Monday, September 12, 2011

Dots Everywhere!

The first model that we make sued to center around the dots on the floor of my lab.  With the renovation, I got a new floor, complete with much less 'spotty' tiles, so that kind of went out the window.  Instead, I went to filling my board with dots, but that wasn't great either.

This year, I took advantage of our great art studio and superstar Mrs. Silverman, and made myself an art.
"One art, please!"

I took one of those large rolls of white paper, some brushes, paint, and water, and made a drip painting (think Pollock, but dots without many streaks, and not as good).

This was the subject of our first model.  It's great because:
  • The number of dots isn't necessarily knowable (because of the super tiny ones), so we must come up with some sort of predictive and approximate description
  • The number of dots isn't necessarily a single number, because there are some streaks there - what counts as a dot?
  • The most common approach involves sampling a portion of the area and using proportional reasoning; this is right in their wheelhouse, so we can concentrate on the other demands of creating their first algebraic model
  • The uncertainty comes in two distinct varieties: random (from the selection of the sample - can be reduced by sampling more areas or bigger areas) and systematic (I left few dots near the edges of the paper, and the left side has a higher density than the right side)
Here are a few of the first whiteboards of the term!
We'll need to work on good symbol choice, but fun's a good place to start :)

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