On Sat, Jul 13, 2013 at 4:16 PM, Peter Duveen <email@example.com> wrote:
> My mind focused on this sentence in the Common Core Standards: "For > example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)^3 > = 5^(1/3)3 to hold, so (51/3)3 must equal 5. "We want" and "must equal" > seem like rather coercive terms for a scholarly subject like math. Or is > this math teaching, so students are fair game for coercive language and > tactics? I find it very hard to make sense of this statement. It goes > against the grain of my approach to exponents, in which I explore with the > student possible interpretations for the use of negative numbers, > fractions, zero, and 1, as exponents, based on the properties of/operations > with positive integral exponents greater than one. > >
The sleight of hand you may not notice, because already successfully brainwashed, is this:
"to be the cube root of"
where the word "cube" is slipped in as the one and only accepted model of 3rd powering.
But at Winterhaven PPS, a Portland, OR magnet school for geeks, a Geek Hogwarts, it is commonly taught that a triangle will serve to demonstrate / model 2nd powering.
The Pythagorean is shown / proved with two equilateral triangles, the areas of which add up to the equilateral triangle of the hypotenuse. a**2 + b**2 = c**2 (three triangles).
Note Python notation ( ** for power).
The high school analog: a tetrahedron as a model of 3rd powering. Topologically simpler than a cube.
Why not at least dabble? This is tourism, not dogmatism. We're young. Give us the big picture.
It's no big deal, at the mathematical level, making the swap, but the Common Core's building in "cube" here is testament to its intention to slam the door on other modelings.
Schools with self pride will and do counter this door slamming.
Here's something to brand on, a way of differentiating from the pack, the mediocre.
Is that wise, to force the "cube" as the only 3rd powering model?
Aren't young minds the most supple?
Should we be putting our finger on the scales so blatantly, and with such prejudice, at such an early age?
American transcendentalist philosophy / Medal of Freedom winner R. Buckminster Fuller thought it extremely important that we prevent hardening of the mental arteries too early, by staying flexible about the powering model.
This was one of his core exhibits of where we might go wrong, by skipping over an alternative, bleeping over a road not taken.