Saturday, April 21, 2012

Probability and Confidence

Every time I teach I learn something new and never has this been truer than with my graduate class this semester. Last Thursday we were exploring issue of probability. We started out developing the concept linguistically trying to identify those things in our lives that were likely, probably or certain. It always amazes me how so many people don't like to say something is certain; even the sun rising tomorrow morning.

We talked about the difference between theoretical and experiential probability and how the latter is so much more interesting. We tossed coins and used an automatic on-line coin tosser that tosses a coin 1000 times in twenty seconds. I can't think of a better way of showing the law of large numbers.

We concluded class with a really interesting activity in which you place five cubes in a bag; the cubes can either be, say, red or blue. The task is then to work out how many of each by pulling one out, recording the color, putting it back in, shaking the bag and pulling another. This continues, not for a predetermined amount of time, but until the person pulling the cubes feels confident enough to infer the number of each color. I've done the activity many times before but have never had  such an interesting discussion about it. We decided that not only did it demonstrate the relationship between probability and confidence, something that is taught in statistics classes, it also demonstrated something about one's personality. Some students must have pulled 30 or 40 cubes before they wanted to say how many of each color there were while others wanted to say after just 10 or 15. Isn't that neat? It's almost like a personality test. Some wanted certainty while  others settled for a risk.

The sad thing is that we will not perhaps be able to do this in the future until 6th grade as probability is not included in the elementary school Common Core math curriculum. This is sad in a way because without the topic of probability math takes on an air of certainty. Perhaps this is not a bad thing for young children and something had to go?

On the other hand, when you stop to think about it, the concept of probability is involved in just about every aspect of human life. Every time we wonder if it will rain, or whether our favorite team will win, or whether we will get an A on a paper. In fact any time there is uncertainty.

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