I’m currently TA for two sections, one at 12:30 and another at 2:30. The other day, the students had a midterm from 11-12. They didn’t yet have a new homework assigment, so the instructor asked me to answer questions from the exam and preview upcoming topics. I also decided to use a few minutes of this section to perform an experiment. For some reason, the mood in the first class is much different from the 2:30 section. Participation is much lower, which tends to put me a little on edge, which probably has the effect of lessening participation even further. There are far fewer students in the second section–10 as compared with 20–which probably contributes to the difference. But how? Asking a question is on some level an admission of weakness. When a student works up the courage to actually ask a question it is often the case that a new fact appears to contradict what they thought they knew. Unforunately, it seems more likely that a student will suppress any such contradictions versus risk being seen by other members of the group with their hand raised.
The human brain is a machine built for pattern matching, be it in social interaction or studying mathematics. In either situation the human brain can pick out small deviations from a known pattern, provided the person has some interest in the topic at hand. The scientific method was crafted around this idea. But we simultaneously have an amazing capacity to suppress contradictory information; managing your day-to-day web of social interaction, for instance, would be impossible otherwise. I believe this ability hampers participation in the classroom setting. If you feel that everyone around you understands a lesson, then social pressure may lead you to convince yourself that you understand, too.
I remember as a child, I believed that the word “approximate” meant “exactly”. I also remember the particular point in time when this notion was corrected. One day I was reading the nutritional information on the back of a bag of Skittles attempting to discover the number of candies inside the bag. I knew to simply multiply the serving size by the number of servings per container. But I was confused when I read that there were “approximately 20 servings” per bag. How did the good people at Mars Candy know this? I imagined the machine that filled the bag had a device to hold precisely one serving size, counting out 20 servings. But how could the machine operate so accurately? It wasn’t until I discussed this question with somebody else that I learned what approximate actually meant.
Thinking back, I’m amazed at how far I went to rationalize my false understanding as opposed to questioning the assumption about the meaning of the term “approximate”. In my experience, recognizing (and eliminating) such feelings of contradiction is a core learning process, albeit one which can be embarrassing in a group setting. I found a paper which suggests an exercise to induce dissonance with the purpose of teaching the concept, Bringing cognitive dissonance to the classroom.. But I believe the exercise has additional applications. To summarize, you first lead the class in an “attitude survey” where the students respond on a 1-5 point scale, from strongly agree to disagree. There are four questions:
- World hunger is a serious problem that needs attention.
- Our country needs to address the growing number of homeless.
- The right to vote is one of the most valuable rights of American citizens.
- Our government should spend less money on nuclear weapons and more on helping citizens better their lives.
This is followed up by a behavioral survey, where the respondents are wether or not they perform each of the following actions on a “regular basis”:
- Do you personally do anything to lessen world hunger?
- Do you personally do anything to help the homeless?
- Did you vote in the last election for which you were eligible?
- Do you personally convey your feelings to the government?
I performed the survey in an anonymous manner, just asking people to follow along in their heads. I wasn’t in love with the questions, but with the idea of the exercise. When I asked how the class felt after answering the questions, someone responded by saying they made him feel that his generation was maybe “too passive”. The next response was a little more on point, describing some feeling of discomfort between attitude and behavior. Unfortunately, both were a little off the mark I was shooting for, which was recognizing cognitive dissonance. I didn’t necessarily want people to attempt to rationalize or, worse, ignore their response to the questions. I was hoping to have them identify a general feeling of discomfort, and subsequently prod them into asking questions later during section.
I want to try exercise again but need to think further about how to modify it. Maybe perform it the first day? Then, afterwards, move to a more mathematical example. State two “theorems” from a previous course but omit certain hypotheses, choosing these statements so that they are contradicted by a certain example. As graduate students, identifying and clearing up confusion becomes an automatic process, but that didn’t happen overnight! What other ideas do you have for increasing participation among those who could benefit the most?
