The danger of giving homage to mathematical incompetence

Yesterday afternoon, a friend mentioned that in his experience people are usually embarrassed to be exposed as illiterate, but they don't seem to care whether they are exposed as mathematically incompetent. That observation resonated with me. In fact, not only aren't people embarrassed about being mathematically incompetent, but many people seem proud of being mathematically illiterate. They use their mathematical incompetence to socially bond with other people who are mathematically incompetent. More than a few times, someone in the room has mentioned that they're not very good with numbers and several other people in the room immediately come to their rescue indicating that it's okay to be mathematically incompetent because they too struggled with mathematics. I don't think it's any coincidence that American students are so deficient at mathematics compared to the students in many other countries while, at the same time, Americans have such bizarre public policy priorities (e.g., a zero tolerance policy toward terrorism at the same time that thousands of Americans are dying needlessly of treatable medical conditions and while millions of American children are subjected to terribly underfunded schools that will ruin their lives). After yesterday's conversation, I pulled out an 1988 book by John Allen Paulos, Innumeracy: Mathematical Illiteracy and Its Consequences. here's what Paulos has to say right in his introduction:

Innumeracy, an inability to deal comfortably with the fundamental notions of number and chance, plagues far too many otherwise knowledgeable citizens. The same people who cringe when words such as "imply" and "infer" are confused react without a trace of embarrassment to even the most egregious of numerical solecisms. I remember once listening to someone at a party drone on about the difference between "continually" and "continuously." Later that evening we were watching the news, and the TV weather forecaster announced that there was a 50% chance of rain for Saturday and a 50% chance for Sunday, and concluded that there was therefore a 100% chance of rain that weekend. The remark went right by the self-styled grammarian, and even after I explained the mistake to him, he wasn't nearly as indignant as he would've been had the weathercaster left a dangling participle. In fact, unlike other failings which are hidden, mathematical illiteracy is often flaunted: "I can't even balance my checkbook." "I'm a people person, not a numbers person." Or "I always hated math."
Paulos suggests that part of the reason for this ignorance of mathematics is that the consequences are often not as obvious as those of other weaknesses. On the other hand, the problems caused by innumeracy are serious, often times matters of life and death. Paulos lists the following examples: Stock scams, choice of a spouse, newspaper psychics, diet and medical claims, the risk of terrorism, astrology, sports records, elections, sex discrimination, UFOs, insurance and law, psychoanalysis, parapsychology, lotteries, and drug testing… Why do people struggle so much with mathematics? Paulos points to natural psychological responses to uncertainty, to coincidence, and how problems are framed, as well as anxiety, romantic misconceptions about nature and the importance of mathematics. One of the biggest consequences of innumeracy are "unfounded and crippling anxieties" and "impossible and economically paralyzing demands for risk-free guarantees." Paulos mentions that politicians are rarely helpful, because they are often "loathe to clarify the likely hazards and trade-offs associated with almost any policy." It's been a while since I read Innumeracy, but I highly recommend it. It is a timeless book filled with examples to remind us of the importance of a precise understanding of mathematics. Paulos indicates, "The book will have been well worth the effort if it can begin to clarify just how much innumeracy pervades both our private and/or public lives." By the way, if you know someone who is struggling with mathematics, Paulos book is a good place to start. He is an excellent teacher of math as well as a clear writer. If you know someone who wants to understand basic math, refer them to the many free video lessons at Khan Academy. Once we master math, I would suggest that we turn to biology. It is my firm belief that all of us would be much better off with an understand of human beings based on the understanding that humans are human animals.

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Ripped off because we don’t do well at math

I'm in the process of reading Stopped Getting Ripped off: Why Consumers Get Screwed, and How You Can Always Get a Fair Deal, by Bob Sullivan (2009). He starts off by asking you to pretend that you are in a restaurant and you are presented with a menu that he illustrates on page 5 of his book. You are asked to assume that you ordered the onion soup (the price is clearly listed on the menu as $.60) and the "Lancaster Special Sandwich" (the price is clearly listed on the menu for $1.95). The question he asks is this: "How much should you leave for a 10% tip? I'll wait for a bit while you do your calculation in your head. No calculators, please. What did you come up with? [more . . . ] The answer is 25.5 cents, so either 25 cents or 26 cents would be an acceptable answer. What Sullivan next states is shocking:

If you answer this question correctly, consider yourself part of an elite group, because when the US Department of education asked US adults to answer it as part of a nationwide study, only 42% answered correctly. Less than half of American adults were able to pick two numbers from the list, add them, then perform the most basic of all percentage calculations--simply moving the decimal point one column to the left to calculate 10%.

Innumeracy is literally killing us. Try to think of a major issue facing our country that does not require a basic proficiency in mathematics that most of us don't seem to have. Think of the environment, energy, national budget, climate, health care, evolution being taught in public schools, space exploration, public health issues (e.g., the importance of vaccinations), the true cost of the "war on drugs," reform of financial institutions or taxation policy. Since most Americans cannot understand how to calculate a 10% tip, there is little chance that they could meaningfully participate regarding most of the big issues facing our country. These are truly painful words to write. Just think of the many math-related claims that got math-ignorant voters excited during the last presidential election, including Sarah Palin's claim that American could live long and prosperously on Alaskan oil (when straight-forward calculations based on known reserves showed that there is only enough Alaskan oil to supply America's current rate of use for six months). Imagine how different things would be if most Americans could actually calculate the minimal chance that they would be affected by an act of terrorism, and if they were able to compare that risk to the immense numbers of lives that could be saved by much more modest expenditures. But it's not even clear whether most Americans can benefit from further training regarding statistics. It's certainly true that many health care professionals don't adequately understand basic problems involving risk. The reasons so many of us are innumerate are not easily addressed. We desperately need proficient math skills to tamp down our fears. I know it has been tried (and abused) before, but a sinister thought enters my mind. The information presented by Sullivan makes me wonder whether we should make voters take and pass a rudimentary math test before allowing them to vote. How indignant could a rejected voter be if he/she can't figure out a ten percent tip? Understanding the many math-based claims asserted by candidates is sometimes the only way to see past their slick acting abilities. I'm not seriously suggesting a poll quiz, though I'm sure that my frustration is showing through. What we really need to do is provide better math education all the way through school. It appears that we are paying dearly for the many grade schools that fail at math education, individually and as a country.

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How to fear

The June/July 2007 issue of Scientific American Mind presents in article by David G. Myers entitled "The Powers and Perils of Intuition." (this particular article is not available online except to subscribers).  The starting point for many articles on intuition is the work Kahneman and Tversky, who explored shortcuts we…

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