Sunday, October 20, 2013

Comparing Distributions in AP

One of the toughest topics for AP Stat students is the idea of comparing distributions. I know this is a tough topic for them because it consistently shows up on the AP exam and students consistently make the same error... they don't COMPARE the distributions! Most of the students have been taught to describe a distribution using Shape, Outliers, Center, and Spread (SOCS in my classroom), but the *compare* part is a struggle for them. This year, my partner teacher and I decided to try something new to help students with this topic...

The Setup
We had already taught this topic, but from previous years, I knew that students would forget. We had worked problems in class, they had a homework problem the night before on comparing distributions, and we had talked over and over about how important comparative language was. We had done "notice/wonder" but decided to reinforce it differently this year....

The Stations
Since this topic has appeared on several AP exams, I pulled 4 of them to use as questions in class. I intentionally chose problems with different kinds of graphs (dotplot, boxplot, stemplot, and histogram) and asked students to compare the distributions. I set 6 minutes on the timer and away they went...

(I love these plastic frames! I have them in portrait and landscape. They are on my "must-have" classroom list)

After the timer buzzed, we traded problems and they repeated the process.

Time to Grade!
We graded the problems one at a time. Each time, I projected an "ideal" student response from the AP Central website and conducted a whole class discussion on why that response was scored "Essentially Correct." Each student was given a Peer Grading paper that Partner Teacher created and asked to grade their partner's paper and give them feedback. Honestly, if I had a bit more time, I would have created some "less than ideal" papers and walked them through how I wanted them to grade the paper in more detail. Maybe next time! Overall, it was a good experience on writing legibly and checking for the required elements.

The "Real" Assessment
When I graded the quizzes for that chapter, I actually left this question for the last because in the past, it has been a real weakness of my students. I am so pleased to report that of the 95 students, only a few students forgot to write using comparative language (higher/lower/wider/narrower/etc). This is such a change from previous years that I truly feel this activity was a huge part of the difference.

Overall, I was very pleased with this activity and need to figure out how to use it more often. Thanks to my #efamath friends for encouraging me this summer to use more strategies like this! :)

1 comment:

jdyhnt said...

I always draw great ideas from your blog posts, things I can use in my own class or things that spark other ideas. I really like this one about comparing distributions rather than just describing one. Besides helping on the AP test, it is real-world-application focused, which I appreciate, having been an industrial statistician for 30+ years before coming back to teaching. Thanks!