[Edu-sig] a non-rhetorical question

[kirby urner]

On 7/7/07, Michel Paul <mpaul at bhusd.k12.ca.us> wrote:
> I was very happy to see this book come out recently:
>
> "Mathematics for the Digital Age"
> http://www.skylit.com/mathandpython.html
>

Hey thanks for sharing that.  I wasn't aware of this resource.

They give a succinct summation of the "math through
programming" approach:

"""
We believe that starting in college is too late. Many
concepts are completely accessible to middle and
high school students. And there is also another side
to the relationship: just as mathematics helps achieve
a deeper understanding of computer programs,
some hands-on experience with computer programming
helps make mathematics more tangible, familiar, and
easier to grasp.
"""

> >here we are in 2007 and most high school
> >math classes are stuck in the calculator era.  What happened?
>
> Marketing.  Cleverly appropriating teachers to perform free advertising
> and sell product by calling them 'leaders'.  Getting textbook publishers
> to feature calculator sections in each chapter, thereby creating a
> status quo where technological integration has "already been handled".

Well, we're going to be using marketing too.  I'm eager to compete, as
I think math through Python has way more integrity and relevance than
all this crappy TI stuff they dish out.  Tiny screens, very black boxy, all
the algorithms hidden from view.  Programming a rational number class
is way more likely to produce insights than just going (1/3) + (1/8) on
a calculator (presuming it has a rational numbers feature).  Plus the
job-relevant skills you pick up doing real programming...  CP4E is just a
better way to go.

> Also, I believe part of the problem is the perceived division between
> CS and mathematics.  CS has grown to become its own discipline and
> its own department at the university level, so when we talk about
> integrating CS into math classes, people are apprehensive, thinking
> we're adding some "other subject", some "additional layer", to the
> math curriculum.

Yeah, that's the overspecialization I was talking about (Knuth talks about
it too, and Bucky of course).  Good thing we have the philosophy department
as a kind of switchboard between these disciplines (meant semi-sarcastically
with regard to most of today's academic philosophy, but earnestly too, as
philosophy remains a great source of overview and perspective).

> For example:  >>> for x in domain: x, f(x)  There's actually LESS layering
> going on there.

Right.

> It does make sense in our math-phobic educational climate to show beginning
> programming students how they can do fun things without having to worry
> about the algebra, and quite a lot of good effort has gone into this.
>
> But simultaneously, I think it makes tremendous sense to show students how
> a kind of algebraic thinking is fundamental to our technology and to weave
> this into math classes.
>
> - Michel

And here is where Polyhedra come in, as mathematical, visual *and* very
amenable to an OO approach.  Yep, philosophy is where it's at (echoes of
Plato).

Kirby