## Tuesday, November 29, 2016

### The Fun of Teaching Probability and Statistics

There are so many interesting real-world examples from which to draw!

The last chapter my students studied was about probability, and the current chapter is on the normal curve.  I've been writing quiz and test questions (I don't really like using the "test bank" that comes with our adopted curriculum materials) recently and having fun.

For example, last week I spent a lot of time sick in bed--playing Yahtzee on my phone :)  As I played I realized that I was constantly calculating expected values, probabilities, etc., in my head, and that some of these would make excellent quiz and test questions.  But that was last chapter's material.  No problem--my bonus question on each chapter test relates to last chapter's material, to keep it current in the students' minds.  I could use a Yahtzee question as a bonus question for this chapter's test!  Example:  I need 4 5's in order to score 63 points on the left (of the Yahtzee scorepad) and thus earn the 35 point bonus.  On my first roll I got two 5's and on my 2nd roll I got one 5.  What is the probability of getting 1 or 2 5's on my 3rd and final roll?  Example:  On my first roll I got a 23345. I keep the 2345 and roll the remaining die.  What is the probability of getting a 1 or a 6 on either of my next two rolls, thus getting a "large straight"?

Today we had 3 2-hour block periods (don't ask), and I spent about 20 minutes each period today teaching my students how to play Yahtzee.  My rationale was simple:  if they understood how to play the game, they'll be able to better understand what I'm asking on their test.  They'll be able to devote all their brain power to calculating the probabilities rather than trying to figure out exactly what I'm asking.  In another couple years I'll probably have to do that for playing cards, too, as entirely too many students today don't know what comprises a standard deck of cards (and hence have difficulty understanding probability questions about drawing from a deck of cards).

My current master's class is on testing/measurement/assessment, and one of the last chapters in our book was about standardized tests.  We read about stanines, deciles, having a score in the xth percentile, etc.  Since standardized tests mostly assume a normal distribution of scores, questions about stanines, deciles, etc., are great questions for our current chapter on the normal curve.  Throw in a little SAT score information gleaned from the College Board and you have a smorgasbord of questions that can be asked, all of which have some applicability to the students themselves.  Example:  given that the average SAT math score is such-and-such with a standard deviation of this-and-that, what is the minimum score that would place a student in the top decile?  Example:  what fraction of test scores are in the 5th stanine?

If you're creative enough and thoughtful enough, writing test questions can be quite enjoyable.