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Mar 9, 2010 at 8:12 comment added gowers I too was going to suggest calculating square roots by means of successive approximation. I wouldn't go as far as to discuss the subtleties of the real number system, but this would allow them to feel it at an intuitive level.
Mar 9, 2010 at 6:12 comment added Bruce Westbury @Pete: This behaviour is as old as mathematics. It certainly is not helpful. On the positive side communicating mathematics does seem to be a skill that is getting better appreciated.
Mar 9, 2010 at 4:07 comment added Pete L. Clark @Bruce: your edit and new reponse is appreciated. I was speaking out against a sort of strange behavior that mathematicians sometimes exhibit, which is to grossly exaggerate how early certain concepts could/should be taught and learned. This is really not helpful. Let me try a little honesty: I did not know one iota of calculus until I was 16 years old. When I was in middle school I had my hands full learning about division of polynomials. Any talk of limiting processes would have sailed right over my head. (And I was a strong student.)
Mar 9, 2010 at 3:39 comment added Pete L. Clark @BW: Please see my response.
Mar 9, 2010 at 3:31 history edited Bruce Westbury CC BY-SA 2.5
New answer as I was way-off.
Mar 9, 2010 at 2:28 comment added Bruce Westbury Could someone say what "middle school" means? Thanks.
Mar 8, 2010 at 21:10 comment added Pete L. Clark Sin(x) in middle-school algebra? Again, this is off by several years from actual middle-school curricula.
Mar 8, 2010 at 21:04 history answered Bruce Westbury CC BY-SA 2.5