The end of a very frustrating day in academia. It's mostly off-topic (not dealing directly with the storm to come), but shines some light on why it is coming at all.
Below is an edited version of an email which I sent to a colleague in our college of education.
I am also rather distressed by your comment:
"A PhD is a terminal degree which means we are capable of self-teaching material we are unfamiliar with".
I know a great deal of mathematics, computer science, statistics, engineering and physics. I would still have much trouble teaching something like Abstract Algebra, and I have had several courses in the subject. It's not all 'just math'.
The problem, which is very close to that of our meeting today, is that mathematics is one of the most tiered subjects there is. As one of my administrative superiors told me, many subjects have an 'Intro' course, after which one can take any number of courses. This just isn't true for our discipline, until about the senior level. That is why we take the issue of prerequisites and previous material so seriously.
It is also upsetting to experts in other fields (especially education) that success at one level of mathematics is no guarantee that one will ever succeed at higher levels. A previous administrative superior couldn't understand it at all, which is one of the reasons why he publically stated that learning algebra was unnecessary 'for anyone'.
In (not so) short, this is why I take the problem of training future mathematics and science teachers so seriously. With all too many school administrators having the idea (as another administrative superior told me) that 'anyone can teach math', no wonder that we have the problems that we do.
I have been party to many discussions on mathematics education on usenet and elsewhere. Every single time, my honorable opponent criticizes how the subject is taught. They then either offer no ideas at all, or ones which have already been shown to fail elsewhere.
Ponder this: Mathematics has been taught as a discipline in its own right for about 2,500 years. The subject itself lends itself to brutal editing and revision, so that only the most robust facts and proofs survive. Given those millions of man-years of developing and teaching the subject, isn't it reasonable to suppose that we are doing some of it correctly, or at least we might know better than outsiders?