provocative opinion Indicators of Declining Mathematics Acumen among Chemistry Students Carl W. DavM University of Connecticut, Storrs, CT 06269 C. F. Reynolds recently wrote that "computers are limitine" our world" and armed that s l -o- -~ and ~ v inaccurate data makes inference drawing a more problematic exercise than computer-oriented scientists like to think. He asserta, by implication, that scientists of the future may he prejudiced by the use of computers into treating solely computationally tractable problems. In fact, the computer is exerting a much more malign effect on the intellect of students, as will be demonstrated forthwith. In a recent Physical Chemistry examination, I asked students, given the wave functions for p, and p, orbitals whose origins were a t (0,0,0), to show by explicit integration that a p, orhital located a t (R/2,0,0) is orthogonal to a p, orbital located a t (-R/2,0,0) (where (x,y,z) is the notation employed). I had taught the class how t o do such a problem when the orhitals bad their centers on the z axis hut had inadvertently switched axes in typing the exam. Ahout half the class ignored the instructions and attempted to solve the problem placing the orhitals on the z axis and converting to spherical polar coordinates. Ahout half the class left the orhitals where thev were supposed to be, attempted to switch to spherical polir coordinates (ina)rrectly)and proceeded to "integrate" about the r$ axis. One student's originality and honesty was striking (and engendered this note). First, there was an asterisk on the paper with a notation "Please, give me some credit for this?! I'm a computer geek not a math wiz." Then there was a drawing, labelled "Crude numerical integration", which is shown in the figure. Finally, there was the equation (?!?):
-
for the value of
loZr
sin3R ~ R
Forget the fact that only a minority of the class can do calculus in a quiet, plodding, careful, intelligent way. We
3 sin 8
,7518
. I 102 ,9925
5
1.5
I.
2.0
2.5 X
8
One student's "crude numerical integration"
have been failing t o teach calculus for years, and no one is surprised t o discover this "fact". What is more important is the emerging signal that the computer/caiculator revolution is arriving, with a generation of students who are not only reluctant to learn calculus, hut are in fact reluctant or unable to learn any non-computational-based mathematics. They are, i t appears, unable todo traditional analytic work in any language other than the language of their math classes. Once removed from a formal mathematics environment, they revert to numericism, even when i t is not needed, rather than employ the tools they "learned" in the sterile atmosphere of mathematics classes. One can argue that one case out of a class of 25 is not indicative of a trend. But my 15-year-old daughter can't compute the product of simple fractions without a calculator in hand. The State of Connecticut had handed out calculators to all children (during examinations) so that computational skills will not interfere with their "higher order" "thinking skills". The future is coming into view, and it is desolate.
Volume 67
Number 1 January 1990
31
