It's the day of the Calculus AP Test. It's surreal to be here after being a bit overwhelmed in July. Last time I went on about things that went poorly. Since then I realized there's a lot more to add to that list, but it's probably counter productive to list them all. The revelation, is how to move on.
In the midst of AP review, it became clear that I didn't hit a fundamental concept hard enough. And that is how many different ways and contexts you can discuss this relationship. Props to Glenn for pointing out the bonkers desmos graph.
That was the theme all year long. Kids couldn't believe how much this subject is really about vocabulary and context and not a lot of raw skill. Raw skill is kind of the difference between a 4 and a 5, but by more or less ignoring the hardcore algebra, I have several capable of a 3 or 4.
The importance of that relationship pops up in questions like this one.
A completely symbolic question. Very little algebra. It's all words and notation.
So that gets me thinking. Would it be smart to spend the first semester on concepts alone? Something I haven't liked is "holding back" on concepts simply because it's not February or whatever. Is it necessary to shield students from integrals until you've exhausted derivatives? Couldn't you introduce the concept and save the mechanics for later? It seems like I could do myself a lot of favors by covering Calculus conceptually first and coming back with algebra and calculators at the end. A lot of the material I covered with integrals felt like it came up too late to really implant itself. Combine the goal of early and often AP material exposure, and dragging the course through its natural progression really limits when you can start using that stuff.
The second thing getting in my way is assessment. It needs to change. Regular assessment seemed only to serve the needs of having grade entries in the gradebook. I don't know that kids learned a lot from them. I could do some sort of weekly thing in the fall, but in the second semester it was really getting in my way. This curriculum is so spiraled I find it hard to isolate into nice, testable units. Well, nice, testable units that tell me something anyway.
Homework felt kind of useless too. I couldn't find a reason for assigning it other than, it's an AP class, so....yeah. I'm lost on this one. The whole completely optional thing is going to devolve into a waste of time because they'll stop doing it. Dropping the hammer on due dates and flinging 0s changes their grade from a measure of knowledge to a measure of punishment. But I have this nagging urge that they should be doing something when I'm not around? Weekly concept question or something? Again, blah.
And look, this is and is not all about the AP Exam. I've never taught a course with a 3rd party indicator of "success." I avoided tricks and shortcuts like crazy. I dislike a lot of the same things about overtesting as you do. But, honestly, the AP Calculus Exam is pretty good. Sure you can game it with tutors and everything, but kids without access to that stuff have a fighting chance if they get a chance to see how simple the material can be (and yes I know AP Exams suffer the same poverty/racial bias as others). I really wish the Calculus I was exposed to was more in the spirit of the conceptual rather than an overload of capital letter formulas. I get it way more than I did while taking it and I don't want my students waiting that long.
I either hate scripted curriculum or just really enjoy wrapping my head around subjects, because I'm ready to break Calculus apart and the year isn't even over.