Mathematics, a Human Endeavor

  (7-12)
Harold Jacobs; W.H. Freeman, 3rd Ed., 1994; $49.

Mathematics, A Human Endeavor was clearly a textbook ahead of its time. After going through its third revision in 1994, it is as popular today as a classroom text and a teacher resource as it was back in the late 60s. It is a recommended favorite of teachers in the Leadership Program in Discrete Mathematics. Much of the mathematics is connected to real world applications, and there are many science and mathematics connections. The book is jammed with problem-solving activities and ``What if ...?'' questions, and emphasizes mathematical thinking. It is also full of photos, drawings (e.g., from Escher), and mathematical cartoons (e.g., from Peanuts, BC, and The New Yorker). The following background is adapted from information provided to us by the publisher:

In the late 1960s, Harold Jacobs, teaching at Grant High School in Southern California, began exploring various mathematical applications for use in the classroom. He decided to write a textbook, something original, for those students who had not done well in mathematics. Neither the author or the publisher anticipated the response of instructors to the book when it was first published. Much to his surprise, Harold Jacobs found that he had taken the mathematical community by storm. And the author is still teaching students and finding ways to introduce them to the beauty of mathematics--to motivate them to see beyond its apparent difficulty. (W. H. Freeman, private communication.)

Content. Technically, this is not a ``discrete mathematics'' text, but many of the topics included are in fact discrete. The book has an eclectic list of topics, including the following.

• inductive and deductive reasoning;
• patterns and sequences (e.g., Fibonacci numbers);
• symmetry and regular polygons;
• combinations, permutations, and Pascal's triangle;
• probability and statistics;
• logic and puzzles;
• network (graph) problems--including Euler paths and trees.

Classroom Use. This book is most often used as a supplementary text or resource for bright 7-10th grade students, in a variety of courses, including mainstream 7th- or 8th-grade mathematics. (One 8th-grade teacher's students requested that she use the book all the time instead of their regular text.) One teacher used it in an Applied Mathematics course, which also included computing. Another used it for students off the ``calculus track''; the course proved to be popular enough that ``on-track'' students took it as well. Other teachers have used it as a resource for themselves.

Comments. This book invariably draws enthusiastic comments from teachers. One comment was especially strong:

I've been using this book for over 20 years. I've used it for a senior elective for college-bound students who have had a rough time with the traditional SAT curriculum. I've used several topics in a general math class (inductive reasoning, sequences, combinatorics, elementary probability). I've used activities from it in traditional courses (functions, conics, logs). No matter what school I teach in, I make sure that I have a classroom set of this book. (Marilyn Goldfarb LP `93), private communication.)

The following are comments from other teachers who have used this text.

• A wonderful all-around reference. Perfect for self-teaching. Good combinatorics section.
• This is my favorite math text book.
• A ``must'' for every library.
• It was written with ``people who don't like math'' in mind. It has a nice tone, develops the topics nicely, and goes into some depth.
• The supplemental transparency package is a definite ``keeper.'' The material in it is excellent.