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How Big An Issue Is Innumeracy?

Posted August 18, 2016 9:37 AM by Bayes

I came across this New York Times op-ed article from 1989 written by John Allen Paulos and thought it was especially relevant today. How much is innumeracy effecting the world today? Is it something that should be eliminated, like illiteracy? Or is a certain level of innumeracy to be expected? I included the Taylor Series table as an example of mathematics that some know and many do not. Should all be expected to understand Taylor Series? What level of mathematics qualifies someone as innumerate? Here is the op-ed piece...

THE ODDS ARE YOU'RE INNUMERATE

Innumeracy, the mathematical analogue of functional illiteracy, afflicts far too many literate people, even widely read and articulate men and women who might cringe if words such as ''imply'' and ''infer'' were confused. They generally react without a trace of embarrassment, however, to even the most egregious numerical solecisms. Once I was at a gathering of writers in which much was being made of the difference between ''continually'' and ''continuously.'' Later that evening, as we were watching the news (another measure of how enjoyable the occasion was), the television meteorologist announced that there was a 50 percent chance of rain for Saturday and a 50 percent chance for Sunday as well, and concluded that there was therefore a 100 percent chance of rain that weekend. I grant the mistake was not hilarious, but no one even smiled. The recent ''Mathematics Report Card'' released by the Educational Testing Service indicates that more than weather reports are at risk. The rampant innumeracy of our high school students and of the educated public in general is appalling, and since this innumeracy can and does lead to muddled personal decisions, misinformed governmental policies and an increased susceptibility to pseudosciences of all kinds, it's not something that can be easily ignored.

I'm not primarily concerned with esoteric mathematics here, only with some feel for numbers and probabilities, some ability to estimate answers to the ubiquitous questions: How many? How likely? With megaton warheads (equivalent in explosive power to a million tons, or two billion pounds, of TNT) and trillion-dollar budgets a reality, people should have a visceral reaction to the difference between a million, a billion and a trillion. (It helps to note that a million seconds takes less than 12 days to tick by, while a billion seconds requires approximately 32 years, and 32,000 years must pass for a trillion seconds to elapse). They needn't be aware of how fast human hair grows, expressed in miles per hour, or of how many basketballs would fit in the Grand Canyon, but they ought to know roughly the population of the United States, the percentage of the world's population that is Chinese, the distance from New York City to Los Angeles, the odds of winning their state lottery and a host of other common magnitudes. Without a grasp of such basic numbers, just to cite one example, it is impossible to appreciate the silliness of canceling a European trip because of fear of terrorists. In 1985 when, out of the 28 million Americans who traveled abroad, 17 were killed by terrorists, you were almost 25 times as likely to choke to death (one chance in 68,000), about 300 times as likely to die in a car crash (one chance in 5,300) and nearly 2,000 times as likely to die from the effects of smoking (one chance in 800, the equivalent of three fully loaded jumbo jets crashing each and every day of the year).

Still, what do numbers, probabilities and mathematics in general have to do with books and literature? A couple of minor points first. In addition to the usual reasons for innumeracy, avid readers of fiction sometimes have an extra vulnerability to numerical myopia. Their habit of reading about individuals in extreme and dramatic circumstances may exacerbate the natural tendency we all have to give considerably more weight to unlikely but gripping events than we do to more mundane ones. Novels, after all, must be novel, and if, as Tolstoy's chestnut says, all happy families are the same, it's not surprising that the premises of most stories are biased toward the unusual, the special and the rare. (Soft news reports evince this same bias. Willie Horton, the furloughed murderer, seemed to receive more attention than did a decline in the Massachusetts crime rate; likewise, three stranded whales in Alaska may have received more notice than the famine in the Sudan.) Specific instances of quantitative inaccuracy in works of fiction are common, but frequently can be attributed to the characters rather than to the author, or they can be interpreted as having been inserted for effect. These deliberate exaggerations occur in books as dissimilar as Rabelais's ''Gargantua and Pantagruel'' and Gabriel Garcia Marquez's ''One Hundred Years of Solitude,'' and are certainly nothing to get indignant about. My suspicion, however, is that the allusive, metaphoric use of language in literature, so at odds with its more literal use in scientific and mathematical contexts, hides many unintentional clinkers as well.

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#1

Re: How Big An Issue Is Innumeracy?

08/18/2016 10:08 AM

You could write a book "Mathematics for Morons"....or maybe 'Mathematics for everyday use" would be better.....don't want to put anybody off....It would have a 50% chance of being read by 1% of the people....

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Re: How Big An Issue Is Innumeracy?

08/18/2016 10:14 AM

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Re: How Big An Issue Is Innumeracy?

08/18/2016 11:04 AM

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#3

Re: How Big An Issue Is Innumeracy?

08/18/2016 10:59 AM

My pet peeve is news reporters mixing up million and billion as if million is just an adjective meaning "a lot" and billion is maybe just a more forceful adjective.

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#5

Re: How Big An Issue Is Innumeracy?

08/18/2016 12:41 PM

Innumeracy is a problem that (among other things) effects elections and the course of our country (the US, but others, too).

I'm not trying to pick on Hillary Clinton, or make this political (politicians of all parties will quote meaningless numbers), but I'm reminded of a recent speech by Hillary laying out her plans for expanding entitlements, and her plan to pay for them. She said, "We'll go after the rich!" And the crowd cheered and applauded.

