Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Inactive » calc_reform

Topic: more bait
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Paul Zorn

Posts: 325
Registered: 12/6/04
more bait
Posted: Apr 24, 2001 11:04 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Dear colleagues,

Lots of good ideas about partial fractions ... the subject
seems to be a good catalyst for thoughtful reactions (none
exothermic, so far) on larger issues. This is exactly the
kind of thing that keeps me (for one) interested in this
discussion group.

A note on just one part of Arch's recent (interesting!) posting:

> ... Quadratic equations: a thing of the past ...

I'm not sure how far Arch would take this, and don't want
to put words in his ... uh ... fingers.

I agree with it *if* what's meant here is that there's more
to mathematical life than the busywork of factoring expanded
equations and expanding factored ones.

But in other ways I think quadratic functions are excellent,
accessible, and generally under-appreciated tools for helping
students understand key ideas that should matter
in calculus courses.

1. They're the simplest functions on which (in some sense) calculus
can actually be ``done''.

2. They illustrate about as simply as possible the interplay
between algebraic forms and analytic properties --- completing
the square is a *great* example (and a look ahead) of altering
algebraic form to reveal structure.

3. They're the local prototype for the DIFFERENCE between ``any'' calculus
function and its LINEAR approximation.

4. They're the local prototype for QUADRATIC approximation of
``any'' calculus function. ``Tangent parabolas'' can help
make sense of concavity and of the second derivative test in
single variable settings. In the multivariate context the idea
of quadratic approximation seems almost essential to making any
sense of classifying stationary points --- at least, I've
never really understood it any other way.


Paul Zorn zorn@stolaf.edu
Department of Mathematics http://www.stolaf.edu/people/zorn/
St Olaf College 507-646-3414 office
1520 St Olaf Avenue 507-646-3116 fax
Northfield Minnesota 55057-1098



To UNSUBSCRIBE from the calc-reform mailing list,
send mail to:


with the following in the message body:

unsubscribe calc-reform your_email_address

-Information on the subject line is disregarded.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2016. All Rights Reserved.