Teaching Statistics with Clickers (Part 2)
Here’s another way I use clickers in my stats courses.
Creating “Times for Telling”
Through accounting procedures, it is known that about 10% of the employees in a store are stealing. The managers would like to fire the thieves, but their only tool in distinguishing them from the honest employees is a lie detector test that is only 90% accurate. That is, if an employee is a thief, he or she will fail the test with probability 0.9, and if an employee is not a thief, he or she will pass the test with probability 0.9. If an employee fails the test, what is the probability that he or she is a thief?
- 90%
- 75%
- 66 2/3%
- 50% [Correct]
I adapted this question from Gelman and Nolan’s book, Teaching Statistics: A Bag of Tricks, and used it to create a “time for telling.” “Time for telling” is a term coined by Schwartz and Bransford in a 1998 article in Cognition and Instruction. It refers to the idea of creating conditions under which students are ready and interested in hear an explanation of a concept or technique. Students often don’t start a class session this way, but instructors can work to create these conditions.
Since I asked my students this clicker question after they had read the section on Bayes’ Theorem in their textbook but before we had discussed the theorem during class, most students did not understand the theorem well enough to apply it to solve this problem. As a result, only 23 percent of the students answered the question correctly.
I then followed Gelman and Nolan’s suggestion and conducted a classroom experiment in which each student chose two numbers at random from a sheet of random numbers between 0 and 9. Students who chose a 0 for their first number were told they were thieves; other students were honest employees. Students who chose a 0 for their second number were told that the lie detector test gave an incorrect reading for them; other students had accurate lie detector test readings.
I then asked for a show of hands from students who were reported as thieves by the lie detector test–those who were thieves and had accurate test readings along with those who were not thieves but had inaccurate test readings. I counted these students, then asked the students who were not actually thieves to put their hands down. Roughly half of the students put their hands down, demonstrating to the students that 50% was likely the correct answer to this question.
At this point, having seen that most of the students had likely submitted incorrect answers to the question, the students were ready for me to explain the solution to this problem to them. The students were “ready” in a motivational sense because their curiosity about this problem was piqued and thus they wanted to listen to my explanation. The students were also “ready” in a cognitive sense since they had spent several minutes trying to understand the question at hand and thus they had thought enough about the question so that my explanation was likely to make sense to them.
The clickers helped here in two ways. One was that they encouraged all students to get “ready” for the time for telling, not just a few of them. The other was that the bar chart generated by the classroom response system showed students that most of them were wrong about the question. This, I think, generated additional interest in the correct explanation.
These “time for telling” questions can be difficult to write, but when you have one, it can be very effective. What “time for telling” questions have you asked with clickers?