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.