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Re: The Wisdom of Studying Calculus
Posted:
Dec 31, 2012 10:59 PM
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On Saturday, October 8, 1994 9:11:06 AM UTC-4, Lou Talman wrote:
> Bob Hayden recently wrote:
>
> > There was a time when only a tiny fraction of the population took
> > calculus. Most of them knew what it was for -- they were in college
> > majoring in engineering or science. (In my first college physics
> > class, they started teaching calculus because the Math. Dept. didn't
> > cover stuff fast enough to suit them.) Today about half our young
> > people go to college, and many take calculus in high school. It's not
> > clear to me that they ARE ever going to use calculus in their life
> > after school. Have we just kept teaching the same stuff out of
> > inertia?
>
>
> This stimulated the following responses (quoted mostly in part):
>
> Eric Sultenfuss:
>
> > I once asked my high scool calc teacher why we learned calculus. He gave
> > me two reasons, neither of which had anything to do with practicality.
>
> > First, he said, calculus was an art, much like music. It could be used to
> > create the same beauty. Second, whether or not the student ever goes on to
> > use the actual formulas of calculus, he or she has learned a new way of
> > thinking about life, and a deeper understanding of natural processes.
> >
>
> > Whether or not he was full of manure I'm not sure, but it satisfied me at
> > the time, and it could be an interesting topic of discussion should anyone
> > out there want to pursue it.
>
>
> Stephen Weimar:
>
> > That's a good question. If calculus is of no use to anyone else except
> > those interested in the sciences or engineering, then why teach it to
> > everyone? It would seem like a waste of time for a Humanities major to
> > have to take a calculus class if s/he will never use it. What purpose will
> > this serve?
> >
>
> > If we are trying to teach kids math, and they see no use for it in their
> > daily lives, then how willing are they to learn? I can see that as more
> > students realize that calculus is of no use to them if they do not plan to
> > go into the sciences or enginnering, less will be willing to learn
> > calculus. Do we want this to happen? Is calculus no use to the
> > non-science people? If, not, how can we convince them otherwise?
>
> John Conway:
>
> > I'm intrigued by some of the remarks about "whether they're ever going
> > to use calculus in their lives?".
> >
>
> > A few of them are, no doubt, but probably most aren't. So
> > what does this say about whether we should continue to teach
> > it?
> >
>
> > It's not clear to me that we should. But one thing is very
> > clear indeed - if we do continue to teach calculus to students
> > most of whom aren't going to use it, we should plainly do so
> > very well! Only then is there some hope that they'll appreciate
> > its beauty and power.
> >
>
> > (***Material Deleted***)
> >
> > On balance I think we should continue to teach it, because
> > those who are ignorant of the calculus are forced to remain
> > scientifically illiterate.
>
> Walter Whitely:
>
> > If we are going to select mathematics on the basis of:
> > fun, beauty, interest, cultural history ... I suspect that
>
> > Calculus will not make the top of my list, nor the list of
> > many students I teach (e.g. math for commerce - our largest
> > program, education, fine arts ... ). WHen I ask second year or third
>
> > year Math Majors about their worst experience in math, the most common
> > answer is series in calculus (in spite of John Conways eloquence).
> >
>
> > With those criteria - I would propose, say projective
> > geometry, or the theory of polyhedra.
>
> We do not teach mathematics in general, nor calculus in particular,
>
> for "fun, beauty, interest, [or] cultural history". Sultenfuss' high
> school teacher, in his second and more cogent reason, was close, as Arnold
> Toynbee would have agreed: "The calculus, even a taste of it, would have
>
> given me an important and illuminating outlook on the Universe...
>
> One ought, after all, to be initiated into the life of the world in
>
> which one is going to have to live. ...[T]he calculus, like the
>
> full-rigged sailing ship, is...one of the characteristic expressions
>
> of the modern Western genius." [A. Toynbee, _Experiences_, Oxford
>
> University Press, New York, 1969] (This quotation also appears
> in at least some editions of Sherman Stein's calculus textbook.)
>
> While I find Toynbee compelling, I think even he has missed the point.
> Here is what Mark Van Doren wrote:
>
>
> > 'Language and mathematics are the mother tongues of our rational
>
> > selves'--that is, of the human race--and no student should be
>
> > permitted to be speechless in either tongue, whatever value he
>
> > sets upon his special gifts, and however sure he may be at sixteen
> > or eighteen that he knows the uses to which his mind will eventually
> > be put. This would be like amputating his left hand because he
>
> > not seem to be ambidextrous. It is crippling to be illiterate
>
> > in either, and the natural curriculum does not choose between
> > them. They are two ways in which the student will have to express
> > himself; they are two ways in which the truth gets known.
>
> [M. Van Doren, _Liberal Education_, Beacon Press, Boston, 1959]
>
> Van Doren was a poet, and I do not think it an accident that he
> chose the metaphoric "mother tongues" to elaborate his subject.
> Richard Skemp, in his work on the psychology of learning mathematics,
>
> wrote of language and mathematics as "calculi of thought". Note the
> mathematical metaphor from one whose orientation lies more toward
> mathematics than toward language.
>
>
> The upshot of all this, I think, is that language and mathematics are
> both something for which English possesses no word, but only
>
> metaphoric terms. They are, to use still another metaphor, high
>
> order cognitive tools, and the mind that is uncomfortable with either
> is poorly equipped.
>
> Language and mathematics are tools of the well-equipped mind. Calculus
> is very much in the mainstream of modern mathematics. One can argue,
> with Whitely above, that other topics are more "relevant" to many; one
> does not thereby put them into the mainstream.
>
> Ought we to make calculus interesting? Of course--that is simply good
> teaching; but there are a dozen devices we can use, and no single
>
> instructor will use them all. But let us not forget that students bear
> their own responsibilities, and that one of those responsibilities
> is to undertake tasks whose wisdom they do not presently understand
> and may never admit. Perhaps the real question we should address is this:
>
> Have we taught students that they bear this last responsibility?
I sincerely have no clue what calculus may lead me to in the future but, I know very well that I will and have done just about everything to excel in it. I am still struggling immensely as with difficult concepts I learn best when someone talks to me. I don't know why, but it works. Would anyone be willing to help be understand a few problems?
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