[Edu-sig] Algebra 2

[kirby urner]

2008/10/7 Matt K <matt.kameron at gmail.com>:
> I'm changing pace slightly, after making 2 points:
>
> (1) Dot notation does exist in Maths. Its just called "subscript" notation
> instead. But its the same thing. I try to make a habit of using subscripts
> (and sub-subscripts) as much as possible because it shows the same logical
> relationship.
>

Subscript in the sense of "dictionary key" more than "index into
sequence" as the former is more like __dict__ or __module__ (namespace
ideas), the latter more like a sequence wherein order matters
(namespaces are more cardinal than ordinal, more like dictionaries,
e.g. an arbitrary mix of Klingon and Chinese characters as subscripts,
no collation assumed).

> (2) The fractions you show don't have beauty. In continued fractions, its
> recursion that has the mathematical beauty.

I think rank and file math teachers over-hype this "beauty" business,
then hypocritically suppress fractals pre-college, even in the face of
obvious public demand and clear relevance to the complex plane, an IB
topic at least.  Why not just say "interesting" or even "cute".  In my
own curriculum writing, I try harder to be less disappointing to youth
e.g.

>
> (3) A practical question - can any high/middle-school teachers give me clear
> pros/cons of using programming as a tool to teach algebra? I'm rewriting the

I've taught high school math professionally (elite Catholic academy)...

Remember our gnu math curriculum aims at comprehension of RSA
pre-college (the public key thing).  We actually assign
'Cryptonomicon' as required reading in some electives.

So you need group theory, Fermat's Little Theorem (don't have to prove
it), Euler's (more general).  Not any of it in exhaustive detail of
course, just a first pass, opening doors, showing there's life after
calculus.

> Year 8 maths program for next year (13-14 year olds) and am considering
> trialling using Python. The students are the school are very tech-savvy and
> I wouldn't aim to teach them anything more than formulas really... formulas,
> basic IO and some ifs. Maybe (maybe) could do a basic for i in range(20)
> loop, but nothing more than that.

Lots of sequences to get going (polyhedral and figurate numbers
especially, per Oregon Curriculum Network web pages).

Generators useful.

OEIS is available to each student, for independent study.

Vectors require VPython.

>
> Note that I am the computing teacher in the school; the majority of my
> teaching is the computing studies subjects for older students (15-18 year
> olds).

I'm a math teacher for Saturday Academy, or was doing that recently
(lots of public write-ups).  More recently I've been developing a
Python Briefing for mature adults only, mostly teachers who already
know a thing or two about math and computer science, though rarely as
much as I do (grin).

Kirby