Re: Relational Theory & the New Math

From: Laconic2 <laconic2_at_comcast.net>
Date: Fri, 15 Oct 2004 07:36:24 -0400
Message-ID: <EaKdnRwvpojVK_LcRVn-hQ_at_comcast.com>


"Dawn M. Wolthuis" <dwolt_at_tincat-group.comREMOVE> wrote in message news:ckn82k$uce$1_at_news.netins.net...
> A colleage of mine was talking today about how the New Math of the 1960's
> and following grew out of the efforts of Bertrand Russel and others at the
> start of the last century to derive mathematics from logic. This is when
> set theory started getting introduced in a big way in schools. Russell's
> approach has been largely abandoned as a basis for mathematics (IIRC).

I got some exposure to the rationale behind the "new math" when I was in the peace corps. (What??? Yep!)

The real goal of new math, according to these sources was not to change the subject matter, but to change the methodology.

Math had always been taught as a king of catechism, where the students got facts drilled into them by just sheer discipline and repetition. They wanted an approach that would involve the children in thinking and discovery more. They found that there was no hope of getting math teachers to change their methods while dealing with the traditional subject matter, so they introduced "set theory" as a trojan horse, in order to get teachers to start using the new methods.

I was teaching future teachers, and I was having some trouble getting the basics of set theory across to them. When I read of a guessing game that uses blocks of different colors shapes and sizes, and three loops of strings that can be used to teach kindergarteners how to work with Venn diagrams, I tried it out with the kindergarten group in the school, with my students looking on.

Sure enough, it worked. By the end of 45 minutes there were two or three kindergarteners who could manipulate the Venn diagram faster than I could. And that's third world protein deciciency notwithstanding. Well, that's not saying much. But the author of the article told readers o expect that. I could go on, but it's another discussion.

>
> The 1960's is also when Codd started working with sets as a foundation for
> databases. I don't know the status of the "New Math" in our schools and I
> do definitely have an appreciation for set theory. But it is NOT
> everything-- there are other mathematical models that can shed light on
our
> discipline and help us get our jobs done. With relational theory we are
> trying to base everything on set theory, but when that doesn't have what
we
> need, then we add other functions as needed. If we start out recognizing
> that there are a variety of functions required -- those that aggregate
data,
> as well as those that extract sub-values from data, we might not tie
> ourselves unnecessarily to set theory exclusively.

AFAIK, the pedagogic enthusiasm over set theory, and Codd's early work are coincidental.

As far as other tools go, "to a kid with a hammer, everything is a set". The kid with the hammer mentality pervades IT. here are some things I've read: "everything is an object". "In unix, everything is a file". "In unix, everything is a printer." I am not making this up. No matter what the hammer is, the kid with the hammer, tries to force fit everything into one mold. It's not good.

I am, as you know, a relational enthusiast, if not a devotee. But for me, it's only one tools among many.

>
> I think I said that poorly, but thought it was at least worth noting. I
> know I still owe more info on non-1NF, but I don't have it in good enough
> shape yet. Cheers! --dawn
>

I am looking forward to it. Received on Fri Oct 15 2004 - 13:36:24 CEST

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