Thoreau's Lemma
Remember how calculators came and took the bite out of slide rulers. In a world far, far away, e.g. Eli's bunnyhood, engineering students took classes in how to use the things and adding machines were treasures. In small groceries people used brown paper bags, in large ones, very clunky cash registers.
At that point, still lamented in teachers and faculty lounges world over (and, as Brian would point out, in the US Republican Party), actually knowing how to do arithmetic became less of a necessity and more of a party trick, what was needed was the ability to set up the problem and punch the numbers into the $1 calculator, $10 if you have to do logs or trig functions.
Thoreau, who Eli spars with in a friendly manner, brings news of the next frontier. Students everywhere rejoice, calculus class is no longer needed.
I usually use Mathematica as my calculator, especially when explaining homework in office hours. I can refer back to variables and quickly make graphs or manipulate symbols. So while going over homework with students in my biophysics class, I pull up Mathematica and one of them says “Is that just like Matlab?” My eyes bugged out. A biology major who knows Matlab? This is the subject of my interdisciplinary hopes and dreams. So I asked what she uses Matlab for. “My boyfriend is a mechanical engineer and I have to do his homework for him.” My reply was “Your boyfriend should do his own homework, and if you’re a biology major with Matlab skills you should be working in my research group.” . . . . . . . . (Yes Chip, Eli left out a paragraph, go to the link and see if it changed the meaning of the piece)Sort of like most students can't remember long division, why should they, all they need is to be taught MatLab (the affordable version) or Maple or Mathematica (the high cost ones) and to find a function. The same thing happened with statistics, all you need is R or SAS or Statistica. To the joy of mathematicians and statisticians they now only have to teach the lemmas.
Contrast this with my discovery yesterday in biophysics: I gave them an activity in which one step required that they calculate the derivative of a*x^2-b*x. I know that calculus isn’t a prerequisite for the course, but they’re all juniors and seniors and the biology department requires them to take a quarter of calculus. Alas, most of them could not remember it.
Symbolic algebra/calculus programs are the calculus versions of calculators. A light has dawned. Death to ten blackboard long proofs.
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13 comments:
The next logical step, of course, is for someone to develop a program which will accept as input an essay by some pundit, and spit out an essay
And while we're on the subject, in certain situations people actually write programs to do multiplications in log space. This makes a lot of sense when you expect *'s and /'s to be much more common than +'s and -'s, for example when dealing with long chains of conditional probabilities.
-- frank
...spit out an essay telling you what to think.
-- frank
Oh, and the fixed hyperlink.
-- frank
I still don't trust Excel, and have to check sample answers by hand.
I think what needs to happen is more "order of magnitude" classes: I know that Caltech offered one that was very popular, though I didn't take it. Basically, you need to know enough to be able to tell when an answer is wrong, so you can double check what happened, even if you don't need to actually do all the math yourself.
http://www.its.caltech.edu/~oom/
-MMM
The biophysics students weren't people who had learned derivatives but got rusty because Mathematica always does it for them. They were people who never learned what a derivative even means. There's a big difference.
You left out Octave, which is even cheaper than Matlab, i.e. free, although it may not be 100% compatible with Matlab.
> don't trust Excel
No shit. My beloved makes her living finding and fixing spreadsheet problems (and data flow and associated human density gradient problems).
Academic research on spreadsheet (and proofreading) errors:
http://panko.shidler.hawaii.edu/My%20Publications/Whatknow.htm
Mathymouse says,
Sometimes Eli's irony is hard to distinguish from his ... mangenesia? ... but surely he would admit that math is all about being sure that you're right.
Let the engineers have their Matlabs and their Mathematicas. They need answers, not proofs.
But the mathematicians really will never be comfortable with proofs that only a computer can verify (http://en.wikipedia.org/wiki/Computer-assisted_proof#Philosophical_objections).
(And yes, Mathymouse's students have to be able to compute in their heads, at least to one place)
MM
"I think what needs to happen is more "order of magnitude" classes"
Couldn't agree more. Except the concept needs to be inculcated long before leaving high school.
I'm really a very nice tutor, really I am. But I sometimes despair when dealing with year 10 or 11 students who really, truly cannot deal with decimals, percentages or powers. Simply because they've never learnt to recognise multiples of 10 or 100.
MinniesMum
Look on my works ye mighty and despair...
I'm not going to worry about high tech machines until they make one that can replace a broken ski edge or make a trashed Huffy rideable.
"The History of Numbers" points out that place notation, with a zero, was (re?)invented in India and exported to Europe via the Arab traders. It certainly made keeping accounts and other calculations easier. While the abacus was (and probably still is) popular, the first mechanical calculator was AFAIK Pascal's; one can still purchase plastic versions.
In college I used Marchant calculators (on which one had to be carful about dividing properly). Of course in the intervening 50+ years computers have taken over most of those roles as well as some of the more symbolic parts of applied (and even pure) mathematics.
That's good. Have most students learn (higher) mathematics (and statistics, please) as these become necessary for their chosen subjevts. [I'm sufficiently old fashioned that I think all middle/high school students ought to larn Euclidean geometry and some of the associated proof methods; part of the culture.]
On another blog thre was an article about Mersenne primes; most of the readership commented they didn't follow, didn't understand (and clearly didn't wnat to). This included a retired 2nd grade teacher who of cours taught 2nd grade arithmetic for her 37 years of service; oh well.
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