
Re: A statement on what is wrong with standard calculus
Posted:
Feb 25, 1996 11:24 PM


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' >TI85. > >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 TI85 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://wwwcm.math.uiuc.edu
"It is unworthy of excellent persons to lose hours like slaves in the labor of calculation." . . . Gottfried Wilhelm von Leibniz

