### Inadequate Teacher Training

This story about the inadequacies of teacher training prompted me to dust off my soapbox and get right back up on it.

I have long maintained that teachers do not receive adequate mathematical training. I teach at a university that is well-known as the main source of teachers in our state, and I have to say I'm appalled at how little math these teachers are required to know before they enter service. Elementary-school teachers take nothing above the level of college algebra. They do spend a year in a course that goes over various concepts in elementary mathematics, which is a good course and an asset to them. But they never get high enough to really understand what's going on in mathematics. One would hope that a well-educated teacher would at least have experienced calculus and understood what the purpose of all that algebra was and why it is so important to master it, before going on to teach a state core curriculum that emphasizes algebraic concepts at the earliest of ages. One could further hope that at some point in their training, future teachers would encounter the concepts of logic and proof. But alas, one would hope in vain.

While the standard in the college algebra course remains relatively high, the elementary-school math course suffers from grade inflation and extremely low standards. A friend of mine who taught that course, in a state of utter frustration, once showed me her class' quizzes. The students were routinely getting 0 or 1 out of 10 possible points; they had written no mathematics whatsoever. And these same students, she told me, were coming into her office outraged that they were not passing the course. Their opinion, evidently, was that if they came to class and warmed a chair, they were entitled to at least a C, more likely a B (simply because they needed the B for their GPA's in their competitive program).

Part of the problem with elementary- and secondary-level students starts at the college level, where their teachers are trained. It is entirely possible, even somewhat probable, to get a teaching credential and wind up teaching a geometry class having never encountered the concept of rigorous mathematical proof. I've met future math teachers (not elementary teachers or other-subject secondary teachers, but math teachers) who had made it up to calculus and never really been able to master algebra. It scares me to think that these people, good people as they are, are being given the responsibility for training our future mathematicians and engineers when they don't even know the subject themselves. They are being given an impossible task, and when they muddle through it as best they can, someone else lowers the standard to make it look like they're succeeding.

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