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:
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 non-geeks).
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 (>= TV-14), 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 add-ons. 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 calculator-based stuff they were doing out in 'burbs. Good thing we have Max.**