It seems to me that we college teachers have done an absolutely rotten job of conveying to schools, parents, and school teachers what we expect or would like from their students. We don't even communicate among ourselves about problems as they arise.
For example, somewhere in the last 50 years 3-dimensional geometry got lost from the curriculum--not through any conscious decision or recommendation from an August Body, but through our not communicating to schools and to ourselves that it is important and we shouldn't let it slip away. It used to be possible to take solid geometry in either school or college. Now you can't find it anywhere, although students really need it after elementary calculus.
In the 80's we began to get a wave of students who had calculus courses in schools (often at the expense of a solid grasp of fundamentals, it would appear ). It seems clear that instead we've always wanted students who are ready for calculus, not ones who know some of the punch lines but none of the complete stories.
In the 90's the floodgates have opened and there's hardly a topic in the first two years of college that isn't being taught in some of the schools. Result: general chaos of expectations.
There's also the matter of calculators which, according to our local teachers, are generally believed to be perceived as important tools by the college community. I doubt that this was ever the case and I now have students taking second semester calculus who don't know the sine of pi or natural log of 1 without their calculators. (Translators note for non-college teachers who have snuck in to view the sordid details: that's horrible!)
We've also managed to cut off communication with our potential friends, the folks in education. Granted, they speak a foreign language, psychologese, but have you noticed what the rest of the world thinks about our language? Even though ideas in education are a lot mushier than they are in mathematics (but I guess that could be said for a lot of areas) and some of the folks in education are obviously a mite defective (as opposed to mathematicians, who are paragons by definition) I think there's potential to learn a lot with them. Especially since most math departments haven't been getting exactly rave reviews as centers of great teaching. I believe that we have a really wonderful subject but some formidable problems (Rochester, research funds drying up, serious overproduction of PhDs, gradual attrition of upper level undergraduate courses and enrollments). Since I don't believe in conspiratory theories, I think, in the immortal (and now slightly politically incorrect) words of Pogo, "We have met the enemy and he is us".
Although we've had some serious communications problems, I'm not sure they will be easily solvable via the Internet--although I think it should at minimum provide us a much better means of communication among ourselves. And I think the Internet could also be useful in reaching other groups--school teachers, parents, school administrators, those in education.
Set me straight and I'll immortalize you here.
[Back to Communicating.]