Even if you took every penny that the rich have - not just income but accumulated wealth - there simply isn't enough money to pay for even a fraction of her new spending plans. (Go find the video by Bill Whittle 'Eat the rich'; it's a few years old, but nevertheless it's eye-opening).

Her plan would have to include new massive amounts of deficit spending - on top of a deficit that is unprecedented for a peacetime economy. Needless to say, the crowd at her rally neither understood, nor cared.

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Re: How Big An Issue Is Innumeracy?

08/18/2016 1:12 PM

Million, Billion, Trillion, it's all the same, right?

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Re: How Big An Issue Is Innumeracy?

08/18/2016 1:26 PM

As Senator Everett Dirksen once said, "A million here, a million there - pretty soon you're talking real money."

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Re: How Big An Issue Is Innumeracy?

08/19/2016 1:55 AM

Speaking of mixing up 'millions' and 'billions'.... the quote often attributed to Dirksen, starts 'billion here, a billion there', though he never actually said the 'pretty soon you are talking about real money' part.

Arg.... you were just trolling, right? Got me hook line and sinker. I'm not too proud to post anyway.

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Re: How Big An Issue Is Innumeracy?

12/30/2016 1:40 PM

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#8

Re: How Big An Issue Is Innumeracy?

08/18/2016 5:52 PM

I see it every online with people convinced they can do math using nothing but the alphabet and some random symbols from long dead ancient languages and just shake my head.

Some days I think that if they had become carpenters they would be the guys who figure they can drill holes in board with a screwdriver bit driven by a circular saw that has it's power cord plugged into their butts.

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Re: How Big An Issue Is Innumeracy?

08/18/2016 8:38 PM

Biological energy source? I think I can make that work,, mathematically....

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Re: How Big An Issue Is Innumeracy?

08/18/2016 10:07 PM

Technically speaking, Greek isn't really an ancient dead language....

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Re: How Big An Issue Is Innumeracy?

08/20/2016 8:28 AM

I wouldn't know. Where I went to school Canadian was considered a foreign language.

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Re: How Big An Issue Is Innumeracy?

08/20/2016 8:40 AM

Lol, canadian should be considered a foreign language!

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#11

Re: How Big An Issue Is Innumeracy?

08/18/2016 11:26 PM

It's a huge problem. But education is not the exclusive solution. We need to allow for those with dyscalculia, for whom math education really doesn't work:

https://dsf.net.au/what-is-dyscalculia/

Care is needed before assuming that innumeracy derives from lack of math education. Those with dyscalculia are hugely disabled in modern life.

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Re: How Big An Issue Is Innumeracy?

08/20/2016 8:34 AM

And yet they go on to become public and college level math teachers and professors without so much as a second thought.

Given my spelling and genral typuk skills look likethis withoutu spele check may be I shoudl go onot become s enginels teacher or typicl clss instriecotr.

(Given my spelling and general typing skills look like this, without spell check, maybe I should go onto become an english teacher or typing class instructor. )

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#13

Re: How Big An Issue Is Innumeracy?

08/19/2016 4:04 AM

In the UK as a kid I would hear teachers, parents and just about everyone else talk about the three 'R's"

Reading

wRiting

aRithmatic or for my US cousins... Math!

This was considered the backbone of all learning, and without being the master of the three 'R's" one would get no-where in life.

As for "counting".... don't get me started. I was in my local store and the checkout girl could not work out the change, as the till would normally do it for her!
Same in the local bar.... the till works out the change to be given.
In school we were not allowed to use a calculator, these days, no problem take your scientific calculator into the Math exam!

That is the reason IMHO is why no one can count anymore, let alone perform complex equations!

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#14

Re: How Big An Issue Is Innumeracy?

08/19/2016 3:28 PM

The example of the probability of dying from a terrorist attack abroad is not a mathematical issue, but a news media issue. You tend to expound on this in the next paragraph. We hear about the deaths by terrorists on the news programs, but when is the last time we heard about a choking death? Let me see...how about Mama Cass? When was that? In 1974?!?! Car crashes are only noted when it is a celebrity, or there is a multiple vehicle collision with multiple deaths. So, yes, the general public will be more frightened of a possibility they've been told about repeatedly. You don't really expect the general public to actually look up the odds of dying in different manners do you? Well maybe around Halloween some teens will get into these statistics. Back to the current vein of thought. Remember, terrorist attacks are reported on / about for at least three weeks afterward, and the repercussions and responsibility for allowing such to happen for two more weeks.

I do find it fascinating that Weather Nation is now posting the chance of rain by the hour for the next day as well as by the day for the week, and not rounding up or down to the nearest 5 or 10. Yes, we can see there is a 23% chance of rain between 4 and 5 PM. They seem to be a bit poor at the prognostication, at least in an area down wind of a Great Lake, where a meteorologist as good as say Dr. Lyons would be hesitant to calculate a probability to the nearest whole number for a given locality, but it is a mathematical attempt at prediction. Actually, watching projected radar is much more pertinent and helpful, but I would like to see the formulas and variables used to come up with the rain probability percentages, particularly in the local mentioned above. It must be fascinating.

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