#UnsexyMath Days 3/4: Bias and Sampling

A recent instagram post lead to four people (both IRL colleagues and #mtbos members) complimenting and asking for more info. I had a conversation or two with Kate Nowak and others about the need to share more “unsexy math” – the regular-but-still-pretty-effective things we do more often in our classroom than the super awesome projects or really pretty foldables. So here goes my first one.

To start of our new geography/statistics course, our students are creating a survey inspired by some aspect of human-environment interactions (if you didn’t know this (like me), this is apparently a HUGE part of what is learned in HS World Geography). After administering the survey, they’ll create propaganda and administer it, then re-administer their survey to compare the results.

The entire idea behind project-based learning though is that most of what we do in the classroom should be tied to the projects our students are currently working on. So to hook our students, we decided to try to survey them on the cuteness and strength of hippos, show them a video of Fiona the hippo, and re-administer the survey. It worked! For some, at least. There were a handful in each class that changed their rankings after the video. So then I told them about the project and the majority got really excited. “You mean we’re going to try to brainwash our peers? Sweet!” I think they might get disappointed when we have to turn down some of their propaganda ideas for legal and ethical reasons later this month but it’ll still be good. Another lesson to learn.

Anyway, after the project intro, we talked about bias. I asked students what they thought bias was, then I projected four questions with varying levels of bias on the screen:

  • Do you think bike helmets should be mandatory for all bike riders?
  • Do you prefer the natural beauty of hardwood floors in your home?
  • Do you eat at least the recommended number of servings of fruits and vegetables to ensure a healthy and long life?
  • Do you want your kids to receive a faulty education by having their school day shortened?

After reading them to themselves, they offered up thoughts on which ones were more biased than others, what made them biased, what the questions were trying to imply or what responses they were leading you to, and how to eliminate bias as much as possible from them.

Then we did some vocab matching. You can see the list of terms they are learning about here. These students mostly know each other from their PBL courses last year, but in the first few days we’ve spent time doing a lot of collaborating on Geography (and Biology and English) course work, low-floor/high-ceiling math warm-ups, talking points, etc. I was still shocked by how much conversation was happening within most groups. The goal was to see what they could match based on the context clues – could they figure out “nonresponse bias” and “size bias”, for example, just based on knowing what “nonresponse” and “size” were? (For the record: 18/20 groups could. The fewest amount of correct matches was 3, greatest was 8.)

After they checked and copied down the correct vocab terms and definitions, I projected four examples and explained them a little more. Students identified at least one correct type of bias for each example. I was happy.

To end class we started talking about sampling methods. I had each class come up with a question we could ask students (“How often are you late to school?”, “Do you like the school’s food?”, “What’s your favorite food?”, and “What’s your favorite color?” were the suggestions) and we created Frayer models for each sampling method with our “example” going along with the question the class wanted to ask and how we could use that method at school. I thought this would be important as they are actually going to be surveying students (or other things at the school… I’m really hoping one group does something on amount of trash/recycling or use of our refillable water bottle stations!), so hopefully when they’re doing their survey design they can choose an appropriate method.

We didn’t get through all of the survey methods in 3/4 classes, so we’ll finish that slideshow up Monday/Tuesday along with some/all of the questions on the student work document linked above.

This wasn’t anything monumentally new. They wrote or typed a lot of notes while I talked up front and projected info on the screen. But there was a lot of peer-to-peer and whole-class conversation and for that, this unsexy lesson was a win.


Project 1 – Carnival Game

This past week our students finished up the first part of their first project in our physics/math project-based learning course. Our first unit has been mostly about measurements and data analysis, so students created carnival games and then we hosted a carnival at a football game last week. They collected data at the carnival and are going to analyze it, write a report, and give a presentation this week.

I didn’t get any pictures of the actual carnival due to being the adult-in-charge for the first part of it, but the day before the carnival we were able to have one of our self-contained classroom come visit and play the games with us. Some pictures of that are below!

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What I loved most about this was the interactions. The games weren’t the best and we were loud and everyone else near us probably hated us during this time but everyone was having so much fun. The self-contained students obviously don’t get to be out with the rest of the students very often, and the regular students got a great opportunity to learn patience, encouragement, and how to better explain the rules of their games.

This has been the highlight of the year so far. We’ll see what, if anything, will top it.