Nancy Crisler, Patience Fisher, and Gary Froelich;

W. H. Freeman (for COMAP), 1994; $36.

This book was developed to fill the need for a high-school level
discrete mathematics text [8]. It is addressed to
the student, and is less sophisticated mathematically
than either FAPP or *Excursions*. Teachers of students in
grades 7-9 (or average students in grades 10-12) have been very pleased
with it; but teachers of more advanced students have found it
less useful. Overall, the comments on this book
have been more mixed than those on the previous three. However,
the book can provide a good introduction for a teacher who has not
seen discrete mathematics previously.

- 1.
- Election Theory;
- 2.
- Fair Division;
- 3.
- Matrix operations and applications;
- 4.
- Graphs and applications;
- 5.
- Recursion.

Each chapter begins with a group exploration and a set of exercises to introduce the topic. This is followed by short lessons and exercises. In another article in this volume [8], the authors give more detail on the content and development of the text.

It's an excellent book. It's very concrete, interesting, and to the point. Starting with the first chapter, where there's an election activity on soda preferences, there are many good activities that involve the students. The exercises are conducive to group work, and range from very basic to challenging. (Diane DePriest LP `93, private communication.)She supplemented the text with logic puzzles, and material on permutations and combinations which she created.

A teacher who chose *not* to use the book for a
12th-grade course felt
that it ``looked too easy,'' and feared it could have a
``bad effect on the reputation of the course.''
A college faculty member was disappointed that the book ``does not
point out where the mathematical structure is,'' and does not do more
``summing up'' of the mathematics topics learned.

On the other hand, an elementary school teacher advises teachers of elementary or middle grades to use the text:

It lends itself best of all the texts to adapting ideas to the elementary and middle grades. Also, the instructor's manual is user-friendly for teachers who are not familiar with discrete math, and would otherwise be afraid to try it. I also encourage them to order the COMAP modules on graphs. (Penni Ross LP `94, private communication.)