My official verdict on the first year of Calculus is that it went ok. I invented an assessment structure that I stuck with. We had a reasonable amount of time at the end for exam review and when the kids recounted the exam experience there was no imminent sense of dread. They all gave it an honest try. At the beginning I had minimal expectations: no quitting, no being scared of the exam. Both were accomplished. Didn't translate to exam scores unfortunately.
What I did learn, is that we have a pulse:
Two weeks after score reports, you get a breakdown from the College Board with everything in quartiles. I've obscured some data just a bit. To my utter surprise, the free response went better than the multiple choice. Overall neither are what you would call good. But to build a class from nothing and be able to get them to make a dent into the very high level language of that exam is progress.
Coming out of the exam, question 4 and question 6 were cited as the hard ones. I barely scratched the surface of differential equations, so even these metrics are nice to see. Clearly I was able to make headway when it comes to f / f' / f'' relations and table-based integration/differentiation.
What's going to move us forward? I learned some hard lessons from our AP review. In summary, we spent a couple weeks going over free response scenarios clustered by topic. I grouped released questions into seven categories: Data Tables, Differential Equations, Fundamental Theorem Relations, Particle Motion, Conceptual Integration, Rate Analysis, and Volume. That subdivision happened too late.
Rather than wait until exam time to introduce those ideas, these are now my units. All of them have overlapping skills. All of them can be discussed if I spend the first six weeks laying the conceptual groundwork. Meaning, we spend the first six weeks taking glancing blows at all the topics. I'm not going to rush u-subsitution or anything, but if we can discuss the concept of integrals, even just simple ones early and often, we'll benefit from it later on. I'm almost tempted to introduce the course as Better Understand Physics with how important f / f' / f'' is to the whole thing.
Rough order (I have 5 grading periods until the exam):
1st PREP: limits, derivatives (implicit but no chain), and integrals (no u-sub, no logs) and their basic relationships
2nd POS/VEL/ACC: integrals and area, FDT, SDT, graphical relationships
3rd PARTICLES: derivatives (all rules), integrals (all rules), final value vs final position
4th RATES/DATA: calculator based f / f' / f'' relationships, average values, related rates
5th DEQ/VOL: differential equations, volume
Those are at best, extremely simple ideas for what I want to accomplish. I have a long list of standards I'm still trying to sort. Much like Pivot Algebra II, I want to hit the same conceptual notes over and over and over. I'm going to cover all the skills, don't worry.
Assessments are changing. Sarah Hagan has this very intriguing A/B/Not Yet style of grading. It seems perfect for Calculus. Implementation details remain. AP grades are painted with such broad strokes that the difference between an 81 and an 88 is pointless. Even the 0-6 scale I was using for skills is too much of a gradient. Mock AP sticks around. They'll take half an AP test in December and half an AP test in March. I'll use them to filter out who should bother with the exam. Last year I had 50% take it, this year I want 66% or better. There's going to be more AP stuff too. When doing exit interviews, it was pretty universal that they were thankful for how much AP stuff we did, but they wanted more, and sooner. I was inclined to agree.
I pushed a lot of the early limit principles to Pre-Cal last year. That group is now my new band of Calculus kids. I'm hoping that saved me 3 weeks or more.