My precalculus students have recently taken a test on sequences, series, & the binomial theorem. The students run the gamut from they-could-teach-themselves-out-of-a-book to please-take-my-hand-and-do-the-problems-with/for-me-over-and-over-again. It dawned on me while I was helping this latter type of student to study that she had no concept of what might have been some good things to study and review before taking the test: formulas for explicit terms, partial sums, pascal's triangle ...
I thought over the notes they took, and I'm wondering if it ALL was so foreign and important sounding to her that she saw it as:
sdlkfoe sdoowieur sdeoe 5 = sdlfoein sdifuoeen
oeiwonewio sdf e3dof soieen sdeid nli lskejoi i9 dflk
so maybe she couldn't parse through it all and figure out what was important to know. I know when I was presenting the stuff, I had them do examples, and I had them write down the formulas and I discussed why they work and how to think about them .... but apparently, for some students, I have to stress what's important before, during, and after. And then maybe I should make them get out their red pens and BOX all the key things.
But this doesn't sit well with me. It seems that I'm doing the thinking for the students that way, and they'll never learn to sit back and reflect on what may be important to know without someone spelling it out for them all the time.