Book title: Innummeracy: Mathematical Illiteracy and Its Consequences
Author: John Allen Paulos
The problem that resulted in this book is far-reaching: the public simply doesn't understand mathematics. Statistics, ranging from a 10%-off sale to the sort found in opinion polls, are unfathomable to the general populace. Probability, especially in the context of gambling, is understood by only a scant handful of people. The list of misunderstood mathematics is nearly endless.
In the first few chapters of the book, Paulos describes various issues that the innumerate (that is, those who don't understand numbers and math) often have issues understanding. He describes the issue to a reasonable level of detail, then derives answers for them. Don't let the use of the word 'derive' scare you off: the answers are readable and readily understandable to a general audience. In some cases, if you're really rusty, you might need to read them a second time to grasp the solution.
Later chapters, however, are not written for the innumerate. They are attempts to convince the reader that mathematical education needs to be improved. I think that everyone agrees that education should be improved, but he offers suggestions that are impractical or nonsensical.
Ultimately, the problem of this book is a lack of focus. Paulos could have written either a book that tackles basic mathematical issues that the general public doesn't understand, or he could have written a book that describes the consequences of innumeracy. He tried to do both, and stuffed both topics into a single slim volume. In doing so, he shortchanges both audiences. The result is a book that is good, but does not fully address the needs of anyone.
For me, this book was preaching to the choir. I have a maths degree, which I put to use more than I ever imagined. I am consistently amazed, and disappointed, to find out how many people cannot (or have convinced themselves that they cannot) perform basic mathematics. I am especially disappointed by the number of people who distrust statistics, but don't know how to evaluate the statistics that are presented to them. Questioning statistics is an excellent exercise, but simply questioning them because they are statistics and not questioning them on their
content or the methods used for reaching them is nothing short of ignorant.
personal website of John Allen
Paulos (complete with annoying animated gif of rotating dice)
archive of Paulos'
monthly 'Who's Counting' column for abcnews.com
Amazon's page about this book