Date: Jan 14, 2013 4:27 PM
Author: Dave L. Renfro
Subject: Re: Do We Learn All the Math We Need For Ordinary Life Before 5th<br> Grade?

Richard Hake wrote (in part):

> ABSTRACT: In response to my post "Einstein on Testing" [Hake (2013)]
> at <> the following lively exchange was recorded
> on the archives <> of EDDRA2 [non-subscribers
> may have to set up a "Yahoo account" as instructed at
> <>]:
> a. Literature major and Standardista-basher Susan Ohanian
> <> stated that she (paraphrasing) "never
> seemed to gain any insight from solving the calculus problems in
> Courant's text, which struck her then as plodding and now as without
> meaning."

Courant's book is definitely a classic, regardless of whether she's
talking about the 1937 translation by McShane or the very similar
version co-authored with Fritz John that came out in 1966. I base
this on the many reviews I have at home of the various versions of
Courant's book (in my extensive collection of math book reviews)
and on the 1966 version that I've owned since about 1973 (and
which I have often mentioned in various internet posts over the
years, a few of which are listed below for those interested [1]).

Being a bit amazed that a literature major would be working through
Courant's book, I looked up the post that Richard Hake took this
from. What follows is a bit more detail about the Courant book matter:

* I like to tell the story that Hans, a newly minted Ph.D. in physics was
* stunned to find out he was married to somebody who never took calculus.
* I don't know quite what he expected from an MA in medieval literature,
* but the first year we were married he gave me an ugly calculus book for
* Xmas, explaining it was a classic in the field (Courant). The second
* year we were married I gave him a notebook with the problems worked out.
* I never seemed to gain any insight from this exercise, which struck me
* then as plodding and now I don't have any idea what any of it means.
* Nonetheless, doing calculus for love is a far better reason than the
* one promoted by Obama, Duncan, Bill Gates, et al.

Wow, this sure sounds fishy to me! First, and this part isn't fishy,
the fact that Hans thought to recommend Courant's book to her (given
her situation) strikes me as really naive and out-of-touch. I'd like to
say I'm stunned to find that a Ph.D. in physics would think Courant's
book was appropriate for her, but unfortunately I'm not. Second, and
this is the fishy part, I simply don't believe she (correctly) worked
even 20% of the problems, and yet her wording "with the problems worked
out" suggests she worked all of them (or at least, her wording was carefully
constructed to leave this possibility open). Indeed, quite a few of the
problems--perhaps as many as a third of them--are challenging enough that I
would expect the average (U.S.) upper level undergraduate math major
to have difficulty with them. Also, the words "plodding" and "no insight"
don't fit with the problems in Courant's book. It's as if someone said
she had carefully read all 3 volumes of "The Feynman Lectures On Physics"
and found the endeavor to be plodding and gave no insight into physics.


Dave L. Renfro

P.S. For what it's worth, I've also never taken a calculus course.
This, of course, shows that we shouldn't equate having taken a course
in Subject X with knowing Subject X. Neither implies the other, and I
can find counterexamples for both directions in my own experience.