[Edu-sig] Re: More on intro to Python (today's 3 hr training)

Kirby Urner urnerk at qwest.net
Thu Mar 31 20:59:34 CEST 2005


> > So my general question is, as usual:  wouldn't this be an interesting
> > and intelligent way to teach math?

<<SNIP>>
 
> I think it would be ... were it not for the following "facts":
> 
> 1) subjects are taught in a compartimentalised way, leading to easy
> testing/grading ...
> 
> you don't teach introductory numerical analysis
> at the same time as
> you teach introductory computer programming
> at the same time as
> you teach introductory calculus
> at the same time as ....
> 
> (exception: many learn most of the useful math stuff in their physics
> class first, at least in North America.)

Yes, there'd need to be some rewiring, resequencing, that much is clear.  

In my experience, a lot of people are attracted to programming and would
welcome more exposure from a young age.  A high school track might mix
programming with discrete math topics plus mix in stuff currently considered
more college level (some group and number theory), in an introductory way.  

This would be an alternative to the standard pre-calc/calc track, which
dominates and currently leaves little room for serious alternatives.

In the old days, a king would hire some Merlin character, a tutor, who
presumably had a custom curriculum for his ward.  Nowadays, with everything
done factory style, we have fewer opportunities to experiment with
alternatives -- but it's still feasible.

> 2) A mathematical limit is not the same as a small but finite numerical
> precision.  Mathematicians would probably cringe at the thought of
> teaching about using these two side-by-side in the same course.
> 

They shouldn't cringe.  The finite numerical precision methods use a sigma,
whereas at the limit we get the swoopy Riemann sum notation.  The difference
is encoded in the notation.  Mathematicians have nothing to fear.  Having
them together helps advertise the power of calculus -- at the limit we often
get this closed form other function, amenable to direct evaluation, no
for-loop need apply.

> Of course, if one has the freedom to be able to cover many "unrelated"
> topics to the same group of students, one can get away with it.

That's the trick.  How might we make this more feasible?  Too much lock
step, too much enforcement of curriculum designs inherited from a
pre-computer age.

> However, I don't know of many places in North American Universities when
> you can do such a thing  (One exception might be the University of
> British Columbia where they introduced a general 1st year science course
> covering biology/math/physics/chemistry.)
> 
> However, I wish one could try it.  (In fact, I'd love to be given that
> opportunity one day!).
> 
> André

I hope you get it.  I have something like this going with high school aged
students.  I mix Python and math topics however I like, for a few Saturdays.
They don't get academic credit, but it looks good on college applications,
plus they even learn stuff.

Kirby




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