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
On Sat, 24 Nov 2007 06:31:15 -0800, Alan Kay alan.kay@vpri.org wrote:
Hi David --
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.
Random data point: I had "new math", though in the 10-12 years age group.
I'm pretty sure I'm the only one who got it and I am, admittedly, something of an outlier. (I immediately started working through different bases, including base 11, which made hex and binary easier the following years when I started programming.)
I haven't been able to teach it to a younger kid, unless that kid has "instant" math, in which case it's not really teaching so much as a brief introduction.
squeakland@lists.squeakfoundation.org