[Squeakland] Panel discussion: Can the American Mind be Opened?

[Alan Kay]

Hi David --

At 02:25 AM 11/24/2007, David Corking wrote:
>Hi Alan, You digressed into 'new math' and I disagree
>
>You wrote:
> >
> > Separate issues are: what parts of the real stuff should be taught to
> > children, how should the teaching be done, etc. This is very important in
> > its own right - recall the very bad choices made by real 
> mathematicians when
> > they chose set theory, numerals as short-hand for polynomials, etc. during
> > the "new math" debacle.
>
>When I was 16 I moved schools, and joined a cohort who had been
>educated in the Schools Mathematics Project, a English incarnation of
>'new math'.  I had kind of a traditional classical math education up
>to that point, and I felt like a fish out of water for a few weeks.
>My first impression was that my new classmates thought much more like
>real mathematicians, and at first that seemed like a pointless stuffy
>homage to academia.

Of course, I was referring to elementary school new math in the US, 
which tried to teach arithmetic via set theory and polynomial bases 
for different numeral systems. It would not be at all surprising if 
the SMP were better.

The point is not about the worth of set theory and number theory 
(both good topics for high school) but about whether they are 
appropriate for younger children. I have degrees in both pure math 
and molecular biology, and I agree very strongly with Papert's view 
that various kinds of geometrical thinking, especially incremental, 
are better set up for children's minds, and also allow deeper 
mathematical thinking to be started much earlier in life.

One way to think about this is that "mathematical thinking" (like 
musical thinking) is somewhat separate from particular topics - so 
the idea is to choose the most felicitous ones.


>Later I learned to enjoy the math for its own sake, but I had another
>surprise a couple of years later.  The SMP kids seemed much better
>equipped for the world of applied math at university and technical
>college.  Set theory and number theory are vital for computer
>scientists (as I understand), matrix algebra and numerical methods for
>engineers.  So when I got to college (to study engineering), I was
>glad to have had a chance to try my hand at real nineteenth century
>math in high school.
>
>By the way, I never learned, even today, any kind of general algebra
>or shorthand for polynomials, so I cannot comment on that.

I think you did, since "356" and all other numeral forms of numbers 
(whatever their base) are shorthands for polynomials (the 3, 4, and 6 
are the coefficients for polynomials of powers of ten in this case).


>It didn't hurt that in those days, most math teachers in England were
>math major graduates (so perhaps an example of the benefits of the
>Hawthorne effect we discussed.)

Why call this Hawthorne? I don't think this is what you mean here.

Cheers,

Alan


>By the way, the SMP still exists in a cut down form:
>http://www.smpmaths.org.uk/
>It didn't go down in a public fireball like 'new math' in the US, but
>instead seems to have been quietly squashed by the all powerful
>National Curriculum steamroller.
>
>Best, David