Innumeracy: Mathematical Illiteracy and Its Consequences

Rating: 0

John Allen Paulos

The goal of this book is to argue why people need to have a basic familiarity with mathematical concepts and quantities and to define what this "mathematical literacy" would involve. The technique that is used for this argument is primarily anecdotal. Paulos describes a variety of mathematical skill that he feels people need, and then gives evidence of the types of real-world problems that come up on a regular basis for non-mathematical people that they handle badly because they lack the mathematical skill in question. The structure is generally effective, and the writing is fun and easy to read. However, I don't entirely agree with the choices of what mathematical skills are fundamental, and in the cases where I disagree, I don't find the examples of why they are necessary compelling.

While Paulos doesn't talk about this until late in the book, one of the things that I really appreciated was the time he spent discussing why so many people aren't mathematically literate. His opinion is that most pre-college math classes are taught in the wrong way, focusing on computation and learning facts rather than on gaining an intuition for numbers and how they interact with each other. He also touches on factors contributing to math phobia and the lack of social stigma to being unable to handle mathematics as compared to the stigma of being unable to read. I think that many of the examples that he gives in this book to explain why mathematics is important would be useful to show to math students, either as motivation or even converted into exercises to solve on their own. Hardly any of his examples require math beyond arithmetic.

There are a small number of basic mathematical skills/concepts that Paulos focuses on. These include statistics, probability, basic logic, and quantity estimation. In general, I agree that mathematical literacy should include an understanding of these concepts. Statistics in particular pop up everywhere, from advertising to news to risk information on medications and most people don't know how to evaluate those statistics. Probability is hard to get an intuition for initially, particularly when it comes to understanding how to combine probabilities, and it comes up in many of the same places that statistics do. I thought that these sections of the book were nicely done. The section covering logic (really, implication) was brief but also useful. The difference between causation and correlation isn't that hard to understand, but I don't remember explicitly learning about it in school.

The criticism I have of Paulos is his focus on gaining intuition for mathematical quantities. He isn't just talking about estimation, particularly as it is taught in school where you basically learn how to do arithmetic after rounding. He wants students to also be comfortable with what I've always thought of as "stupid estimation games" - things like "What is the volume of all human blood in the world?" or "How long would it take dump trucks to cart away...Mount Fuji, to ground level?" No, the answer isn't "Who cares?" Paulos feels that these are simple problems that that if you aren't able to solve them you don't have a good basic grasp of quantity. My reaction is that I can have a perfectly fine grasp of quantity but not have a good knowledge of trivia such as how much blood is in a human body or how big a mountain is. Both of these come down to not being able to come up with any starting numbers on which to base my estimations.

Now, there are two points to this objection. One is that not being able to come up with base figures doesn't have much to do with a knowledge of quantity, but rather has to do with not knowing about some external, non-mathematical object. So, even if you think that people should have intuitions for the size of a mountain, that isn't a mathematical literacy issue. It is, perhaps, a cultural literacy issue. But my second point is that I don't agree that these are valuable facts to know. I can go along with Paulos that people should be able to, given a question like the above, figure out what one or two simple facts they could reduce the question down to and, given those facts, how they would combine to give you an estimate. I'll continue from there to say that you should also be able to figure out, if the fact you originally reduce to isn't available, what other fact you could look up that would allow you to get the result. Basically, being able to relate quantities to each other without getting hung up on preciseness. But I don't see the necessity of having an intuition for quantities that don't impact my life. And I don't feel that Paulos gives an argument for that necessity.

Overall, I guess I give this a '0'. Not a lot here that was new to me, though the presentation of it is good. But, joined with the fact that I just disagree about some of this stuff (and at times got rather irked), I can't bring myself to highly recommend it either. Unfortunately, it's probably most compelling for an already mathematically sympathetic audience.


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