What Should I Teach?

I'm in a quandary.

One of the courses I teach is called "pre-calculus". In accordance with California's mathematics framework, our district has combined the trigonometry standards and the few math analysis standards into the one pre-calculus course. So far, no trouble.

Let me stop here and explain how much I like California's math standards. Like 'em, like 'em, like 'em! Like 'em so much I want to be them for Halloween! (Don't remember where I heard that before, but now that I've used it, I should probably promise never to say that again.) They're not perfect--in fact, they might be somewhat too stringent in pushing Algebra I down to 8th grade--but it's good we have them. They're not fuzzy, either. They state in certain terms exactly what students are supposed to know and be able to do at each pre-8 grade and in each named course after that.

I follow the standards religiously. If the standard says my students are supposed to know something, I teach it. If the standard doesn't say they're supposed to know it, but I think it's something they should know, I wait until the end of the school year and if I've covered all the standards and there's still time left over, then comes the good stuff. I have the standards cross-referenced with the sections of the textbook that address them. I'm way too into this!

The problem arises when the calculus teacher expects that students will know something that I didn't cover. "They've got to know this!" he says. "Then you teach it to them. I've got to cover these standards here." "But they don't need to know that for calculus!" "Perhaps not, but they do need to know it for my course." We're very friendly when we have these discussions, but I see his frustration. There are pre-calc topics he doesn't cover that I do--topics that are in the standards--but he covers topics I don't so that when the students get into his AP Calculus class, he can move that course along a bit quicker.

Some of the math teachers at my school have what I consider to be peculiar beliefs. They think we should cover a little bit of geometry at the end of Algebra I so that the geometry classes go faster. Why do we want geometry classes to go faster? So we can cover some Algebra II at the end of the geometry courses. Why do that? Well, you get the idea.

There is one advantage I can see to that plan. When standardized testing comes around in April, our students will have covered more of the standards in each course than would students who started learning the material in September as opposed to late in the last school year. Still, some course somewhere would have to be compressed, and the standards are pretty stringent the way they are now. Which course should be compressed? Why, whatever one is below the one I'm teaching, of course!

So, what should I do? Should I teach to the standards--the standards that the students will be tested on in April? Or should I teach what the calculus teacher "needs" to have taught? Would I be depriving the students who won't go onto calculus by cutting out material they're supposed to learn and covering material needed for calculus? Am I short-changing my students who will go on to calculus?