Eugene Volokh has an interesting (and frightening) series of posts on the innumeracy of both the general population and the press. There are anecdotes that I'd like to think that aren't true, but fear that they are, about science students unable to do simple arithmetic. We've become much too dependent on "computing machines."

I see Volokh's point, which is that knowing how to set up a problem is obviously important, and a computer usually can't do that for you, but if you know how to set up a huge complicated product, does it really matter whether or not you could actually carry that calculation out by hand? I mean it's good to know how to do long division and such so that you know what it is your calculator is doing, but...if you tell me, hey, go divide 30957831630187 into 395813975.3196588476...guess what, I'm not going to do that by hand.

...go divide 30957831630187 into 395813975.3196588476...guess what, I'm not going to do that by hand.

Did anyone suggest that you should? What in the world does this have to do with Eugene's point, which is that many simply trust what comes out of their computers (or what some leftist interest group spews) and not only don't bother to check the math, but are in fact unable to?

I may not choose to do the division problem that you posted, but the fact is that I could if I wanted to. Which means I could also solve more useful problems when presented to me, without having to rely on a calculator. I don't know why people seem to think that thinking on your feet is bad or useless just because the thinking involves doing math.

By the way, the answer (by hand) is 1.28e-5 to about as much resolution as you probably need.

We're at a point where the 'teaching computer' from Ender's Game is within reach. That is, not one of the cheesy 'Math Blaster' like games, where they just tally up the score. But one where there's real analysis going into the original curriculum, then the student evaluation, but then -- most especially -- on the focus of further studies.

There's no point blasting someone that can't add two seven digit numbers if it becomes clear they can't carry. Back all the way up to 9 + 9 and shore up that aspect of the student's knowledge.

Extending this to art or literature is more complex. But math and literacy should be eminently amenable to this approach.

Keith,

"in multiplication and division the accuracy of the answer corresponds to the least accurate of the quantities involved... perform the division and round off the answer to a number of significant figures equal to that in the least accurate quantity in the computation." - Technical Mathematics, 2nd edition, Donald Rice and Raymond Knight, copyright 1954(pre-calculator era)

I think the thing about basic arithmetic is it gives you a lot of the "tool box" for doing other things and understanding how problems are solved.

While I was doing my A levels (pre-degree courses) I had to spend a term (semester) helping the first year (11 year olds) maths class.

Firstly I was surprised they had calculators, the year before when I did my O levels we had a paper which required no more than log tables and no calculators or slide rules. Second, I was shocked to find that even with calculators they didn't understand the basics of how to formulate the numbers into a simple problem such as: a bus is 3.75 metres high, the bridge is 4 metres, how much room does the bus have to pass under the bridge?

That was in 1986, after my degree, in my first job, we did a couple of days helping local schools in a business game exercise - this time with 15 year olds. I could understand that they had problems working out how many cubic centimetres are in a cubic metre. However, I was astounded that I had to explain how to calculate a volume to them.

Reading the current A level maths papers from this year and comparing them to the ones I did, they're very different - providing the students with pretty much all the information they need and requiring very little analysis in, for example, integration.

It is a worrying trend, or just a sign I've turned into an old fart.

I always make the first exam of the semester closed-book, closed-notes, no calculators, and little or no partial credit. I usually encounter a small number of very frustrated students who cannot recall the values of trig functions at 0, pi/4, pi/3, pi/2, and so forth. They usually don't do well on this exam, or on subsequent exams where calculators are allowed.

Another calculator-student pet peeve arises in what should be simple "back-of-the-envelope" design calculations. For example, given an orbit radius (accurate to within 100 km or so), a spacecraft power requirement (accurate to within 100 W or so), students will size a solar panel with as many significant digits as their calculators will provide! It's hard to beat this (mal)practice out of them, but usually by the time they finish senior design, they are sufficiently aware of my opinion on the subject that at least they don't do it around me.

The problem here is not just mathematics. None of the subjects are being taught as in depth as they once were.

But you can be assured that little Johnny and Janie know its OK for Billy to have 2 daddies or for Margie to have 2 mommies. They know that Juan Carlos doesn't have to speak English to get his schooling. They know that it's OK, for Abdul bin Achmed to show and tell about his Koran during Ramadan, but Billy knows better than to make the Sign of the Cross before he says Grace over his PB&J. He wouldn't want to offend Achmed.

There isn't time to teach what needs to be taught if so much time is spent on multiculturalism.

Discipline also enters into the time factor. When I was a young lad, I went to Catholic grade school. At the time I didn't understand the need for the amount of discipline involved. Sister Mary Michael, Sister Germaine and several others I was taught by ruled with strength, love and intelligence. They were in charge of the class and we knew it. If we forgot, a ruler to the palm was a gentle reminder. I never felt a need to seek counselling because of child abuse.

The teachers have had discipline removed from their hands by liberalism and parents who think little Johnnie or Janie can do no wrong. The kids complain about the teachers and the teachers are the ones who are in trouble with the school administration. If I, or my brothers and sister, had EVER gone home and "complained" about getting in trouble at school, we would have been in trouble all over again. My dad didn't own a ruler and my palm was generally not where he aimed. I never felt a need to seek counselling because of child abuse by my parents either.

Discipline also affects the kind of analytical thinking math takes. I you never are taught to think, or are never made to think for yourself, you never analyze. If you get taught that 3 + 3 is 6 or maybe 5 or maybe 33, it strips the need for being exact. If the name of a 4 legged mammal that barks is spelled d-o-g, or d-u-g or m-o-u-s-e, then nothing is incorrect. If nothing is "wrong" there is no need to analyze. If every answer is acceptable there is no need to analyze.

If you haven't read it, get a copy of, Cultural Literacy: What Every American Needs to Know by E.D. Hirsch Jr.

It's a great view of what ISN’T being taught. And my experience from my kids and grandkids is that things are worse not better since Hirsch wrote his book.

I agree completely with you Steve. I am a teacher currently, and have seen what happens when children rule the classroom. When I taught in the inner city, I was afraid to send kids down to the office, for fear that the administration would tell me I was too weak to take care of my own problems, rather than helping me with classroom discipline.

And, that statistical mistake is pretty sad. You'd think people doing stats would check their simple problems.

This reminds me of Asimov's short story, The Feeling of Power, which involves a future civilization rediscovering basic mathematical principles (lost because computers handled everything).

The similarity with the Asimov story was discussed in some of the Volokh threads linked to.

And people wonder why we're homeschooling our kids.

And here I am regretting that I never learned how to do math with log tables and don't really know how to use a slide rule. Though if I had to, I would be able to figure it out.

It seems to me there is also an old Twilight Zone or Outer Limits show based on The Feeling of Power. I searched but did not find it anywhere.

Maybe my recollection of the story is so vivid I "see" it as TV, but I doubt that.

Any help here would be appreciated, it's driving me nuts!!

the best examples of innumeracy may be found at NASA
headquarters. Listening to Sean O'Keefe denigrate
foamologists was truly grating. He's one of the many
there who don't understand MV(Squared)

You're all missing the link, the math Geek TV series "Numbers".
Math failure that I am, had to go for CPA, this program is so kewl! http://www.tv.com/numb3rs/show/25043/summary.html
Mike