Re: [xmca] a minus times a plus

```I was trained in mathematics at the University of Cambridge (UK)
for my undergraduate studies, concentrating more on pure
mathematics (including algebra).  I am able to roll out a
rigorous abstract proof of why "minus times minus" is a "plus",
using only the basic axioms of real numbers (actually you only
need a few of those axioms).

However, abstract proofs aren't likely to be useful for non-math
specialists and struggling neophyte learners of algebra.  in
order to pull off such a proof, or even just to understand just
the few lines of proof, you almost need to be a mental masochist.
Who likes to go through mental torture?

Can we condense four thousand years of human development of
mathematical understanding into an easily digestible four minutes
for learners?

thus the huge gulf of understanding still persists.  that's why
as an educator, i feel so useless being unable to help other
people.   :-(

F.K.

2009/6/4 Mike Cole <lchcmike@gmail.com>:
> I am currently reading article by Fuson suggestion by Anna Sfard on whole
> number operations. I also need to study Anna's paper with exactly this
> example in it. Not sure what moment of despair at deeper understanding hit
> me. Now that I am done teaching and have a whole day to communicate things
> are looking up!! Apologies for doubting I could have deep understanding of
> why minus x minus = plus and minus x plus = minus. At present my
> understanding remains somewhat bifurcated. The former is negation of a
> negation as david kel long ago suggested, linking his suggestion to Anna's
> comognition
> approach. The second I think more of in terms of number line and