ProbStats Assignments: Graph of the Week and Significant Digits

We finally got some tech issues and scheduling issues taken care of and were able to start homework last week. About 1/3 of my students didn’t complete all of it and about 1/4 of them didn’t write well (they were supposed to do a paragraph and multiple students made lists or wrote 2 sentences). BUT the other 5/12 of my students did an awesome job for their first time around.

Their Monday assignment is to respond to Turner’s Graph of the Week. They respond in an online discussion board (we use Canvas for this class) and have to post something on their own but are encouraged to reply to their classmates as well. Last week’s topic was the relationship between fast food sizes and obesity rates among children. Here’s my favorite exchange:

R: The graph(s) show obesity in children since 1971 and show the serving size of fast food in the 1950’s vs now. 1st graph (obesity): The x axis represents the years from 1971 to present and the y axis represents the percent of children who are obese. 2nd graph (fast food): The x axis represents the years since the 1950’s and the y axis represents size of the food. Some observations I can make from these graphs is that fast food and obesity are growing in size through the years. However, children of ages 2-11 are not as obese as they were in 2003 whereas children ages 12-19 are still becoming obese. I foresee obesity and fast food servings continuing to rise in the next 10 years.

J: Very interesting prediction R. I’m not quite sure about the fast food servings sizes increasing as I predict the next marketing tactic used by fast food companies will be healthier eating by reducing sizes.

A: I agree with J to a degree. I do believe that the portions will become smaller, and there will be “healthier” options, I don’t think this will truly change the climbing rate of obesity. Simply because there are better options presented, just opens up an aisle to a new kind of customers. However, that does not prevent or discourage those that simply want to eat unhealthily from doing so as they have for so long.

The other days of the week, students are supposed to select a Significant Digit to discuss. I’ve asked them to summarize what they read, make any connections they can to other things, use this new information to make predictions about the future, and ask questions they still have.

Here are a few good posts from Tuesday:

J: Equifax’s share price has fallen by 35% after the company publicly acknowledged there security breach. Unfortunately, most companies don’t take security seriously until something drastic like this happens. It’s disgusting that such a large company could be so negligent with there security especially considering that hold over 143 million American’s data. This includes social security number, which are supposed to be kept private.

H: The paragraph labeled “$60 Million” talks about how much money the movie “It” made this weekend. The paragraph explained that this would have been the best weekend if it wasn’t for the fact that this was the second weekend the movie was in theaters.The movie achieved a record-breaking $123 million opening the week before. The movie knocked Hotel Transylvania 2 down to third place. Why was the movie so successful? Why was the second Hotel Transylvania more successful than the first? What cinemas played It?

T: Apparently, according to Bloomberg, rich people nowadays are interested in buying submarines. The article focuses around the M7, a submarine that looks like a huge yacht that can go underwater. What fascinates me about it is how much it entices me to want it. Though, what truly baffles me is why anyone would buy it. I mean, unless you’re going to live in it, I doubt anyone smart will drop at least 2.3 billion on it…

These assignments will continue throughout the first semester, which is when we learn about data collection, analysis, and visualization and probability. I began the Graph of the Week in my regular ProbStats class but I don’t think it’s going to create as much thinking and conversation if they just respond on paper. I need to figure out a way to create a space for that.

#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.