
Re: New Math: What am I missing?
Posted:
Mar 5, 2007 1:11 PM


Nothing much. I've made the point here repeatedly that folks I spoke with who actually worked on these projects (e.g., Joe Payne, now retired from the U of Michigan) say pretty much the same things regarding "the" New Math. The Dolciani books got there firstest with the mostest and became for most of the nation "THE New Math." End of story.
You may be one of the few to actually find out for yourself. I wonder what impact this experience might have on your thinking about judging the efficacy of books or methods you have no or very limited experience with or exposure to. And I use the word "you" more generally. Imagine if reading a book or teaching from it, or observing a quality teacher use it were a requirement for those who want to spout off about the efficacy of the book. Whatever would Paul Tanner, Wayne Bishop, and a host of other pundits do?
On Mar 5, 2007, at 12:48 PM, Adrian wrote:
> So, in my pursuit of the perfect math program, I stumbled across > the Gelfand Correspondence Program pretty quickly. Even faster > than that virtually anyone will quickly find stuff like the > Singapore Math program or Saxon or whatever. However, not only are > all the books out of print, but virtually everyone I talk to  > mathematicians, included  seem to all know what an abject failure > New Math was. You cannot even terribly easily acquire and look at > a representative textbook. Well, I have finally gotten a hold of > two books: _Geometry_ by Moise and Downs as well as _Modern > Algebra_ by Allen and Pearson. I guess you never "really" know > until you actually try to teach your kid out of it, but flipping > through these books I was immediately impressed by the following > > 1) These books are totally doable. They are not as hard as > Singapore. These are not your standardsbasedwe'retiredof > dumbeddowneducation books  not that they are dumbed down per se >  just that they're not super hard, either, so that normal kids > can do it. > > 2) They cover normal material. It's not like after you get through > these books you know a whole lot of set theory but still cannot > factor or something. These books cover the material of high school > algebra and geometry just fine. > > 3) They do include set theory and lots of discussion of logic and > methods of proof. It is not formal set theory and they aren't > trying to cover decidability or some such thing. It's just really > basic stuff like "List the subsets of {a,b,c}." They talk about > how to use the contrapositive of an implication to prove something >  a little bit of p's and q's  that sort of thing. > > It strikes me that this is it. Am I missing something? Because we > don't do it with books like this in high school, this sort of stuff > is standard fare for first courses in abstract algebra or > combinatorics. Is this unteachable? Really? Is this absurdly > formal? These sorts of characterizations of this material are just > ridiculous! Do I just have the wrong books? Maybe these aren't > representative of New Math? Is that what it is? > > Also, I have largely associated "New Math" with this University of > Illinois program that I found back when I first looked into it just > long enough to find out that even if it was good it was "out of > production". (So, I just dropped it in favor of other things at > the time.) The Illinois project was interesting enough in that it > had some mathematicians in the background, but the main program of > New Math  the SMSG  was not only headed up by a mathematician, > but a guy that got his PhD from Princeton under Lefschetz! The > more I am looking into this  looking at the books and materials > as well as the people involved  the more it looks like New Math > was just mathematics handed down to society by its mathematicians. > And, through some sort of ridiculous politics it has now fallen so > out of favor that it is all but disappeared. The MAA keeps records > on it, though. Do they keep all the "Back to Basics" stuff on > file? Do you think the "New New Math" will be preserved by th! > e MAA? And, the MAA still publishes monographs by mathematicians > for high school students under the banner of the "New Mathematical > Curriculum". What am I missing here? > >

