What Matters

This was my first year teaching AP Calculus. It's been an incredibly busy year and I've been fighting to get out from beneath a crushing workload all year long. Hence the long gap since my last post... and the long period of silence before that! I have high hopes of being able to use this space to reflect on some of the things that went well this year and other things I want to work on.

Let's start off on a high note- the projects my AP Calculus students did at the end of the year. After the AP exam we still have 5 weeks of classes. We covered some material I'd skipped and another topic or two I felt that they should be exposed two before taking their next calculus course, if they're going to take more math that is. After that I cut them loose to work on independent projects individually or in pairs, but with the admonition that if they worked with someone else I'd expect twice the awesomeness that either would have achieved alone.

I was inspired to do this by some other calculus teachers, most notably Sam Shah. I gave my students a rough list of ideas and told them that I'd actually prefer it if they came up with their own topic. I was thrilled with their work and the presentations they gave to the class. Even the groups I worried were going to fall flat rose to the occasion. Here is a brief description of my students and their projects.

• Two students worked individually to artistically render different related rates problems. One chose water being poured from a watering can into a plant with the excess coming out of the bottom. Another depicted an athlete sweating at the same time he drank from a water bottle. This was a great avenue for these students to apply their artistic talents to calculus.

• A student looked at a hypothetical plot of land and investigated the respiration rates of different species of plants that could possibly be planted there to evaluate each plant's contribution toward producing oxygen, food food, and also the impact it would have on the soil and the water it required. This was a lot to bite off and it didn't get reach fruition, but the intent was spot on.

• A student looked at how the mass of a container changed over time based on what was being poured into it. I was hoping to see something more complicated than a cylinder, but the rig itself turned out to be challenging to construct so I was fine with the final product.

• For one of the weekly reflections earlier in the year I gave the students a choice of two prompts. One was to evaluate a claim about the length of a meandering river. Only one student tried it, and didn't get very far. One of his peers picked it up and analyzed 4 different rivers using LoggerPro and Excel. He got 1.93, which is remarkably similar to this article, which he found after his analysis was complete.

• A pair of students tackled the dating pool problem from Think Thank Thunk. They came up with their own creepiness rule, which included a clause that one could not date a person who was equal in age to (or younger than) their own child. This made life difficult, but they complicated matters a bit by looking at issues of sexuality and how the LGBT population factors in. They had difficulty tracking down precise data, but came up with results similar to those that Sean's students got (one's dating pool is largest at age 39).

• Two students wrote a related rates problem, solved it, and then turned it into a song. My video is of appallingly poor quality, but the audio is where it's at.

• Finally, earlier in the year one of my students was visibly appalled at my attempt to model 3-D solids using cross-sections on top of curves. I'll be frank- I tried really hard, but failed miserably. He wanted to do better and produce something that future students could relate to better than my ill-fated attempts. He generated a complicated curve using Desmos and then exported it to Excel as a string of points. We sent it to AutoCAD as a polyline (love their policy of letting educators use the full program for free- I know how I'm doing my 3-D solids next year!). We layered a rectangular array of polylines over it- all parallel to the y-axis. Then we trimmed them to the original curve and extruded each as its own polysolid. This was tedious because the height for each had to be set to be the same length as the polyline it was going on top of (he was stacking squares). He wanted to have 346 different squares, but I talked him down to 22 or so. It still turned out really well. 
  

        The icing on the cake was that we sent it to the #-D printer in the technology department! So he            had a model to show the class and took it home with him after his presentation.

         By the way, I used to teach AutoCAD, so this wasn't completely off the cuff. 

Can't wait to do projects again next year! AP scores came out today. I am psyched with how my students did, but I'm more excited about sharing these projects.

More news to come, hopefully in the near future. Headed off on a big trip and I am going to be blogging about it here, so stay tuned!