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Topic: Common Core snippet a little distressing
Replies: 73   Last Post: Jul 26, 2013 6:27 PM

 Messages: [ Previous | Next ]
 kirby urner Posts: 3,690 Registered: 11/29/05
Re: Common Core snippet a little distressing
Posted: Jul 13, 2013 10:44 PM
 att1.html (3.6 K)

On Sat, Jul 13, 2013 at 4:16 PM, Peter Duveen <pduveen@yahoo.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.

Here's a famous figure from his magnum opus:

[image: Inline image 1]
http://www.rwgrayprojects.com/synergetics/s09/figs/f9001.html

selfish), then how about in literature?

What's a transcendentalist anyway?

You mean like Thoreau?

Kirby

Date Subject Author
7/13/13 Peter Duveen
7/13/13 Robert Hansen
7/13/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/15/13 kirby urner
7/14/13 Wayne Bishop
7/14/13 kirby urner
7/14/13 Wayne Bishop
7/15/13 kirby urner
7/15/13 Robert Hansen
7/15/13 Christian Baune
7/15/13 kirby urner
7/16/13 Wayne Bishop
7/16/13 kirby urner
7/14/13 Wayne Bishop
7/14/13 Joe Niederberger
7/15/13 Joe Niederberger
7/15/13 Joe Niederberger
7/15/13 Robert Hansen
7/15/13 kirby urner
7/15/13 Robert Hansen
7/16/13 kirby urner
7/16/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/15/13 CCSSIMath
7/16/13 Joe Niederberger
7/16/13 Robert Hansen
7/16/13 kirby urner
7/17/13 Joe Niederberger
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 kirby urner
7/17/13 Robert Hansen
7/18/13 Wayne Bishop
7/17/13 Joe Niederberger
7/17/13 Joe Niederberger
7/17/13 Robert Hansen
7/18/13 Wayne Bishop
7/18/13 Joe Niederberger
7/18/13 kirby urner
7/18/13 Joe Niederberger
7/20/13 kirby urner
7/19/13 Joe Niederberger
7/19/13 kirby urner
7/19/13 Joe Niederberger
7/19/13 Joe Niederberger
7/20/13 kirby urner
7/21/13 Joe Niederberger
7/23/13 kirby urner
7/24/13 frank zubek
7/24/13 frank zubek
7/24/13 kirby urner
7/25/13 frank zubek
7/25/13 kirby urner
7/25/13 frank zubek
7/25/13 frank zubek
7/25/13 frank zubek
7/26/13 frank zubek
7/26/13 frank zubek