On Mon, Feb 22, 2010 at 6:14 AM, Pam <Pamkgm@hotmail.com> wrote:
<< SNIP >>
> On a side note - THIS is why I care about Devlin's comments. I really couldn't care less about the philosophical/mathematical nature of whether multiplication is repeated addition. And if elementary teachers teaching that multiplication is repeated addition is interfering with an understanding of post-graduate pure mathematics, well, too damn bad (and how laughable).
Good clear expression of a position Pam.
Early skills building is not a mirror image of some later specialty.
One hears this chorus saying "teach it that way and you'll ruin their ability to understand it my way."
To this chorus one might respond: your way is not the only way (not the only game in town).
On the subject of exponential debt curves, it's easy to get into a situation where every asset on Earth is "owed" thanks to an out of control model of what banking is all about.
We raise kids in a world where the collective debt load of "the richest nation on earth" (?) is already crushing and apparently cannot be repaid.
At the same time, planet Earth is an open system, receiving a generous energy income from the Sun (solar fusion furnace) that is both interest free and efficacious.
Where does this asset show up in the economic bookkeeping?
I would submit that our cultural storytelling, our "myths" if you will, is in a shambles. This is a root cause of a stagnating economy. We're not making enough sense, even to ourselves, let alone to our children.
Addressing this deep existential problem is the task of any civilization under the sun, and requires the contributions of both mathematicians and philosophers.
The way K12 mathematics is taught today, there's very little encouragement to "zoom out" to contemplate the bigger picture. It's a heads down, blinders on, narrowing affair. This needs to be countered.
Boosting the role of storytelling need not be at the expense of skills building.
On the contrary, providing a context, a real one, is more likely to be motivational.
Quoting myself from a few posts back:
""" The whole idea of making storytelling the core of a math class, as unifying heuristics, is somewhat "out there" from the standpoint of 1900s math teaching practices, but it's innate in many cultures, as any anthropologist will tell you, and really the burden of proof should be on those who refuse to tell stories: when did that ever work? Disney's 1959 little masterpiece shows what a difference it makes to add story (context), ditto that Time / Life book in the 1960s.