On Jul 15, 2013, at 11:18 PM, kirby urner <firstname.lastname@example.org> wrote:
> When people say they're raising a number to the 3rd they often say "cubed"? Why? We explain why.
It wasn't arbitrary. They chose the most natural analogy available and it stuck. That should be the lesson. Why did it stick, everywhere? What is it that makes cubes so much better than tetrahedrons for teaching about the power of 3?
> But could there be a different shape instead, associated with 3rd powering, 3rd rooting? Sure.
Maybe, but I am certain it would have never been tetrahedron, before, now or in the distant future.
> And we branch off and explore a network of connected topics based on that premise.
What premise? That it was just by chance that "cube" became associated with x^3 and not tetrahedron? Is that what you believe? Seriously?
> Now you tell me what I'm talking about has nothing to do with raising a number to a 3rd power?
You keep missing the point. I am saying that tetrahedrons have very little (none) intuitive value to students learning about the 3rd power. The cube analogy is safe for the next billion years. My criticism is in the context of teaching students about x^3. If you are talking about exploring tetrahedrons and their unique properties with 10th and 11th graders, after they have competed algebra and geometry, then I think you have a great idea. Throw in your etymology lesson if you wish. But, as you would put it, if you don't teach them why the cube analogy dominates, then you are just wasting their time.
> You accuse me of obfuscation when it's been precisely about the number sequence 1, 3, 27, 64.... ? > I don't get what you mean. Your criticism is hard to decipher.
I am judging your material and statements based on their teaching value. You opened this discussion with a statement to the effect that if you are learning about cubing using cubes then you are old fashioned. It seems like you have some great material, for a 10th grader, but comparing it to cubes and their use in teaching x^3 seems like nothing but an act of sabotage on your part.