Very few tests are well designed, but I believe the AP Calculus exam is a pretty well designed and consistent exam. One thing that amazes me is that in 6 Free response questions (FRQs) they test a majority of a course. While that is great for the test, it isn’t good for teaching. It makes it hard to use these items in class in the fall continuously, but I want students be familiar with the format and types of questions asked way before they could confidently complete an entire AP Question. I’ve watched my previous iterations of Calculus struggle with the FRQs, but never implemented a system to “train them” because I always started in the middle of the year. This year, my first full academic year of AP Calculus, I’ll be implementing FRQF’s -> Free Response Question Fridays to address that gap.
Every Friday, students will work on an actual AP FRQ (even if they aren’t computing answers to all the parts). I casually had read of Polya’s How to Solve it and his 4 step problem solving strategy on the #MTBoS, but hadn’t implemented it rigorously. I sat down this week and read it (well…I read the first two sections and skimmed the dictionary….). I planned on implementing Sarah Carter’s S.O.A.R. acronym – which is how I’ll be introducing it to kiddos in August. (P.S. I made some nifty INB notes for SOAR last year, hung a kite in my room…and never referenced it again after September. Hence the deliberate planning this time around).
Speaking of giving credit to where credit is due, in my internet search to find something like an AP Calc version of this AP Stats FRAPPY resource, I found this problem solving guide by Florida DOE “Research Based Strategies for Problem Solving in Mathematics” (PDF). They break down all four parts of the process and have activities and prompts for each of the areas. I’ve taken some of their ideas as I’ve written my FRQF’s.
I’ve written the first month or so of my FRQF’s – focusing mostly on Polya’s first step in the process – understanding the problem. The first involves mostly just ensuring that students know what the problem is asking and understanding the situation. We’ll be breaking down this year’s ridiculous Volume problem (#5). Problem not included, because College Board be CRAZY.
Students are answering questions like these:
- Summarize what this problem is about in your own words.
- What do the variables r and h stand for?
- What are the units to describe this funnel?
- What is the height? What is the radius?
- What are the restrictions on the values for h?
- What is the shape of the cross sections of the funnel?
I’m hoping that by focusing on the thought process behind answering questions like these by May we’ll be able to let our knowledge shine instead of being bogged down by words.
P.S. Interested in looking at FRQF’s? Comment or tweet at me (@jakewinfield) and I’ll share my work. I’d love feedback too 🙂 Since I’m using AP Released Items I’m erring on the side of caution.
This summer I’m not moving across the country and I know what I’m teaching – which is a first! I’ve been out of school for two weeks and have just 3 weeks before I go on vacation. Time to get busy.
Things to do this summer for next year before my road trip in the west:
- Re-organize AP Calculus and create standards to implement SBG next year.
- Flip my Calculus class and make lessons for the first two weeks [at least] (I’ve decided to use showme for now because it lets me upload files for free, lets me prep lessons and record later and I can upload links to a course website. I’d prefer if it uploaded to youtube straight away, but I think this will be okay – I won’t know until I get some student input. I originally was going to use an ELMO, but I spent too many hours and not making any progress.).
- Create a course outline, units and standards for Statistics, and as many quizzes/exams as possible. This is a new course for us and I’ve found enough resources to build out a course, but it’ll be a bulk of my work this summer.
- READ. I’m in the middle of 3 different education books. I want to finish a couple of those up, in addition to my leisure reading, before I move apartments (I read 500 pages in 3 days this week….while also doing a summer program)
All this, and more (syllabus? First days of school?), in less than 20 days. Then, who knows how much I’ll be able to do on the road.
Today I wrapped up and checked out, ending my fourth year in the classroom. Unlike other years, there doesn’t seem to be as much of a finality to this year as every other year. I think there are two main reasons for that.
1) I switched preps almost completely in January when a teacher left. I never got all my classes going full-steam ahead. By the time we all found our groove we were gone.
2) I’m going on vacation for the 3 weeks before we start school and won’t be online/able to prep. I’m using June to bust out as much work as possible to make the next year smooth.
Even though it doesn’t feel like it is over, it is. I don’t think I made significant progress on my goals for the year – although others disagree. With that in mind, here are three big takeaways.
- Teaching is teaching. Students are students.
- I moved across the country this year to a school with a majority of latino/latina students, where in the past almost 100% of my students were black. I feared that I’d be starting over and not have some of the same skills – turns out that’s unfounded. Good teaching is good teaching. Students are students. Now, obviously, there are caveats to this to be a culturally responsive teacher and I’ve learned a ton but it was not a challenge this year.
- Problem/Project based learning and performance tasks are pretty darn awesome.
- I spent this year implementing and using performance tasks, which I’ve changed my implementation of throughout the year. My biggest take away is that these tasks have to be CAREFULLY scaffolded – not only within a unit but within a course. I saw students struggle because they were asked to do new work. That’s a growth I’m still working on. Long term, I unintentionally started all projects as group projects. In the second quarter onward, the task dictated the size of the group – and our last 3 projects in Geometry were all independent, and in August that wouldn’t have been possible.
- Awesome parts: Once students begin an engaging project, all I did was manage behavior and answer questions. Students HAD to think differently about the mathematics and apply it. I have to be incredibly diligent about which questions I answer and how.
- Not so awesome parts: Assigning 3 projects in 3 preps simultaneously means 100 projects to grade. That’s a pain in the butt – and I didn’t get caught up for weeks. Class culture of waiting for answers is toxic with projects/performance tasks – and led to some students failing projects and therefore the course.
- Teaching gets easier.
- I’ve probably worked twice as hard this year as any previous year – but I know exactly what I want and find it with ease. I have teacher moves that have become pretty natural – but still need to add onto these and be intentional with lessons. Even though it doesn’t seem possible in year 1, teaching gets easier with time and practice – I just keep asking myself if that’s what I’m best at and what I want.
Back to writing unit plans….a.k.a. scouring the internet to find a place to start.