Thursday, August 23, 2007

More for the Queue

Math Forum:

Re: Problem solving with technology - TRE Study
Posted: Aug 23, 2007 1:09 PM

A traditional dynamic is students seek the endorsement, blessing, of some teacher who has a track record with other teachers and/or admissions departments. "This teacher isn't lying" is the reputation a teacher would like, about his or her students. So there's a quality control aspect to it: a teacher becomes known by the caliber of his or her students.

A factory floor approach to education tends to render this process somewhat more anonymous, in that teachers think they have ways to fade into the woodwork and not have reputations as individuals, but only as schools, as faculties. They hide behind state certification or whatever.

I think with the Internet we're moving back to an age where teachers are individually tracked and judged. You either have an impressive portfolio, and lots of stellar students claiming you as their teacher, or you don't. Publication still matters, but that's interpreted more broadly, given cyber-space and multimedia.

Many of tomorrow's teachers will begin their careers on YouTube. We see that already.

In the case of the gnu math stuff I write about, we have relatively few teachers over 30, though I think that's changing as we recruit more people from NASA and like that.


Math Forum:

Re: More Prototyping (gnu math thread)
Posted: Aug 23, 2007 12:56 PM

A lot of this gnu math stuff works backward from what we anticipate will remain important technologies just beneath the surface in many scientific and engineering applications, namely tcp/ip and sql.

At the college level, we expect decision points leading to pure math of the type Adrian endorses. Until then, K-12 has a "keeping doors open" design, which means we have technical careers more generally in view. This low level numeracy training is not about becoming a math professor any more than teachers of the English sequences expect only professors of that discipline to emerge from the ranks of its test takers.

However, it turns out a lot of traditional topics remain key even where tcp/ip and sql are motivating elements. Graph theory, a branch of topology, and spherical geometry (displaced by Newtonian calculus in recent memory), will remain important to many high schoolers, since our network of hosts is GIS/GPS mappable, with databases supplying the storage infrastructure, including DNS lookups.

Specialization comes later, in a liberal arts context, where the faculty are supposedly at the top of their respective games and therefore recruit more effectively, as chief advocates or avatars for their respective disciplines.

Our K-12 students, in the mean time, will have developed their critical thinking skills to a point of not being easily bamboozled ("virtual presidents" metaphor), so that departments that've slipped a bit will have a market-controlled way of measuring the discrepancy, which will presumably goad at least some faculty teams into returning to former glory, whatever that means in that context.

So anyway, we'll still have lots of geometry (with geography a combined topic, as the Egyptians intended), with lots of vector algebra, lots of calculus (though more compressed, by today's languid standards).

I expect O-notation to make a bigger splash, per Knuth's suggestion.

Old text books will still be usable/minable, especially as their copyrights expire and they appear on Google. The most up-to-date frameworks for contextualizing this older content will remain cyber-spatial, as now.

This is what I anticipate in any case. I may be off base in some of the details. Venn Diagrams definitely have a bright future. Data structures, OO... I'm pretty secure in my predictions around Python, as those are already coming true in many contexts.

Gnu math isn't owned and operated by me in a vacuum. I need to pay attention to my geek peers, and I do.

That's why I think I'm safe in saying MVC is here to stay, as a key heuristic, along with SQL and TCP/IP. Authors of strong K-12 alpha-numeracy writing (which includes lots of attention to Unicode) will typically demonstrate mastery over these concepts -- a refreshing change next to most of the wimpy stuff that passes for K-12 math stuff today.


Synergeo (#35179):

Re: Cloud Nines
Posted: Thu Aug 23, 2007 10:55 am

There's a lot of engineering testing on hold while people squander their short little lives on dead end projects for which they won't be remembered, or, if remembered, not fondly.

Reflexes have been slow to catch up with the new realities. But hey, that's the human condition according to Synergetics: slow reflexes (see "lag" in the index)

I enjoy screening the movie Idiocracy for people. Took it to Lithuania, along with Revolution OS and The Jerk starring Steve Martin.