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A couple typos fixed, embedded hyperlinks
activated. Date: Thu, 29 Jan 1998 10:56:33 -0800 To: synergetics-l@teleport.com From: Kirby Urner <pdx4d@teleport.com> Subject: Syn-l: Math Centers (was: irrelevant observation) > >After correction, I can confidently say (check me on this) that: > >cos(central) = -1/3 > >cos(dihedral) = 1/3 > >and they add to zero. > >David Chako > This is primo stuff Dave -- how to make friends and gain influence among classroom teachers is by providing these little 'tips and tricks' that segue 21st century geometry into the existing curriculum without so much as a hiccup. Here we have this "yucky" angle of 109.471 degrees in need of PR, and right away we see it's simply the acos of (-1/3). Easily memorable, quickly absorbed. Right now, huge numbers of kids are sitting in rows and columns, calculators on their desks, unit circle on the chalkboard, teacher struggling to impart the sin and cos concepts, relate that to wavilinear stretchout xyz "radio-waves" and so on. In a math center, kids would be sitting at NASA-style consoles -- calculators handy maybe, but a computer screen, recessed and augmented with controls, would be more the focus. The central server would be stocked with lesson plan software, and if the day's unit were on trig-based oscilloscope functions, kids would net-access Java (or whatever) applications with native ties to twist-knobs or push buttons for changing amplitude, frequency, whatever other parameters. I realize it's perfectly feasible to provide whatever controls on screen and have just a mouse to twiddle the cartoon knobs, click buttons and so on, but I think it would be fun and useful to have these standard math center consoles come pre-equipped with generic bells and whistles that programmers could tie to applications (the kids themselves being programmers in many situations), and also with sockets for receiving input from compatible devices. This is important because we're not just training kids for bizapp cubicles here, but for workbench engineering, wherein a lot of the instrumentation controls are not just screen based, and wherein computers are very much used for realtime data aggregation via sensors of various description. The big screen up front shows the teacher's screen, or might be guest-slaved to any console in the room, say if junior is doing show and tell about some project and has slides to share (perhaps pre-screened with an advisor to keep the presentation tightly focussed). The big and small screens all have the capability to show documentaries and history is a big part of what goes on in math centers -- you need to see how hard the adults have worked to get us where we are, what dedication, even if the technologies no longer exist except in museums. What gets kids inspired is a sense of being a part of a long haul critical path project aimed at local problem solving in Universe, and not with an end goal in mind of wiping out humans in other math centers around the world (videogames OK, simulations OK, but making the point of the curriculum be mass death scenario planning is by its very nature demoralizing and tends to implicitly invalidate all the hard work of those long dead adults on screen, who worked their butts off for a more serious purpose than seeing it all go up in smoke). So we show documentaries about the origins of radio and TV (not forgetting Baird in any way), maybe in snippets, and then turn to our Java applet oscilloscopes, then a live interview with some guru in a real lab someplace (teacher moderating, kids asking questions via high bandwidth webcam), back to the applet, more puzzles. Then at some point the teacher can segue back to acos(-1/3) and zoom in on the central angle of an A-modularized tetrahedron, a well-known "home base" in math centers investing at all in 4D geometry (i.e. any with real brains behind them). The A-mod exploded view of the regular tet, the unfolding and inside-outing of the A (from left to right and back), the volumetric equivalence to the B -- this is all old hat to your average 6th grader. And now that we're doing trig, it all synchs. But we don't have lines to infinity so much as chords and arcs on giant spheres, which may seem locally flat. For example, out here at Hanford, we have some very long concrete casement used to detect gravity waves, so-called, but because it's supposed to be perfectly straight, it starts to slant into the earth, as a chord. That's something kids will appreciate. At first, math centers will be more the exception than the rule, and may need to be assembled, circus-fashion, at some point outside of town, versus trashing ancient factory-style school buildings to fit aerospace accoutrements into these ill-suited geometries. Kids will have to be bussed, and won't get more than a few hours of hands-on instruction per week or per month. Corporate logos will no doubt be a part of the veneer, proving to parents that the high tech sector is serious about getting kids conceptually outfitted for real work in the real world ala Project Renaissance -- something the current curriculum is simply not about any more, having fallen way out of synch on so many fronts (and I don't blame the front liners for losing this war for hearts and minds -- their generals failed them). The bizmos are more like those Army recruiting vans, which currently fan out across the country blaring "Be All You Can Be" to sleepy neighborhoods, show John Wayne movies or whatever it is. The NASA versions would be more like the Navy's (storyboard here): fully equipped with zoomable Fuller Projections complete with omnitriangulated GIS/GPS database access, and simulations about keeping terrorists from using this data for goo-goo brained short-circuitings of motherboard earth. We'll tell kids the military is about militating against spazzing out when a trully disciplined response is what's called for -- kind of like what the stereotypical martial arts teacher shares as playground etiquette: if you're really good, you won't find yourself in any physical combat situations at all, and not because you did anything out of cowardice or laziness that gave your opposition an advantage (nor were you a teacher's pet or tattle tail). I expect many teachers will line up to receive certification as math center trainers, and many kids will be at first wide-eyed with respect for this job as well, but may in time be recruited into other walks of life, or come back to these trainer positions after long and distinguished careers as CEOs or whatever. There will be no automatic seniority or social promotion of personnel from federally subsidized institutions -- all will compete on an even footing. Except the government itself may choose to fund some math centers of its own, in competition with the private sector, because it has a mandate to serve and to train in ways commensurate with its own mission-critical enterprise ideals and global responsibilities. In the USA, these may mean NASA itself gets into the act, in which case the staffing may well be preferentially tilted towards individuals with a NASA-style background (including cosmonauts of course -- Russians make some of the best math trainers, I know from experience). Of course other services already have math center like situation rooms, where videogame simulations of tank battles and so on take place. One would hope that the war colleges are likewise serious about 4D geometry, so that strategies aimed at providing real and lasting security at the global level aren't sidetracked by a lot of irrelevancies stemming from Victorian Era factory-based curricula. The last thing we need are more major generals of the Gilbert and Sullivan variety, who know many cheerful facts about the "square" of the hypotenuse, but know nothing whatever about their 20th century American heritage and the 4D geometry it supplies. If you don't know quite a bit of synergetics by this time, then you're simply out of the loop -- forget about your command and control responsibilities for now and go back to school and we'll get you retrained for active duty ASAP. Kirby Curriculum writer 4D Solutions |
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