Who WIns?

 I'm teaching our Statistics and Probability for K-8 Teachers for the first time. Had excellent support and suggestions from Jenna Laib, colleagues Jon Hasenbank, David Coffey and Hope Gerson, and from Stephanie Casey and ESTEEM folks.

Working out bit by bit what we're going to do. Luckily I get to teach it again next year...

We just finished our first week, and I loved how the Day 2 lesson worked out, so I wanted to share it and think about it a bit. I miss the reflection of blog writing about my teaching!

On Day 1 we had started exploring measures of typical. We got out the unifix cubes, and did a bit on how could we make the distribution more fair. It took several rounds of give aways, but we got there. Some tubs of 252 and some with 251. Then each person built a stack as long as their first name. We organized from shortest to longest and thought about how to answer "How long is a 323 student's first name?" We had initial estimates, then talk went to median and mean. We retooled and did full legal names. Much bigger range, but a surprisingly dominant mode. So there was another consideration. Our emphasis was not the number you said to answer the question, but why you would say so.

Each day one of the teachers leads a Slow Reveal Graph, and Day 2 Tessa started us out on Disney Princess Baby Names, so energy was pretty high. If they had to name kids with Disney princess names they'd go with Belle and Aurora. Yvette's great question was what can you say about this without calculating?

Good discussion. I added in that since all of them had 7 elements, we could just look for a total instead of dividing. Some good call backs to Day 1's discussion of mean and balancing or distributing.

Then the main activity. They used NRICH's great millisecond timer tool and each collected 5 points of data for trying to hit 10 seconds exactly. They each found their median and mean, and thought about what would make a better measurement of who was best at estimating 10 seconds. Uniformly, each table decided on the mean. I raised up the idea of how some sporting events use your best score. They decided that they wanted to include outliers, that consistency matters.

The NRICH page that got me started on this idea had a set of data for discussion, which they credited to the great Don Steward, from his awesome Median blog.

Anna	Ben	Charlie
31	36	37
26	19	32
32	39	24
27	36	32
29	20	30

Typically great prompt from Don. They all found Ben had a mean of 30, though they all thought he was the worst of the three. People were divided over whether Anna or Charlie should win. People liked Anna's accuracy, but others were compelled by Charlie's spot on 30 seconds. They had time to propose a new summary statistic to answer the question of who is best.

One table proposed |mean-30|+|median-30|+range, low score wins. Another table proposed just the best score, tie broken by 2nd best time. Voting was mostly in favor of the more complicated statistic. But definitely the Charlie fans wanted best time. 

And then the breakthrough moment! Someone said 'What if we just totaled up how far each guess was from the target?' Absolute deviation! I tried to play calm and cool, and gave them time to think about it.

Revoted, and people went 22/24 for the absolute deviation. My inner teacher was screaming.

They reevaluated their own times using this metric, and decided on a table representative for the class champion. Then, a class championship, three rounds. Very exciting, started close, and then someone ran away with it.

In their summary, lots of great discussion about variation, mean, median and their limitations.