On Thu, Apr 26, 2012 at 2:55 PM, Paul Tanner <email@example.com> wrote:
<< SNIP >>
> When I said "no matter how we interpret "="" I meant within the > boundary created by the definitions I gave. >
Right, and what I'm saying is that, given developments in STEM, we know our AMNs ("amens" or animated math notations) are tending to repurpose the "=" symbol to mean "assignment operator".
Curricula which either (a) bleep over the assignment operator role or worse (b) heap scorn on "computer languages" in bigoted fashion, should be discontinued forthwith, most obviously.
I'm saying that not making room for other meanings of "=" is out of step with STEM, and that the math teachers are falling behind in failing to update their lingo. No "math objects" even, a minimal requirement.
In terms of passing our standards, we see a "no go". NCTM may be trying to palm off CCS (Common Core Standards) on "private corporations" but from my viewpoint here in Silicon Forest, there was no implicit nor explicit groundswell of support for this new "standards movement".
Common Core was mainly for the convenience of big publishing, still having pipe dreams of continuing the wood pulp publishing industry in its humongously wasteful form, as if teachers pushing such abuse of world resources could have any credibility with their still-thinking students.
>> If "=" is a naming device, used to assign names to objects, then all >> the above theorems are blown out of the water, thanks to disagreement >> on definitions. > > It depends on whether this use of "=" as a naming device is within the > boundary created by the definitions I gave. If it is within, then the > theorems apply, if not, then they don't. It's not so much that they > are "blown out of the water" as it is that they simply don't apply > because the definitions for the symbols are not compatible. >
Right. So then it's more a question of "your meme pool or mine?" and I'm suggesting that STEM needn't get sidetracked into propositional calculus based on Frege's wrong turn (he was a greater logician than Russell, most in my circle seem to think, alluding to our earlier "top ten" thread).
Happy Birthday to Wittgenstein (today) by the way. I'm off to a lecture in celebration (though on a different topic -- we'll find a connection).
> Well, except for the special uses in some parts of computer science of > the same symbols like "=", just about all of mathematics including the > use of symbols is based on sets and logic. Take away sets and logic > and the result is that there isn't much left, including in computer > science.
Actually, take away sets and logic and you have everything up to the historical point where those disciplines invented themselves. Of course "logic" goes back a long way, converges with rhetoric, part of the old trivium / quadrivium and all that.
sets are of fading importance to foundationalists on many branches.
New foundations are always in the works, as its an industry, not a finished product.
That is the promise of Logic: many secure jobs, if you keep applying yourselves etc.
However, in K-12 we're not about indulging these foundationalists to the nth degree, any more so than creationists (of whatever stripe).
And where the focus is STEM, we don't segregate the "computer stuff" into a separate bin and tout mathematics as an aloof-and-above subject (how ugly / dark ages).
More airtime for "=" as "assignment operator" is a hallmark / signature of a thinking / working curriculum. I would encourage parents to sniff closely.
If it doesn't pass this sniff test, one of many, and if only expensive wood pulp is offered, then definitely you're invited to join the resistance.
Speaking of which, here's another movie about Occupy, this one out of Portland, my home town.