Repetitititition

Started cracking the door on sinusoidal functions this week (yesterday, actually), with the calculus class. Some good progress, but it is a bit slow going. I'm taking the plan of doing short lectures with short practice problems. The initial push was pretty good: I used a Javascript animation of a point moving around a unit circle, with sin and cos developing alongside it as functions of the angle measure.

That was enough to develop a sense of the shape of the sinusoidal function, and to give a somewhat weak but present justification of d/dx(sinx)=cosx and d/dx(cosx)=-sinx. Today, we covered the same ground again, without the animation, but with me effectively reconstructing it by hand, which allowed me to also make some basic linkage back to right-triangle trig, and to wave my hands a bit around "cos is the horizontal, sin is the vertical."

The students are very clear about the fact that they aren't solid on this, yet, and I'm surprised at how okay with that I am-- it comes from experience, I guess. At this point, I just expect that I'm going to show them this thing, every day for the rest of this week, and then next week, I'm going to get them to show each other this thing. Because, it's a tough concept to wrap your head around, and it's appropriate that it'll take a bunch of seeing it before it clicks.

This is also good, because it gives me an opportunity to develop that "trig wheel" project that's been kicking around the back of my head (which, if done right, would make quite a good Entry 3 for the National Board portfolio...)

We haven't touched radians yet at all. It's a long row to how, this year, especially having lost 5 weeks at the beginning. I'm pretty sure we're not going to get everything in before the finish line, which means that I'd better start deciding what to de-emphasize. I don't plan to cut anything, but there are some fiddly bits around the ends that I won't be able to spend this kind of time on, to make them solid. Still, I think it's better to have something solid, and something else not at all, rather than two things shaky...