(1) to be sure that students who will become mathematicians, know math (and technology)and
(2) to be sure that students who need to use math in other disciplines (which is of course the larger group), know how to do their math with technology?
There is something left out:
(3) to be sure that students who need to use math in other disciplines know math.
Note the difference between (2) and (3).
I hope that "calculus reform" (or "math education reform") hasn't devolved to "using technology." An equation solver will tell students that the solution to 3x=6 is x=2; yet, I still get students (in college!) who, in effect, subtract 3 from both sides instead of dividing, when they do it by hand. That is not satisfactory; technology does not help here.
Also, in response to Victor, I think that high school and college are not just surveys of what subjects are *about*, but rather, should give students a taste of what it's like to *do* these subjects. Students should spend some time *being* physicists, musicians, historians, sociologists. That means doing some nitty-gritty. Go outside: there's a big tree or building. How high is it? What happens when you increase the length of a penduluum; sure it goes slower, but by about how much? How does a medical examiner know how long ago a body expired? (Related: let's measure some arsenic in drinking water.) The fact is, these are good things to do, you need math to do them, and you need to understand the math. If you'll pardon the slang, Magliozzi is full of it; we ought to know better than to let him get away with it, or to try to put the best face on his bald statements.
Math teacher self-loathing is getting tiresome.
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