I blog a lot about peer instruction, but I think this screenshot from this morning’s Calculus 2 class is worth 1000 of my blog posts about just how effective a teaching technique PI can be. It’s from a question about average value of a function. Just before this question was a short lecture about average value in which I derived the formula and did an example with a graph of data (not as geometrically regular as the one you see below). I used Learning Catalytics to set up the question as Numerical, which means that student see the text and the picture on their devices along with a text box in which to enter what they think is the right answer. (I.e. it’s not multiple choice.) Here are the results of two rounds of voting (click to enlarge):

After the first round of voting, there were 12 different numerical answers for 23 students! (Some of these would be the same answer if students rounded to one decimal place like the question asked them to do. But still, that’s a lot of different answers.) When the first round of voting was done, I kept the results secret and had the students discuss their answers with each other for two minutes. Then they revoted, and as you can see, we went from 35% correct to 91% correct just by students explaining their answers and listening to each other. All I did was monitor the discussions — this was all without my input and without looking at the responses (which you’ll remember from this post can cause a bias in the second round of voting).

For me, this exemplifies why I continue to use PI in my classes. Students *learned* something in that 2-minute period of discussion — maybe it’s something as small as “don’t forget to make area negative if it’s below the x-axis” or maybe it’s the entire concept of average value. Whatever. But they are getting it now, and it’s not because of my scintillating lectures — it’s because they’re getting an effective combination of lecture, individual work, and group work, and that’s pretty fantastic if you ask me.