Memory is the great deceiver*
In addition to Calculus, I teach Algebra I among others. I have a tiny (although, I will not specify size for job security related reasons) Algebra I class. Small enough that we've been able to fly through the textbook and any other material I've dreamed up incredibly quickly. We're on the last chapter. After this, I need to sit down and write out a serious plan for what I'm doing for the rest of the year. Besides reading aloud for half the class every Friday (a huge hit).
There's one problem though: I'm just not sure how long it will take to get there and how much review of previous topics we need. We're currently working on roots and rational exponents in the class. Not terribly difficult, but not super easy or intuitive, especially the first time you see them. My students seemed to get everything that was happening. Then we took a break for a couple of days and talked about algorithms, including a class on the Euclidean Algorithm. We took three days and a weekend off from roots. Before then, we'd spent over a week straight working on them. My students knew roots, they could do equations with them, I though that one of the units I'd do after we finished the standard Algebra I curriculum would be imaginary numbers, because of how well they were handling themselves.
Except they seem to have forgotten everything. We picked back up where we started yesterday. Or at least, I tried to pick up where we left off yesterday. My students needed a lot of prodding, and a several explanation that I could have sworn they knew repeated. I was a bit frustrated to say the least. I didn't get angry (that's reserved for my upper level students, who generally misbehave (cue Cole Porter song) more than my freshmen. (Freshpeople? Freshlings? It feels wrong to use the last one, no longer being in college.)
This is something of a surprising development for me. Not that students forget things, but more that they forget these things so quickly after demonstrating a complete mastery earlier. I wouldn't be so frustrated if they'd be having more trouble with roots and rational exponents last week. I guess this phenomenon makes me worry about my Calculus students. We're covering a great deal more material in that class than in algebra and doing so much more quickly. How much can they actually be expected to remember? (Well, actually, quite a bit, given that the AP is rather soon.)
So for all four of my readers, my question is this: How much do you retain after a week from a class? Or, how much do you remember remembering from classes, especially math ones?
As I finish this post, I realize that I don't have a name to sign off with. I was going to use the generic teacher, or, perhaps adopt a pseudonym from a couple of famous mathematicians, but the latter seems overblown and pompous and the earlier, just playing boring. I'm not about to use my name here or any common screen names that I'm known by around the internet (or teh intertubes if you want to be all technical-like). So who am I? (While one would get points for suggesting Canby, I'm not about to adopt that name or that Mathemagician.) (Edit: It does say "Teacher" in the about the author bit on the left. But I still maintain that that is boring.)
*Paraphrases from "The Murder Mysteries" by Neil Gaiman