[Edu-sig] Algebra 2

[Matt K]

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.

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

(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 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.

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).



On Tue, Oct 7, 2008 at 3:42 PM, kirby urner <kirby.urner at gmail.com> wrote:

> On Mon, Oct 6, 2008 at 10:05 PM, DiPierro, Massimo
> <MDiPierro at cs.depaul.edu> wrote:
> >
> > I agree with this
> >
> > 1.  The importance of 'computational thinking' as a math standard
> > 2.  Python as a vehicle for this
> >
> > But it is important to make a distinction:
> >
> > a) a math formula represents a relation between objects and the objects
> math speaks about (with very few exceptions) do not have a finite
> representation, only an approximate representation (think of rational
> numbers, Hilbert spaces, etc.)
> > b) an algorithm represents a process on how to manipulate those objects
> and/or their approximate representation.
> >
>
> There's a whole philosophy of mathematics, and of language more
> generally, implicit in your (a) and (b), inheriting from both realism
> (as in "the reality of Platonic objects") and nominalism (as in "nouns
> point to things" -- with "pointing" considered entirely
> non-problematic).
>
> The linguistic turn (named by Rorty), launched by Nietzsche and
> culminating in Wittgenstein's later works, is about undoing some of
> these gestalts, returning us to a more operational view of how
> language works in the world (or doesn't).
>
> This is getting way off topic I'm sure some are thinking, and I agree,
> so just lets admit we don't all come to mathematics from the same
> perspective, and that this is as it should be.
>
> > While math and math teaching could benefit from focusing more on process
> and computations (and there python can play an important role) rather than
> relations, it is important not to trivialize things. For example:
> >
> > In math a fraction is an equivalence class containing an infinite number
> of couples (x,y) equivalent under (x,y)~(x',y') iff x*y' = y*x'.
> > Any element of the class can be described using, for example, a python
> tuple or other python object. The faction itself cannot.
>
> The way I'd put it is the class Rat (rational number class) spells out
> what fractions might do, in terms of __add__, __mul__ and so on, but
> then there's no limit on the number of fraction objects you might want
> to build from this blueprint, i.e. the type of object is distinct from
> the instances, in a pleasing, teachable, lexical way.  At least as
> relevant as Bertrand Russell's stuff if you ask me, this object
> oriented paradigm.
>
> And yes, no limit on the number of tuples that map to that tuple in
> lowest terms, which is where gcd comes in, gotta teach that.  Pre
> college algebra with no introduction to Euclid's Algorithm for the GCD
> is laughably idiotic and I openly sneer at the idea when I think no
> one is looking.
>
> >
> > It is important to not to loose sight of the distinctions. Math is gives
> us the ability to handle and tame the concept of infinite, something that
> computers have never been good at.
> >
> > Massimo
>
> I like Knuth's take, lectures at MIT (audio on the web, maybe video
> too as I recall), which is very into finitude.
>
> Accepting finitude takes courage too.  I'm glad our computers are
> harnessing it, leaving humans to their fantasies of greater greatness.
>
> Kirby
> _______________________________________________
> Edu-sig mailing list
> Edu-sig at python.org
> http://mail.python.org/mailman/listinfo/edu-sig
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/edu-sig/attachments/20081007/c7e5903a/attachment.htm>