Review: Innumeracy


Amazon.com had been recommending Innumeracy to me for many years, but after attending John Allen Paulos' presentation at the NCTM Annual Meeting in 2008 I decided it was time to buy. Unfortunately, just because I buy a book doesn't mean it gets read right away. Still curious and feeling guilty just letting it sit on my shelf, I decided it was worth part of my winter break to tackle this book.

Compared to technology (one of my other favorite subjects), the mathematical universe moves at a snail's pace. So while Innumeracy was written in 1988, almost all of it is still perfectly relevant today. People still misunderstand, avoid, and often fear mathematics, all of which leads to a personal and collective lack of intellectual power. Paulos fills the book with examples and does a nice job balancing the details of the mathematics involved with ease of reading. (A little experience with probability and the fundamental counting principle helps greatly. It sounds harder than it really is.) For example, Paulos presents this problem:

"A man is downtown, he's mugged, and he claims the mugger was a black man. However, when the scene is reenacted many times under comparable lighting conditions by a courte investigating the case, the victim correctly identifies the race of the assailant only about 80 percent of the time. What is the probability his assailant was indeed black?

Many people will of course say that the probability is 80 percent, but the correct answer, given certain reasonable assumptions, is considerably lower. Our assumptions are that approximately 90 percent of the population is white and only 10 percent black, that the downtown area in question typifies this racial composition, that neither race is more likely to mug people, and that the victim is equally likely to make misidentifications in both directions, black for white and white for black. Given these premises, in a hundred muggings occurring under similar circumstances, the victim will on average identify twenty-six of the muggers as black -- 80 percent of the ten who are actually black, or eight, plus 20 percent of the ninety who were white, or eighteen, for a total of twenty-six. Thus, since only eight of the twenty-six identified as black were black, the probability that the victim actually was mugged by a black given that he said he was is only 8/26, or approximately 31 percent!" (pp. 164-165)

Innumeracy is filled with such examples, enough to make me want to go back through the book a second time and turn some into lesson plans. Most of the examples relate to probability and statistics, because that's where innumerate people are hurt the most. Very few of us are hurt on a regular basis by a lack of calculus understanding, but data are everywhere and misinterpretations happen all the time.

My favorite chapter of the book, and the one of most interest to educators, is chapter 4, "Whence Innumeracy?" Paulos relates a story of his own childhood, where he was excited to work out some mathematics on his own, was shot down by his teacher, and then later learned he was right all along. Paulos goes on to criticize teachers and teacher education programs, claiming a lack of mathematical knowledge on the part of teachers deserves part of the blame for innumeracy. I, like many math teachers, can easily read this as one does about bad drivers: "Sure, there are a lot of bad drivers, but surely I'm not one of them." (Fortunately, I have some test scores that speak for my mathematical competency.) The importance of teacher competency and education programs has received more serious criticism as of late, but like I said, math moves slow, so it shouldn't be surprising (even if it is disappointing) to know that some things haven't changed much (or enough) in the 22 years since Innumeracy was first published. Paulos also targets the shortcomings of the learners of mathematics, addressing math anxiety and a lack of curiosity. Here's the most critical paragraph:

"Different from and much harder to deal with than math anxiety is the extreme intellectual lethargy which affects a small but growing number of students, who seem to be so lacking in mental discipline or motivation that nothing can get through to them. Obsessive-compulsive sorts can be loosened up and people suffering from math anxiety can be taught ways to allay their fears, but what about students who don't care enough to focus any of their energy on intellectual matters? You remonstrate: 'The answer's not X but Y. You forgot to take account of this or that.' And the response is a blank stare or a flat 'Oh, yeah.' Their problems are an order of magnitude more serious than math anxiety." (p. 120)

If you're a math teacher, you know that stare, or that response. It never says, "I understand." It usually says, "Go away," and for some students it's an automatic response, whether they want to understand or not. Fortunately, since 1988 a great deal of work has been done in math education to keep students more engaged with mathematical tasks.

Paulos followed up Innumeracy with a second book, Beyond Numeracy, which I also own but haven't yet read. He's also written a number of other books which are also occupying my shelves, and I hope to get to them all, although, with a semester starting in another week, it might have to wait until another break.

Read more reviews and buy at Amazon.com: Innumeracy: Mathematical Illiteracy and Its Consequences

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