22 - Teaching Linear Algebra with Classroom Voting: A Class Period on Linear Independence

Summary

Over the past few years, Holly Zullo, Mark Parker and I have been working on the NSF funded Project MathQUEST (DUE-0536077) to develop and test a library of over 300 classroom voting questions for linear algebra. We have found that this teaching technique fits well with the course material. We were consistently impressed with the power of this teaching method to engage students and create a more active learning environment, while at the same time students reported that voting made mathematics class more enjoyable. Good classroom voting questions can bring up the important concepts, so that students engage in this material during class time, and leave class well prepared to work through the homework exercises.

To develop this collection of questions, we began by dividing up the topics for the course among the three of us. One person would consider a particular topic, thinking about key ideas, common misconceptions, and the sorts of leading questions that we could ask in order to help the students discover the fundamental concepts. Then we would meet together and the other two people would work through the questions before reading the teacher's commentary that accompanies each question.We would then discuss each question individually, make revisions, and propose new questions in order to adequately cover the topic. Our collection currently contains 16 classroom voting questions on the topic of linear independence and is available at:

In order to show how linear algebra can be taught with classroom voting, I discuss a 50-minute class period, from spring semester 2008, in which I taught the topic of linear independence using a lesson that integrated three of these classroom voting questions.