What is infinitely sad is that the very people who need this book the most are the ones who most likely get their reading from the super market checkout line. I hear this type all the time...."Hey, Marge, look at this bat-baby." Even some of the reviewers who would be most prone to pick up a book like this complain at the "difficult" nature and condescending attitude. So what is the answer - do we leave them blissfully unaware of their stupidity? Gardner answers with a decided, "No" and this is the result - a splendid accomplishment.
Yet there is very little by way of addressing the problem - some of us "innumerates" got to be that way from bad experiences in school; others have an irrational fear of numbers, some just struggle with the abstractness of mathematics; in any case, it would have been helpful had some concrete solutions been presented.
Nonetheless I found the book written with humor and wit - for a book about numbers, it was not dry, but rather fascinating. Too bad it seems that it reaches a rather narrow audience.
Many of Paulos' examples are engaging or even amusing. However, the book wasn't quite what I was expecting, given its title. For me, a word like `innumeracy' sounds like `illiteracy', so I thought the book would be about people who are unable to do simple everyday math, and the consequences of this problem. For example, what about people who can't balance a checkbook, who go to a sale and can't determine whether $100 off or 15% off of a $1000 purchase is a better deal, who can't estimate how it will take them to drive 30 miles at 65 mph? To me, these people are truly the `innumerate', and the consequences of their ignorance are far more serious for them and for society than the people Paulos rails against. Paulos doesn't discuss such problems at all. Instead, he complains about people's irrational interpretations of probability, such as when people avoid travel because of fear of a terrorist attack, but think nothing of the much greater probability of injury or death while commuting in their cars every day.
Paulos points out the large differences in the probabilities of engaging in activities such as these, and he seems to expect that "numerate" people should calculate the corresponding probabilities and act logically, like computers. He seems to miss the really interesting point- -why do people act the way they do? Why do they persist in irrational behavior when they know the numbers? At one point, Paulos does describe some psychology research, in which investigators found that given exactly the same odds, people are more likely to take risks in order to avoid loss, and less likely to take risks in order to gain something. But in the rest of Paulos' examples, he simply describes the irrational behavior of humans, and assumes that the irrational behavior is due entirely to a lack of an ability to deal with numbers, rather than having a deeper psychological explanation. One example of "innumerate" behavior that Paulos cites is a sports writer, who suggests that a baseball manager could create the perfect team by trying out every possible combination of players and positions on the team until he finds the optimal combination. As Paulos points out, when you calculate the number of possible combinations in this case, it would be so high that the players would be dead long before the trials were over. But ordinary people, who aren't necessarily `innumerate', understand what the journalist meant- -that the manager should try out only those possible combinations that make sense, and to use his intuition to try out the more likely possibilities first. By using intellect and intuition, the manager might be able to complete the task in a few seasons, perhaps. This ability is quite fascinating, but after dismissing the mathematical absurdity of following the suggestion literally, Paulos does not go on to investigate what was actually meant, or how people can hone in on good choices and reject bad ones out right in such a situation.
In his blame-assigning section, Paulos goes as far as to suggest that elementary schoolteachers and university professors should be required to exchange places for a few weeks every year. Paulos suggests that the schoolteachers would improve their math skills by learning from the university students in the classes they would take over, and that the professors would make classroom math fun for elementary students by bringing in games and such. Get real! I'm sorry, but it is the schoolteachers who bring to the classroom creative approaches to teaching math, not university professors. When was the last time you ever heard of a university professor playing games in math class? The vast majority of them simply stand at the board with a piece of chalk and write out example problems and solutions for students to copy in their notebooks. It's no wonder that many of the schoolteachers, who were supposed to learn math in college, didn't master the skills they needed. What is really needed is better math instruction at the tertiary level for elementary school teachers, who are in general, very good teachers, even if their math skills may be weak.
All in all, while this book is occasionally interesting, it is much more a discussion of probability and statistics and how people choose to interpret them rather than a discussion of a general lack of math skills in society.
If you are earnestly interested in learning some practical math yet utterly uninitiated in numerical ways this may be the book for you. If, however, you are firmly stuck in your innumerate ways, I doubt that this book is compelling or shocking enough to convince you otherwise. If you are numerate, but curious about how the other half lives, you will need to manage bouts of boredom sitting in the choir while Paulos preaches. I mostly fall into the last catergory, yet I managed to find some revelations and some interesting bits here and there. Also, the author has a friendly, conversational style with a touch of irreverance -- I appreciate that.
Yet I nearly gave up on this book before I reached the halfway point, and I RARELY give up on books. What pulled me through is the author's excellent advice from the foreword: feel free to skip the bits that are too complicated for the novitiate or too obvious for the adept. A generous gift from the author -- take advantage of it and you will enjoy the book all the more. :)
This book focuses heavily on statistics although it does touch on a number of other flavors of math, including fractions and magnitudes. Still, the best concrete examples come from stats, yet I am sure that better books must exist for providing the "gee-whiz! I didn't realize what a boob I was for not realizing X, Y and Z about real life statistics" revelations that may shake the sluggish right brain of the innumerate. This book has the advantage of being thin, though, and it does fit nicely into one's pocket. ;) The book also comments on potential social factors that turn budding math whizzes into the innumerate masses -- I didn't expect it, and it is refreshing.
Some notes to be fair. 1) There are many, many interesting examples (a là Paulos: (more than 20 per chapter) * (5 chapters) = (more than 100 examples overall)). 2) Many of these numerous examples are Paulos' own (including the stock newsletter scam above, I believe). 3) At the time of initial print (1988) the examples evidently were not as well publicized as now (2003).
If you haven't heard any of the examples above and never read any Paulos publications, then the book will be of value to you, especially given Paulos' clean exposition and wit. On the other hand if you've either read some other book by Paulos or heard of any such examples then you might be better off reading his monthly column on ABCNews at http://abcnews.go.com/sections/science/whoscounting_index/whoscounting_index.html.
