101 Great Ideas for Introducing Key Concepts in Mathematics: A Resource for Secondary School Teachers (2001) Posamentier, A. S. & Hauptman H. A. Sage Publications, Thousand Oaks, CA. (240 pages). Hardcover price $34.95. The book may be ordered from Sage Publications (800-818-7243) or through the on-line book companies.

The National Council of Teachers of Mathematics (2001) recommended an emphasis on fundamental mathematical concepts and essential skills for the purpose of giving all students a solid foundation in their preparation for work and citizenship, positive attitudes towards mathematics, and a sound conceptual basis for further study. This is no small task, but the authors of 101 Great Ideas for Introducing Key Concepts in Mathematics have provided a much-needed resource to aid in the accomplishment of these goals.

Posamentier and Hauptman (2001) provide fresh and invigorating ideas for presenting many key concepts in the secondary school curriculum. Suggested teaching ideas are presented in a manner that does not isolate induction year teachers and assumes no previous exposure to the particular lesson topic. At a time such as this, when many of our secondary mathematics teachers are teaching out of their field, sound mathematical resources such as this book are in high demand.

The ideas presented by the authors provide a myriad of resources that direct teachers away from an over reliance on algorithmic rote learning and toward a hands on inquiry based learning approach. Posamentier and Hauptman (2001) focus on developing a strong support for understanding these key issues. Each lesson centers upon the conceptual development of the student when confronting everything from understanding the product of two negative integers to understanding the law of cosines. The book is divided into five lesson strands:

Great emphasis is placed upon the role of multiple representations as a key to successful learning. Suggestions for using visual technologies such as the geometer sketchpad abound throughout the book. Additional emphasis is placed upon the use of ordinary items to help students make connections: for example, using a bow and arrow to demonstrate the concept of domain and range when introducing functions. Although many of the teaching units do recommend the use of concrete devices to help in the development of conceptual understanding, the authors often rely upon the tools (chalkboard and overhead projector) typically found within a mathematics classroom. This reliance is most profound in the trigonometry section. This section emphasizes the need for students to become proficient with symbolic manipulation.

The authors provide a focus upon historical origins of mathematics in an attempt to present students with an attractive learning environment. One lesson calls for an examination of the relationship that exists between the diameter and circumference of a circle. Historical information is provided documenting the use of in the Bible. This discussion can stimulate students' thinking and provide them with an incentive for learning. A rather humorous historical reference is made to Carl Friedich Gauss in a lesson focused upon developing formulas for the sum of an arithmetic progression. These examples demonstrate the authors' goal of providing context for the discussion of mathematical ideas.

Each lesson idea is designed as a stand-alone unit with the exception of the final five lessons. These lessons are combined forming a unit dealing with the factorial function x. Since each teaching idea is a stand-alone unit, the authors recommend that teachers choose selected lessons to attempt in the classroom. Once teachers have achieved a comfort level with the topical ideas they may add further units to the teaching repertoire.

Perhaps one of the most endearing characteristics of this text is the voice used by the authors. The book is written to appeal to all mathematics teachers. Teachers who are struggling with introducing these topical ideas will find the book to be written in such a way as to facilitate their understanding of the topics. The language is easy to understand and the book is very user friendly. In addition, those teachers who have a sound grasp upon these key concepts can find fresh ideas for teaching old concepts presented in a manner that is intellectual in design.