by Derek Smith
Maybe it shouldn’t, but it often amazes me when I notice similarities between tutoring 6th graders and my work as a TA. I don’t mean this in a disparaging manner; I’ve simply observed a few common (though not suggested) approaches to solving problems in mathematics. For instance, many students seem to rely strictly on divine inspiration prior to asking for help! They may remember a few facts from lecture, but leave their book and scratch paper entirely untouched. I often wonder about and occasionally experiment with techniques to increase student engagement and would like to share a positive experience I had last week.
At UCSB, teaching assistants are required to spend a few hours per week in the MathLab, a drop-in tutoring clinic. Most of the core mathematics classes required by non-majors (calculus, differential equations, etc.) use the WebWork system for homework. Students log into the class webpage to view and complete assignments, reducing the need for graders. The downside is that it’s easy for the unmotivated student to simply point at their laptop screen–or cell phone screen–and ask “lazy” questions: Why isn’t this the right answer? What’s wrong with my answer? WebWork won’t accept this answer (not really a question). Additionally, the assignments are usually structured to allow unlimited input attempts, creating a tendency for students to input every permutation of their answer until the system accepts it or they ask one of the previous questions.
This quarter, the professor who I am assisting implemented a “one attempt” policy for selected homework problems. In addition, these problems are more lengthy so as to require the student to write down the details prior to submission. The first few weeks I didn’t give these problems any particular attention during discussion section. However, the students have just covered a selection of basic integration methods. This is possibly the first exposure for many to a situation in a math class where the solution does not follow a prescribed algorithm.
In each section, I asked for a volunteer to attempt the problem at the board. I specifically requested someone who hadn’t worked on it too much. I allotted the last 10-15 minutes of class for this exercise. The student participation had a character that came as a total surprise. A few things in particular stood out. First, level of difficulty of the problem leveled the playing field. I’m sure everyone has been in a classroom where one student seems to be doing most of the talking. Whether you’re the person in the front of the room or in the audience, it’s very easy to lean on this person to keep the discussion moving along. The difficulty didn’t necessarily quiet these personalities, but it meant that their suggestions were not always the correct ones. Secondly, students seemed to have a vested interest in solving these problems! I really expected that most students would simply ignore these problems, if stuck. Those one or two points per week seem to provide genuine motivation. Finally, I think watching a peer get stuck at the board vastly increased the average participation rate. Under regular circumstances people are often afraid to ask “dumb questions”. But when they realize that no single person has the completed picture it suddenly becomes a much more comfortable atmosphere for questioning and brainstorming.
My main reason for recording this experience was that it worked so much better than I expected. Recently, I had a trend of narrowing down the question before asking a student to come to the board. I think that the structure of the assignment (one-attempt, difficulty level) contributed greatly to the depth of the interaction.