I've had former students come back to visit lately and they talked about the expectations of their college professors. One student who's in calculus says that the professor expects them to have a solid, quick-recall grasp of basic graphs (what does the sine graph look like? the square root function? the tangent graph?, etc). Yeesh, note to self on not just teaching that for one week but reinforcing and recalling it periodically.
Then that reminded me of a dream I had the other night. I like memory tools, and I dreamt that one way for the kids to remember the square root of x graphs is that, "SEE, the graph LOOKS like the square root symbol". Nerd alert. I'm going to try that this year.
Then I also started thinking of how to make all these graphs become second nature to the kids. Maybe periodically, and consistently, I can pull out "cards" with (say) pink cards graphs and yellow cards the functions, and maybe they can have a running contest with themselves and keep track of the time it takes them to match them up, and eventually (months? weeks?) we can have a "beat the clock or teacher" contest of a match up game.
I also want them to have the quickness of thought as to, "okay, I don't remember this shape, but hey! let me quickly make a table and plot the points to help myself (without the teacher prompting me or just sitting there and not doing anything)". Hmmmm, how to teach this skill. ... Maybe also a periodic and consistent "game" of "here's a weird function on the board, quick like a bunny, find 5 points on the graph or plot 5 points or something".