Thanks for wrestling with my questioning, Alan (btw - it seems we forgot to share our last two exchanges with the mailing list - my fault - I refrained from repeating your responses extensively here in case it not your intent to post them.)
On 8/16/07, Alan Kay wrote:
Of course, this is far from a scientific survey ....
You clearly know far more teachers than I do. I am shocked to hear that so few US math and science teachers were math and science majors, or were even educated in any college level math and science.
I suspect it is normal worldwide to postpone calculus until the equivalent of "Advanced Placement" courses in years 11 and 12 - I hope it is mandatory to know calculus before going to college for math, science or engineering (and perhaps for social science too.) Perhaps by the delay we then rob many kids the chance to (1) see its beauty and (2) see that it underpins so much of modern science and engineering.
As you point out, the algebraic model of calculus is not interesting to many people, but the difference model would, I imagine, be useful to every aspiring mechanic, lab technician or customer service supervisor.
But what if the secondary math teachers complained loudly? I don't think they are in any decision process that I can find.
I don't know the US systems very well. I would like to think that school boards and education departments consult professionals first. Are there countries where that does happen?
David