# Finding Promise

At long last it's AP Test Day. What started with a hurricane and some kids on the couch has finally finished. When I started teaching Calculus, I had a personal mandate to improve the results on the AP Exam. Though it is just a test, there was no reason in my mind our students couldn't be successful at it. They're more than capable of piecing that thing together.

I started trying to be very specific about predictions and found that in general that back fired. This year, the thought was, let's just look for promise. Who shows the indication they'll be able to make it work on May 15?

### Shortcomings

While I was able to do a significant amount of catch up despite the 12-day delay, a few things just never happened. In AB I still sacrifice things like related rates, in depth discussions of the mean value theorem, and an in depth look at solving differential equations. As a program we weren't grasping the basics anyway, so those fringe things weren't making a big difference. On top of that I just didn't have the time. I needed it for other things.

In BC we pretty much got it all, though I'd say they have some other fringe weaknesses. Mean value theorem, fiddling with Lagrange error bounds, and the more obscure convergence tests.

Despite the shortcomings, in our final review sessions there was very little practice exam material that was not within my students' grasp.

### AB's Long Prep

A majority of my focus was on getting the AB group ready to go. Historically results have shown me that students struggle with free response. They lack some of the exacting finesse you need to make sufficient answers. Starting in March, I removed their standard assessment system and replaced it with released free response questions. In some cases students were given the use of a picture or calculator where normally it wasn't allowed because of where we were at in the material. Students completed 4 of these sets, composed of 9 full length FRQ on the subjects of particle motion, function/rate analysis, volume, and data tables. I tracked their results and some questions were used as follow ups once we had discussed some pitfalls.

If you're interested, Set 1 was 2012 #6, 2008 #4, 2009 #1; Set 2 was 2016 #3, 2017 #2, 2013 #1, Set 3 was 2013 #5, 2014 #2; and Set 4 was 2012 #2.

The goal was to expose them to the language and requirements of a free response questions early and often so that they were less intimated by them when the exam rolled around. In addition to these assessment items, they were given a pack of "ultimate" free response questions that I wrote myself a couple years ago. For College Board reasons I can't post them, but if you are a credentialed AP teacher, please get in touch.

We had many conversations about showing mathematical thought in their answers. There should be a clear setup (what information am I going to use?), work (what am I going to do with the information I chose?), and conclusion (how do I interpret my work?). Students who put the effort in improved dramatically at these as we got closer to the end. In some cases they exclaimed how easy the question was, something I had never heard before.

### BC's Prep Integration

I exposed BC to released material early and often. We were doing free response questions since October. They worked through a full AB exam in December. My challenge with this group wasn't going to be language or organization, but grasping the sheer amount of material we had to cover.

When we got to their unique topics in the spring, I integrated AP-level material at every step of the way. Almost every topic discussion was ended with a look at relevant multiple choice and free response questions. They took a number of Desmos assessments that were structured like free response questions. These kids were very familiar with the requirements of a free response question.

### Final Stages

Each version of Calc wrapped up new material in early April. On April 16, I started doing after school tutorials. My students have a number of commitments, so I made these flexible. AB students needed to see me once a week over the course of 4 weeks. For BC I reserved two Wednesday afternoons for us to discuss whatever they needed.

Each week had a theme. In some cases I covered material we didn't have time for and the last two weeks we talked about exam strategies. My students have limited experience with big exams like this, and time management is something that needs improved. In addition, they will think themselves in circles for 10 minutes on a question they should probably skip. We discussed doing a full reading of the exam before starting any work, helping them to prioritize their time. Finally, we talked about what was really necessary for a passing score. Many many many students are unaware that 45% or so represents a passing standard on this exam.

Out of 62 AB exam takers, they showed up after school an average of 2.64 times. I can't make these things mandatory (I know the sign says mandatory, but that's for effect) or grade them for showing up or anything, so that's pretty good considering it was all voluntary. 40 students did what was requested and showed up 3 or 4 times.

All the BC students attended both of their sessions.

### Results

When we concluded new material I gave both groups a significant number of assignments to work through. Class time was work time for several weeks, with tutorials in the afternoons. Each group got several skills-based assignments and then separate AP-level material. BC worked through another full length exam. AB had a selection of multiple choice and their "utlimate" free response. We went over the AP-level material either in class or after school last week. Students were given access to answer keys.

What will happen in July? I don't really know. I have some good feelings based on my observations the last month. I tried to gauge things based on how students asked me questions. Most knew what to do and were seeking confirmation, with others it was apparent they were at step 0. Fortunately, I think that group was minimal.

I would be very amazed if any BC student got below a 2, they've all shown strong levels of comprehension all year. The BC cut lines are also a little more forgiving because of the content demands. A number (in my wildest dreams, all) of them will pass without question. AB feels like ~70% of them should register on the scale (2+). I scratched in some predictions for each kid, but I'm prepared to be surprised in either direction. Ultimately, I want the 1 to become the minority score in my AB results. How many can make the jump from 2 to 3+ will just have to wait. Fingers crossed for about 70 days.

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