Today ended the meticulous precalculus review I do in my calculus classes. We had an open practice session in which students were given 15 precalculus problems of various types to do. I told the students on Friday that we would be doing this, and that the review session was optional. If you feel like you could benefit from further practice and one-on-one questions with me about precalculus, then make sure you come, I said; and if you don’t feel like you’d get much out of that, don’t come. I was pleasantly surprised to see that I had almost full attendance for both sections, despite it being "early" (ie., < 12:00 PM) on a dreary, rainy Monday. I’m sincerely glad that they came.
I was unpleasantly surprised to find a significant number of students had no clue what the domain of a function was, or else they defined the domain as "the set of all x-values". Or trying to find the domain of y = ln x by converting ln x into e^x. And so on. So we they have more to work on.
I think that not only will I radically shorten the precalculus review for future classes, as I mused here, but that doing so will actually improve the review process by giving students a sense of urgency (= "OMG, this is going so fast, I had better study it") rather than the sense that we’re taking a leisurely walk down high school math memory lane. I think the students who are having problems on this stuff are going to have the same number and severity of problems at any speed; slowing down doesn’t help when the deficiencies are big and deep.
Tags: Precalculus, calculus, college
Filed under: Calculus, Education, Math, Student culture, Teaching
You may also want to considering moving some of the pre-calc topics to later in the semester, like reviewing exp() and log() right before you introduce derivatives of exponential functions. My position is that I want the first bit of genuinely new (and challenging) material to happen as early as possible so that the students get the message that “this is not the same ol’ same ol’.” I’d also consider putting review-ish things on the day before fall break / the big game / other things that compromise attendance (unless something compelling, like an exam, fit my calendar better).
I´m a Comp Sci teacher and I suffer the same problem that you. If at the beginning of the semester the rythm is slow-paced, the students think: “this is easy” and get lazy. But if you “scare” they, things get better.