I am always on the lookout for new pedagogical ideas, but I hold to two unchanging principles: students must be active learners, and they can learn from their confusion. (A thought-provoking article by Steve Kolowich on confusion’s role in education appeared in the Chronicle of Higher Education, dated August 14, 2014: “Confuse Students to Help Them Learn.”) I do hope this second principle is somewhat startling, because I strive to give clear lectures and send off my students at the end of the semester with a firm grasp of mathematical concepts and techniques. Moreover, math should be fun and beautiful, but that’s not what comes to mind when confusion is mentioned. Nevertheless, real learning rarely comes about without passing through a dialectic involving confusing problems.
One reason I embrace confusion is that students say in their evaluations of my teaching that I am able to answer well the questions they ask me in class. They know math is messy and have faith that I will be able to understand their perspective and lead them out of the jungle. One writes, “This subject is outside my area of concentration, but I needed it for my major. He helped me get through [and] understand it better because of his hands-on teaching.” Students also say I am very good in office hours, which is in large part due to my friendliness and listening ability. A student writes, “Dr. Cole did an excellent job of teaching us the material. And if we didn’t understand, he was always helpful during his office hours.”
One way to draw out learning from confusion is to give in-class group activities, which require practice of skills just learned and allow students to learn from one another. I field many questions while the students are working on the activities: there is much less vulnerability in asking me a question in front of two other group members than in front of the entire class.
I am open to constructive feedback on my teaching. A colleague once visited my 8:00am College Algebra class and noticed that many students were engaged and excited, but that there were a few who were not following closely. Upon reflection I came up with a scheme to engage the whole class. Here is how it works. At any time I may call on any student to answer a question. Along with the question, I throw a teddy bear to the student. The student may answer the question or simply pass the bear to someone else. In this way every student has an opportunity to become involved, but there is no shame in not answering or getting it wrong. Passing the bear is a normal part of the game. As a result of this tactic the entire class began to pay attention, and from time to time the bear’s journey generated a healthy dose of laughter.