On Sat, Nov 10, 2012 at 8:53 AM, Robert Hansen <email@example.com> wrote:
> The biggest problem, and Clyde's problem as well, is that the vast majority > of teachers do not have longitudinal experience. They don't know how this > process works because they have never seen the whole process work. They do > not teach mathematics to a student or a class of students for six straight > years, they are only responsible for one of those six years. This is > something I would address first. If teachers had more longitudinal > experience they would understand the progression. Can you imagine the effect > this would have on a teacher's experience? > > Bob Hansen
This sounds too linear, as if all math topics were on this timeline in a sequence and the job is to hit them in the right order, of increasing sophistication.
In actual fact, it's more like a network of multiple highways and byways. Fragments of group theory fit easily in Algebra 1 and make both better, but because Group Theory as a whole is quite sophisticated it gets thrown out until after Calculus. Permutations get left out as objects in group theory, despite all the free computer languages crying out to be sampled. Junior is saddled with the same linear sequence is grandparents had. Is that a good thing? By definition?
A severe reordering of the sequence, to where Carmichael numbers and Fermat's Little Theorem came in grade school, with Euler's Method for the GCD, would not be "harder" or "unrealistically demanding". It'd be as easy peasy as before. The idea that adding some group theory spice to the mix is somehow for the 2% elite high achievers is just stereotyping and typecasting.
Remember how New Math, when taught right, was not hard at all. Intersection and union, Venn diagrams, set operations, a trickle of propositional calculus, truth tables, boolean algebra... this was all very topical and, done right, was a boost. I use these concepts daily in my work. New Math was just the ticket for me, plus I had some old frashioned Brit arithmetic. Here's the mnemonic the Brits taught us: "a red indian thought he might eat tobacco in church" (arithmetic), to which my rejoinder is sure, of course, as tobacco was a holy smoke, not commercial, not Camels.
Anyway, with summer camp and scouting and such institutions, we can work around the fringes, the periphery, with these alternative sequences. You've probably hear of Math Circles. That kind of thing: http://www.flickr.com/photos/kirbyurner/3391860773/ (photo of book cover, Pycon 2009 sequence)
The image we want to discard is you're some kind of Johnny Neutron to wanna Make: stuff with us and learn some group theory along with your Algebra. It's more geek and more girl. Bronies? Getting closer maybe. Not saying you can't learn to shoot (or ride a horse) -- the more usual summer camp activities.
Computers and bandwidth.
Maybe these should be winter camps instead, or instead of school? Or are they schools already? Getting accredited is less important than having sponsors who want to hire our grads. We can work on accreditation as time permits.