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Re: The Wisdom of Studying Calculus
Posted:
Dec 31, 2012 10:59 PM


On Saturday, October 8, 1994 9:11:06 AM UTC4, 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 > > nonscience 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 > > fullrigged 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 raceand 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 wellequipped 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 coursethat 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?



