This book is amazing. Written by Harold R. Jacobs almost 50 years ago, it is a blessing that the content will not likely become out-dated. It presumes nothing more than fluency with arithmetic from the learner, but covers a range of topics that span pre-algebra to advanced algebra. The subtitle is “A Textbook For Those Who Think They Don’t Like The Subject”, but in my opinion it is simply a textbook for everyone (including those who think they don’t like the subject!)
First and foremost, this book goes beyond interesting into downright fascinating. It takes the learner on a safari of mysterious patterns, both in abstract and in nature. It unveils the beauty of geometric solids and mathematical curves. It inspires awe in large numbers, and delight in mathematical tricks.
Despite all this depth, it is accessible. The chapters are short and the prose is comfortable and inviting to read. Much of the instruction happens in the well-crafted exercises. The learner is allowed to discover many concepts for themselves, so that the learning feels more like inquiry than instruction.
The treatment of logarithms in the fourth chapter is particularly impressive. In my years as a tutor I have often needed to provide mathematical triage to learners who become hopelessly confused by this or the other explanation of logarithms. This book puts to rest any question of whether logs can be explained in a clear and intuitive manner. The author draws on the learners comprehension of arithmetic and geometric series and gradually leads the learner through the use of logarithmic patterns and functions without introducing the obscuring notation until the concept is solidly established.
The book is also filled with “experiments” which range from abstract inquiries to mathematical arts and crafts. I opened the book expecting to build a class around it, only to find that the class is already built. All we need is some graph paper, compasses, rulers and a room full of minds ready to learn!
