Well, I am officially through one semester of my first calculus class as a teacher. Before I get into any theories or needed revisions (and there definitely are some…) I want to simply make some observations and thoughts after some reflection:
#1. There’s no substitute for having an answer key made showing all work (multiple processes, if possible) for every single handout you give. The students seem to embrace the idea that I was relearning the calculus, but they got edgy if they got a sense that I didn’t know what I was doing or I was unprepared.
#2. Borrowed and stolen resources are helpful as resources, but you need to make your curriculum your own. I found that even making small edits to the handouts I got from Sam (@samjshah) or James was enough to invest my mind creatively in them more, which made me so much better able to embrace the holistic value of each and every activity.
#3. Advanced math students are never more than one frustratingly-difficult assignment away from behaving just like their struggling counterparts. All of the avoidance, procrastination, off-task, distracting behavior we are accustomed to from the strugglers will show up in any teenager if the math makes them feel overwhelmed and intimidated. (I will admit, “When will we ever use this?” is a question I never expected to get from a student who signed up for Calc voluntarily…)
#4. Advanced Placement might not be all it’s cracked up to be. My class is not AP. Surprisingly, the students spoke rather decisively that they were, at times, deterred from AP classes (for a variety of reasons). AP ties your hands a little bit in the schedule and topics. At the very beginning, I offered an AP prep schedule for anyone who thought they might want to take the AP exam and not a single student took me up on it. And when you consider that AP classes come with questions of grade-weighting, and exams, and GPA and blah… blah… blah (the effects of which are probably overstated anyway…) It seems like making this an honest, in-depth, investigation of calculus for the sake of investigating calculus seems to create the most favorable environment for student risk-taking and teacher responsiveness.
#5. Logarithms and radicals: these two things never quite seem to settle in for students.
Now, I am keenly aware that each group is different, and should I be blessed with this opportunity next year, many of these observations could need some updating.
… but maybe not.