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Discrete Mathematics Through Applications

(7-12)
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.

Content. The book includes the following chapters:
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.

Classroom Use. One teacher used it as a text for a course called ``Math in the Real World'', for students at the 11th- and 12th-grade level with poor mathematics backgrounds. Another used it as a text for a discrete mathematics course for grades 9-10, while another used a draft version for an 11th-grade discrete mathematics course.

Comments. A teacher who used it as a text, who felt that FAPP and Excursions were too abstract and notation-heavy for her students, said:
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.)

Next: Sources for Student Activities Up: Discrete Mathematics Textbooks Previous: Excursions in Modern Mathematics