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Re: A statement on what is wrong with standard calculus
Posted:
Feb 25, 1996 11:24 PM
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What Diana Watson seems to be describing is a calculus course more
interested in the calculator than the underlying math.
-Jerry Uhl
At 6:36 PM 2/25/96 -0500, Diana Watson wrote:
This year, we are using a preliminary edition of a reform
>calculus text being prepared at Clemson University. Students are
>required to use a graphing calculator. Most have Texas Instruments'
>TI-85.
>
>The authors of this text frequently assert that students do not require
>"algebra" to successfully complete this course, and further, that
>requiring "algebra" would make calculus concepts less clear.
>
>There are several things I like about the text, but they are not
>relevant to the present discussion. Here are some of my problems:
>
>1. The authors note in their calculator guide that the TI-85 will not
>compose functions. If you have formulas for f(x) and g(x) and you
>want to enter f(g(x)) into the calculator, you have to work out the
>formula by hand, and then enter it. To my mind, that requires
>"algebra".
>
>2. When first finding derivatives as the limit of a sequence, the
>constants in the functions in the first group of problems all
>contain many significant figures. The claim is that this will
>make the concepts clearer. I personally do not see how working with
>
> f(x) = 2.334965 x^3 - 13,9960.6 x^2 + 4.5967 x - 101.283
>
>will make concepts any clearer than working with
>
> g(x) = x^3 - 3 x^2 + 2 x - 1
>
>will. (The problems are my own invention, but the first will give you
>a flavor of the problems in the text.)
>
>
>3. There are not many problems for calculating derivatives by hand.
>Here is problem 12:
> 12x
> y = 100,000(1 + .05/12)
>
>The students are expected to figure out that
>
> x
> (12x) ( 12 ) x
> (1 + .05/12) = ((1 + .05/12) ) = 1.05116189788
>
>I chose to begin the year with a review of basic exponent and
>logarithm rules (not in the text, I made my own handout). This sort
>of calculation is still beyond the level of most of my students.
>
>When I took calculus (the honors course, at the University of Chicago,
>with a computer supplement) my instructor said that whatever else we
>might learn, by the end of the year we would at least know algebra.
>And he was right. We needed to use algebra in our calculations, and
>so we learned it. We also learned a lot of calculus.
>
>In my experience, the skills necessary to cope with (at least the
>first and third) of the above problems are first taught in a course
>labeled "algebra" which is why I have used that term. I would like to
>know what types of calculations fall under the heading of the
>"algebra" that my students allegedly don't need.
>
>If anyone can shed some light on this, I would appreciate it.
>
>
>Diana Watson
>Boston University
----------------------------------------------------------------------
Jerry Uhl juhl@ncsa.uiuc.edu
Professor of Mathematics 1409 West Green Street
University of Illinois Urbana,Illinois 61801
Calculus&Mathematica Development Team
http://www-cm.math.uiuc.edu
"It is unworthy of excellent persons to lose hours like slaves in the labor
of calculation."
. . . Gottfried Wilhelm von Leibniz
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