Date: Dec 31, 2012 10:59 PM Author: sitavnabi@gmail.com Subject: Re: The Wisdom of Studying Calculus 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?