In this short book, the author seeks to provide simple explanations for each concept that appears in primary and secondary school mathematics. The book’s coverage is extensive, including material on percents, exponents, logarithms, positional notation, probability, statistics, combinatorics, algebra, geometry, trigonometry, and calculus. The author’s premise is that students need to be given justifications in order to “turn school mathematics from a useless and unloved rote to vital and pleasing training in reasoning”. He believes that children in particular are troubled by their own lack of knowledge of these explanations because they realize that mathematics is reasoning-based. Over time, if this uneasiness is not resolved, a fear of the subject develops. A major secondary theme of the author in this book is to help the reader to overcome a fear of mathematics, to be “demathtified”.
Despite the author’s initial emphasis on how mathematics ought to be presented to children, the intended reader of this book is the adult student who has some awareness of all these concepts but does not feel connected to them. Such a reader is sometimes able to perform an isolated computation but does not feel confident drawing upon his or her base of mathematical knowledge to begin to process a random problem presented in some context. The author blames obscure terminology for turning people away from mathematics and for inhibiting the development of a reliable base of mathematical knowledge. Accordingly, one of his strategies in this book is to introduce terminology that makes the concepts more memorable. However, this point is overemphasized in my opinion. In every culture, there are people that readily absorb mathematics and there are people that are turned off by it. So, looking beyond the verbal terminology, the mathematical concepts themselves must also trigger reactions in people.
I found the verbal explanations of some of the mathematical concepts themselves to be far more valuable. Some of them are excellent and do help to clarify. The chapter on trigonometry is exceptionally well written. It is practical and relevant, and it ties together ideas from geometry and physics. The verbal derivations of the formulas for the area and the circumference of a circle are also outstanding. They are very intuitive, and they enable the reader to loosely approximate the value of π. On the other hand, the chapter on probability and statistics is not grounded well in computational techniques. It will only be helpful to students who are numerate enough to absorb and to follow mathematical applications given almost exclusively in words.
In general, the author does not provide enough examples with mathematical symbols to satisfy the needs of the intended reader. For such individuals with a shallow base of mathematical knowledge, the challenge of translating the words to mathematical notation is almost as daunting as the mathematical concepts themselves! For that reason, the most appropriate readers of this book are mathematics teachers. They will gain many insights from the verbal explanations and will be able to incorporate them into their own lesson plans. Moreover, they will be able to share ideas from this book with their colleagues in professional development workshops.
Jerry G. Ianni teaches at LaGuardia Community College.