On Jul 15, 2013, at 1:30 PM, Joe Niederberger <email@example.com> wrote:
> In this particular case, though, I'd have to suspect that Robert just doesn't see it.
Is it too much to ask that if you claim that I don't see "it" that you say what "it" is?
Look, I stacked 1 bag of sand here, and then I stacked 8 bags here, and then 27 bags... Do you see how stacking bags of sand is cubing?
An extreme example? How does that differ from stacking tetrahedrons if the students can't connect it to "cubing" other than it happens to be 1, 8, 27...
Sometimes I think you (Joe) are talking about advanced students who already know cubing (and algebra and calculus) and this tetrahedron stacking an engaging activity. Like figuring out why the sequence 1 + 3 + 5 + 7 ... results in perfect squares. But Kirby produced this as an example of teaching "cubing", only because it happens to result in a sequence of cubes. So does the sequence 1 + 7 + 19 + 37 + ... But neither are very intuitive ways to teach cubing.
We teach cubing with cubes because it is easy to connect the two. It is easy to go from line to area and from area to volume. It is easy to show how increasing the dimensions increases the base of x^3.
 connect: determine through reason that two things are mathematically identical at some level.