[Edu-sig] a non-rhetorical question

[kirby urner]

> Long before we start talking about 'variables' and 'powers' and the
> like -- which is all part of the 'notationally true' world, we need to
> nail down the absolute truths about addition that the order in which
> you add terms does not matter.  Which we can then formulate as LAWS
> about addition.

Yes, I think this is a promising approach.  Traditional Algebra 2 mentions
field properties of say real numbers, but the ties to modulo arithmetic
have been broken.  One hallmark of Pythonic Math is we give the modulo
operator equal time, along with the other basic four.  Division makes more
sense when you have modulo ready at hand, a basic trick in the tool box.
Helps explain / versus // as well.

Only then might we do powering (to show off 2*100000 for example -- for
most calculators simply out of range), then back to modulo arithmetic
for powering modulo a modulus (by overwriting __pow__).

Why all this modulo abracadabra?

Because (a) Python makes it easy, especially to write a P-number that
adds modulo N (P for Permutation) and (b) if you want to explore the LAWS
of algebra, what better way than with (i) totatives of a composite and (ii)
totatives of a prime.  In the former case, we get group properties (laws)
over multiplication, in the latter, a Galois Field.  See my Showmedo series,
Python for Math Teachers.

Too hard for young kids?  I don't think so.  Teaching group theory to children
was always a part of the Alan Kay plan.  Now that OLPC... [ censored ].

Kirby