On a day-by-day basis I'm impressed with how much my students can do.
Solve a quadratic equation? No problem.
Simplify this cube root? Got it.
Find the asymptotes and graph this rational function? Piece of cake (mostly).
Just this week in Math 3 we're working with radicals; simplifying, adding, subtracting, rationalizing, etc. When we concentrate on one task they're golden. But once I expect them to actually remember skills from previous days (weeks, months, courses) I'm out of luck.
Rationalizing denominators is tough when you can't remember how to multiply radicals. I actually mentioned this to the kids today and got several head-nods. "You guys are good with the idea of rationalizing a denominator. But when it comes to remembering how to multiply and simplify after setting up the rationalizing and that's where we struggle."
I've fought this all year with my Math 1 kids. Their retention skills are so lacking. On any given day I could teach a new skill to the class and I'd say a good 75% of the kids could understand and do it. If they chose to (another issue). But the next day it's a toss up to who knows what.
Is it me? I try and teach for understanding, hoping that something will click (instead of just memorizing a formula). I've chosen to decrease the amount of problems I give each night; typically assignments are 5 - 6 problems. Would assigning more help?
In both of these classes I've started giving weekly review problems this semester. Next year I intend to start that from day 1.