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Double Trouble

In my QR class I have students read Joel Best’s book, Damned Lies and Statistics; a great overview of the social construction of statistics and how to be a critical consumer of statistics.  He starts with his nomination for the worst stat ever: “Childhood gunshot deaths have doubled each year since 1950.”  The actual stat is that such deaths each year doubled from 1950 to 1994, a very subtle distinction!  Students are given a take home quiz on the readings (they also read an article) each week.  I like to ask if this means that our society has become more violent, getting at the need for a comparison to population size (i.e. rates).  Margot Black, at Lewis and Clark College, suggested an interesting question: If the current population is 316 million and doubles every year, how long would it take to reach 35 trillion (a number Best mentions)?  First this requires facility with millions and trillions, something we need to treat with care; and second it requires them to start grappling with exponential growth.  One of the wrong answers she received was illuminating.  A student simply divided 35 trillion by 316 million and put down 110,000 years.  So if we had asked to go from 3 to 48 doubling each year, the correct answer is 4 years but this approach of dividing would give 16.  Doubling from 3 to 6 in the first year looks like adding 3, so you can see why someone would then extrapolate to simply dividing 48 by 3 and getting 16 years.  Often a wrong answer is very illuminating into our students’ thought processes.  Rooting out these fundamental misconceptions is a critical part of the learning process.

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