# Teaching Math with Clickers: Practice Question or Discovery Question?

Continuing my reports from the contributed paper session on teaching with clickers I helped coordinate at the Joint Mathematics Meetings back in January…

*“Clickers in the Classroom,” Kimberly J. Burch, Indiana University of Pennsylvania [Slides**]*

Kimberly teaches a “Math 101” survey course called “Foundations of Mathematics.” Topics covered include set theory, graph theory, and counting methods (among others), and Kimberly shared several interesting clicker questions on each of these topics. For example, here’s one of her questions from the unit on graph theory:

How many vertices are there in a tree with 19 edges?

- 19
- 18
- 20
- Not enough information given

Kimberly practices the “classic” peer instruction technique of having students vote individually first, then discuss the questions in small groups, then vote again. She finds that students often converge to the correct answer on the second vote.

In the example above, her students were split between 18 and 20 on the first vote, but after the peer discussion time, most students went with the correct answer, 20. I found this interesting because the “Not enough information given” seemed to be the obvious wrong answer to this question. A graph with 19 edges might have any number of vertices, but a *tree* with 19 edges can only have 20 vertices. Students who don’t realize that trees are graphs with very specific properties might be tempted to go for the “Not enough information given” option.

I suspect that Kimberly used this question after the students learned the relationship between the number of edges and number of vertices in a tree and that this question was meant to assess whether students remembered that relationship. Some students likely remembered that one of these numbers was one more than the other but weren’t sure which one was higher. That would account for the split vote between 18 and 20. Had this question been asked as an exploratory question and not a review question, I’m betting the split would have been between 20 and “Not enough information given.”

Kimberly also mentioned that she uses her clicker system’s priority ranking questions to have her students decide what topics should be emphasized during exam review sessions. Kimberly gives her students a list of 8-10 exam topics, and the students indicate the top three or four toughest topics in order. Kimberly said that this helps her make good use of limited exam review time by focusing on the topics the students find the most difficult.

Kimberly also shared some data from a quasi-control group experiment she conducted. She taught two sections of this survey course and alternated which topics she covered with clickers in the two sections. For example, section A might cover topic 1 with clickers while section B covered topic 1 without. Then for topic 2, section B used clickers and section A didn’t. She then compared test scores for the two sections by topic. For some topics, students using clickers performed better on exams but for other topics, the students not using clickers performed better. And for other topics, there was no difference. The data was generally favorable to using clickers, but the “quasi” part of this quasi-control group experiment made it difficult to draw firm conclusions.

*Image: “Point Marian Bridge” by Flickr user timmenzies / Creative Commons licensed*