Responding to Dave Renfro's post dt. Jan 15, 2013 2:57 AM (which is pasted below my signature for ready reference):
Thanks for that excellent (and most enlightening) response, Dave! I very much endorse your P.S. to the effect that 'having taken a course on subject X' does not imply 'having UNDERSTOOD subject X' (or vice versa).
I believe the links in your message you've provided to previous relevant correspondence are of great value.
I did go through a fair bit of that correspondence - some of it quite assiduously, indeed with paper and pencil in hand! (I must confess I did falter at several points, particularly when for adequate understanding I should have dug out old Calculus texts and the like - I simply do not have that kind of access readily available now).
I'm happy to observe that (at one particular thread discussing some quite subtle points on 'limits') one R. Colacitti was duly grateful to you and others who helped him with his doubts on "derivative using first principles NOT EQUAL TO derivative using power rule". (I wish I'd had something like such an Internet backup resource available when I was studying Calculus myself, way back when - I'm sure I would have gained a far deeper understanding than I did manage to do).
In particular, wrt the posts at "The Unapologetic Mathematician" - which I confess I did NOT work through in detail as it is huge - I was interested to observe that 'our usual suspect' Haim is present in quite his 'usual form'. Lou Talman came up there with a classic (NOT in response to Haim):
"Mathematics involves ideas as well as skills. Teaching either while ignoring the other is unconscionable".
(My observation here is that we too often find examples of the ideas AND the skills both not being explored adequately. This is often the case alas even in basic logical thought processes even aside from any mathematics).
Thanks for having explored that post from which Richard Hake had taken his tale. You're entirely correct in your observation that it smells more than a bit fishy that a "literature major would be working through Courant's book" and her (implied) claim of having worked through 'all of the problems' is even fishier - in fact, it stinks right to high heaven.
As I recall, several of those problems were pretty challenging for me - and I used to possess some fair skills in math, particularly in calculus!
All said and done, I feel I probably could repeat my earlier observation that some may as well have quit schooling by 5th grade or even earlier for all the good that schooling has done for them. This is not to imply that we should cease efforts to educate our youth (as well as others): what really needs to be done is, as I've claimed before, "to redesign our educational [and many other] systems".
Dave L. Renfro posted Jan 15, 2013 2:57 AM: > Richard Hake wrote (in part): > > http://mathforum.org/kb/message.jspa?messageID=8067464 > > > ABSTRACT: In response to my post "Einstein on > Testing" [Hake (2013)] > > at <http://bit.ly/UHjqET> the following lively > exchange was recorded > > on the archives <http://yhoo.it/iNTxrH> of EDDRA2 > [non-subscribers > > may have to set up a "Yahoo account" as instructed > at > > <http://yhoo.it/iNTxrH>]: > > > > a. Literature major and Standardista-basher Susan > Ohanian > > <http://www.susanohanian.org/> 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 ). > > 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: > > http://groups.yahoo.com/group/EDDRA2/message/3602 > > * 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. > >  http://tinyurl.com/b9stek4 > http://mathforum.org/kb/message.jspa?messageID=4071934 > http://mathforum.org/kb/message.jspa?messageID=4126649 > http://mathforum.org/kb/message.jspa?messageID=4161088 > http://mathforum.org/kb/message.jspa?messageID=6122912 > http://math.stackexchange.com/questions/79865/difficul > ty-level-of-courants-book > > 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.