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Re: The Cycle of Education
Posted:
Jul 13, 2009 2:19 PM


RH: > Isn't engagement an ultimate role of the teacher? > Especially an elementary teacher? I don?t know what > teacher school looks like but don?t they teach this > part of teaching? Or is this unfortunately a "knack" > thing and we will always have teachers that have it > and teachers that don't?
Let's remember that one reason the calculators caught on in the first place was they were fun to play with, but also low bandwidth enough to not detract from the teacher up front so much.
With these big LCDs in front of each student, per the digital math format, the dynamic inevitably changes, some experimenting with *not* rank and file layout, but more a horseshoe with a central conference table. This allows for role modeling, multiple hat wearing e.g. when you're at the table, teaching projecting, there's no LCD competing for your attention. Here's a floor plan:
http://worldgame.blogspot.com/2009/06/atworkagain.html
Engagement with the shell is what we're striving for initially, i.e. like with a calculator, there's what's called REPL as in "read, evaluate, print, loop".
So for example we go:
>>> 2*10000 20000
>>> 2**10000 19950631168807583848837421626835850838234968318861924548 52008949852943883022194663191996168403619459789933112942 32091242715564913494137811175937859320963239578557300467 93794526765246551266059895520550086918193311542508608460 61810468550907486608962488809048989483800925394163325785 06215683094739025569123880652250966438744410467598716269 85453222868538161694315775629640762836880760732228535091 64147618395638145896946389941084096053626782106462142733 33940365255656495306031426802349694003359343166514592977 73279665775606172582031407994198179607378245683762280037 30288548725190083446458145465055792960141483392161573458 81392570953797691192778008269577356744441230620187578363 25502728323789270710373802866393031428133241401624195671 69057406141965434232463880124885614730520743199225961179 62501309928602417083408076059323201612684922884962558413 12844061536738951487114256315111089745514203313820202931 64095759646475601040584584156607204496286701651506192063 10041864222759086709005746064178569519114560550682512504 06007519842261898059237118054444788072906395242548339221 98270740447316237676084661303377870603980341319713349365 46227005631699374555082417809728109832913144035718775247 68509857276937926433221599399876886660808368837838027643 28277517227365757274478411229438973381086160742325329197 48131201976041782819656974758981645312584341359598627841 30128185406283476649088690521047580882615823961985770122 40704433058307586903931960460340497315658320867210591330 09037528234155397453943977152574552905102123109473216107 53474825740775273986348298498340756937955646638621874569 49927901657210370136443313581721431179139822298384584733 44402709641828510050729277483645505786345011008529878123 89473928699540834346158807043959118985815145779177143619 69872813145948378320208147498217185801138907122825090582 68174362205774759214176537156877256149045829049924610286 30081535583308130101987675856234343538955409175623400844 88752616264356864883351946372037729324009445624692325435 04006780272738377553764067268986362410374914109667185570 50759098100246789880178271925953381282421954028302759408 44895501467666838969799688624163631337639390337345580140 76367418777110553842257394991101864682196965816514851304 94222369947714763069155468217682876200362777257723781365 33161119681128079266948188720129864366076855163986053460 22978715575179473852463694469230878942659482170080511203 22365496288169035739121368338393591756418733850510970271 61391543959099159815465441733631165693603112224993796999 92267817323580231118626445752991357581750081998392362846 15249881088960232244362173771618086357015468484058622329 79285387562348655644053696262201896357102881236156751254 33383032700290976686505685571575055167275188991941297113 37690149916181315171544007728650573189557450920330185304 84711381831540732405331903846208403642176370391155063978 90007428536721962809034779745333204683687958685802379522 18629120080742819551317948157624448298518461509704888027 27472157468813159475040973211508049819045580341682694978 7141316063210686391511681774304792596709376
>>>
A reason for doing a number that big is precisely to promote "engagement" and, in this case "disengagement" (in the sense of disillusionment) with these far less powerful calculators, which we're allowed to actively "diss" (disrespect) in gnu math, as a part of our outreach to oppressed majorities (e.g. the nongeeks).
We call it "bridging the digital divide", a rhetoric shared with the AlgebraFirsters, even though my school is more into geometry. But then our students are older (>= TV14), know how to type for the most part, and get our cultural allusions, e.g. I might call exponentiation (**) "like multiplication on steroids" (it's a doubled asterisk after all), which'd prolly go over the heads of younger children, but if they've ever tracked baseball, watched the Olympics, they know of these chronic problems and appreciate a teacher keeping it real in that way.
Defining a function is really easy too:
>>> def f(x): return x**3
Then for ordered pairs it's just:
>>> pairs = [ (x, f(x)) for x in range(10, 11) ]
stuff like that. Of course you'll want to save work for teacher review, resuming next session, and we get to that pretty early (though maybe not the first day).
All this amazingly powerful software for free, though you might pay for addons. Haim will bring up hardware costs, but think of what we're saving by not buying textbooks in hardcopy. If you need to print sections, do so, but on your own dime. Given Oregon kids tend to be tree huggers, they nod appreciatively here, find most adults ridiculously wasteful of the Earth's resources. Having real engineers writing curriculum just feels nicer, like someone really cares.
In my experience, high schoolers are grateful to finally gain access to computers from a mature adult perspective i.e. let's unlock the mysteries of these beasts in the process of learning how things work from a mathematical point of view. Keith Devlin calls it "making the invisible visible."
Before long, we're talking about SQL, RSA, a lot of geek lore. Rear Admiral Grace Hopper and Ada Byron get focus, unlike on the AM track, where they don't celebrate people hardly at all, let alone ours. Leibniz is another hero. A lot of these kids maybe delve into 'Baroque Cycle' so know where we're coming from, in terms of connecting math topics to history. Again, we're talking engagement.
Once teachers master the pedagogical skills required for math labs, they're likely to encounter far more motivated students. This curriculum is a far cry from that dreary calculatorbased stuff they were doing out in 'burbs. Good thing we have Max.**
Kirby
** http://worldgame.blogspot.com/2009/07/planningcharter.html (Max is our light rail system, used by many PPS students, part of TriMet).



