I'd change the focus a bit and ask if "machine grading" of mathematics is OK.
In one sense, yes, in that you get immediate feedback from Python if you enter wrong syntax, or a host of other mistakes could get you an exception, either TypeError or ValueError or ZeroDivisionError or...
But in another sense, to really teach math, talking about the exercises part (recall vs recog), you need to have students "show their work" or, in the case of writing algorithms that run on a computer, "show a draft" that maybe doesn't work quite the way it should, and so "teacher, please give me a clue".
So then the teacher needs to be more than an auto-grading robot right?
One reason students hate math pedagogy so much (and never encounter mathematics -- Lou was saved by dint of good fortune) is it's where Uncle Sam or whomever has decided to cut corners and make machine grading more and more a part of the process.
Not to be too crassly commercial, more to underline walking my talk, our school employs no robo-graders and multiple choice questions are few and far between. We teach mathematics for the digital age.
That's in part because our founder, Scott Gray, a successful PhD calculus professor at the university level, had gone to Russia and decided their calculus students were just "getting it" at a deeper level. Why?
The US version of math learning was too formulaic, to "memorize and regurgitate". That was part of it. Too passive. Scott became one of those "kill your television types" and wanted students to take an active role, using whatever tools, and getting feedback. His model: the Maker Cube.
So his company, before bought, was named Useractive, as in "the user must be active" (the student must be engaged and doing something).
The DIY (do it yourself) bias is probably what attracted Dale, found of Make: magazine, who brought Useractive into the fold of O'Reilly Media (which is not itself anti video in anyway, but probably some of Scott's skepticism rubbed off -- he'd moved on by the time of this posting).
Anyway, given our focus on the supply side (the teaching of mathematics) it stands to reason we should not just talk about students and their coping strategies, but about teachers and their bags of tricks.
Do they grade by machine? What other short cuts do they employ? How old a textbook is too old?
Do teachers have any say, any clout, any juice in a school? You'd think they would, but what if you think wrong?
In my assessment the spatial geometry in K-12 is almost uniformly too crude to pass muster. "Not 21st Century" would be my verdict. Too 1900s. But then teachers are in no position to lift a finger.
Theirs is not to reason why. That's the number one message. Here's the textbook, now go teach. Don't complain it's weak on history, of course it is, it's a math book, what did you expect?
This squelching of teachers and their views is paradoxical, especially for those in the "reasoning business", math having links to logic and rhetoric, the rules of fair argument, for judging hypocrisy, conflict of interest etc.
However, my Algebra, a gateway to more digital math, showcases one way to compensate for current shortcomings:
Bring in vectors early, as Python classes i.e. as types of object, that participate in
(a) constructing colorful polyhedrons and screen and
(b) having them rotation and scale
VRML, HTML canvas, OpenGL... old fashioned paper modeling. So many technologies converge at this juncture. With spatial geometry beefed up, we'll be stronger across the board, throughout STEM. I'm not saying to avoid 2D (I've got Tractor Math for that), just don't neglect your sphere packings, your lattices.
Where will the impetus come from though, if not from teachers?
Students know no better, by definition.
I'm thinking competition is part of the answer. Those who've made the right investments (e.g in spatial geometry) will be in a better position to reap the rewards.
I suppose one could say my hopes for a better future come with a Darwinian sheen. I like to expose what's phony baloney.
On Thu, Jul 3, 2014 at 3:37 PM, Joe Niederberger <email@example.com> wrote:
> R Hansen: > >So the talented musical students are either not playing Beethoven, or if > they are playing Beethoven, then Beethoven isn?t a parallel to calculus, or > if Beethoven is a parallel to calculus then it isn?t just playing Beethoven > that is a parallel to calculus, it is understanding Beethoven that is a > parallel to calculus, which makes just playing Beethoven a parallel to > arithmetic. > > Yeah - something like that. The problem is trying to take a rough analogy > too far. > > R Hansen: > >And some people might look at these kids and say they don?t have enough > theory, which floors me, considering how good they are (at what ever it is > we agree they are doing). > > I listen to some of them and say they don't have enough rhythm. And so > there's another imperfect analogy to explore. I mentioned that at the piano > recital I just recently attended, not a single performer could play with > convincing rhythm. Why is that? Because students haven't had enough time to > develop rhythmic sensibilities? Of course not. Its because the teacher > wants the correct notes above all else. > > Kirby asks, earlier on: > >Why has all the joy and imagination been sucked out of math teaching? It > seems deliberate. > > I think there may be a rough analogy with the above. > Details left as exercise ;-) > > Cheers, > Joe N >