[Edu-sig] further exploration

[michel paul]

I took the kids to the lab yesterday.  I had our tech guy install VPython.
It's great finally having a tech guy who has done some programming!  Again,
this is a Functions, Statistics, Trig class, although the curriculum is
actually organized as Statistics, Functions, Trig.  I'm going to suggest
reversing that next time, but in a weird way it actually worked starting off
with statistics and using list comprehension for sigma.  I just told them
don't freak out, this is meant as an introduction, so relax and notice how
you can read the code almost like a natural language, that's all you need to
see right now.  Regarding standard deviation, I said don't memorize
formulas.  Just learn these concepts:  1.  Standard deviation is the square
root of variance.  2.  Variance is the mean of the squared deviations.  3.
Deviation is difference from the mean.  Using list comprehension you can
express each of these thoughts in a set of one liners.  All we need are
functions for mean(L), deviations(L), and squares(L).  Then we're all set to
define the variance(L) as the mean of the squared deviations of L.  That
last sentence right there easily translates into def variance(L): return
mean(squares(deviations(L))).  I know that some of them appreciated the
elegance of that.  There definitely were some who got it.  I think seeing
the ideas spelled out like that is way better than using a statistical
software package.  This way they can own their thinking.  Its just a matter
of getting them to buy into it.  So I took them to the lab and had them use
these functions  and then create histograms using VPython.  I embedded the
VPython syntax for them into simpler functions like histogram(L, intervals),
so all they had to do was supply some data and their preferred categories.
Toward the end of class I clued them in on the 'examples' folder in VPython
and had them explore random blocks and stonehenge.  They loved it.  They
oohed and ahhed when I had them use the mouse buttons to dive in.  And then
I just let them explore.  It was great.  There has still been some
resistance or disinterest on the part of some students, but I think this
impressed even them.  There's still the factor of kids who might remain
resistant because it seems overwhelming and they feel intimidated by it all,
and the 3D stuff might have scared them some more.  I don't know how many
might still be in that category, but that's what I have to find out next.

- Michel
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