and skill in sharing problem-solving strategies and analysis with their students. Teachers in a school or in a district could come together and focus on a given set of strategies over several weeks.

One reviewer noted that a solid mathematics background is needed for instructors using this material with teachers.