From: eugene@wilbur.nas.nasa.gov (Eugene N. Miya)
Subject: Re: Why is calculus so feared?
Organization: NAS, NASA Ames Research Center, Moffett Field, CA
Date: Mon, 6 Apr 92 22:36:23 GMT

Probably several reasons:
1) while researching a quote for another newsgroup I found a great little
description of the Bourbaki.  Without getting into details of mathematical
history, the Bourbaki did not like graphs, graphics, and geometry.  Your
eyes could be fooled (true enough!).  So mathematics is to blame.

2) In the US, we have a particular anti-intellectual bias.  We distrust
experts, theory, and certain things which smack of "thinking."  Skepticism.
So US culture is also to blame.

3) Calculus requires a bit more thinking and memory [replaced by assumptions]
than easy parts of arithmetic and number theory (since replaced with
calculators; hey calculus/calculators, more than coincidence?.....).
Richard Hamming at the US NPS believes that calculus is perhaps the best tool
for teaching his students ("future admirals" he like to call them).
So blame individual humans.

There is really no reason to fear calculus.  It only comes "later" in
the learning curve, and bacause of requisite knowledge needed for some
subjects, we mistake "later" for harder.  A fourth implicit problem,
independent of calculus as a subject, is that as you go "higher" in the
educational system, the pace of teaching also accelerates.  I have a friend
who teaches physics at UCSC, his students were the ones doing chaos work
in the late 70s.  He bemoans the speed of the quarter system.  No chance
to sit and explore where the science is going.  He would love to teach a
1st year calculus class from the perspective of splines.  Splines?  I think
he could do it, but it would be exploratory, and exploring students minds
in this way is perceived by some as dangerous: what if it fails?  the students
would be warped!

Actually the people who fear calculus the most are probably older adult
teacher types who never had calculus.  I wondered about the audience
attending a screening of the film Stand and Deliver.  Less than 10% of the
US population takes a calculus class.  What a film! "What is kal kulus?"
"I was dreaming that I was swimming with dolphins in a sea of complex
numbers..."  [complex numbers in a calculus class?  they are independent
subjects, sort of...]  I had a shock when I saw this film, I recognized a
painting on the wall at the board of education scene: one of the system
superintendents was a fellow who spoke at a retire party for one teacher.

Anyways, my discovery of my real liking mathematics took place in
calculus.  The teacher let the class learn at its own pace.  We had 18
students in a class which was supposed to have 20 (I wonder if they
falsified school records?).  It was supposed to be an interesting experiment:
because the lab sciences frequently required major set up for experiments
they took 3-4 periods and alternated classes.  10th it was bio/geometry,
11th (when they started this, this was my year) it was chem and Alg II,
12th was supposed to be physics and calculus.  Calculus without physics
is understandable, but physics w/o calculus?  Our calculus class watched
as other physics students struggled.  Not enough students to swap times
as we had in the 11th grade.  I looked back at my class: 18 kids, 16 of them
Japanese-American nerds as some would say (slightly more boys than girls),
no one from the elementary school where I attended.  I took photos of my
calculus class as a part of year book.  It was amusing, the only representation
of nerds (except a newly formed computer club [which I started]).  In a way,
the stuff they give you in HS calculus classes is too easy: easy polynomials,
nice continuous functions, non-noisy data......

--eugene miya, NASA Ames Research Center, eugene@orville.nas.nasa.gov
  Resident Cynic, Rock of Ages Home for Retired Hackers
  {uunet,mailrus,other gateways}!ames!eugene
This is the Usenet: do you expect anything other than gross generalizations?
Ref: Mathematics and Plausible Reasoning, vol. 1, G. Polya