I have changed a few of the mechanics of how my pre-calculus level geometry class goes. Most of these are in response to not being able to give students enough individual time to keep them working after they get stuck. This summer, I had a substantially smaller class, when combined with the longer meeting time, allowed me to talk to students about their work several times every class. In order to make sure students are able to make regular progress on the current problem sets, I have limited the presentation and discussion of homework to the first 30 to 45 minutes of each of the 75 minute class. After that, we break into randomized small groups (3 to 4 students) to start working on the next set of problems. I also make sure that each group looks at a variety of problems before the end of class. I think this is allowing students to get past any small gaps or frustration and give better attempts at all of the problems in each set. I am hoping to get fewer students who make no good attempt at problems. I have also learned which students I must meet with daily and which ones will be able to progress using their small group discussions. But the same problems with less individual contact has created a different atmosphere in each of my two sections.
One section of geometry has really responded to everything that we are doing and they have collectively changed the way they attempt problems, the way they discuss problems, and the attitude that they have about math (and hopefully college) in general. When students in this section understand the problem sets, they are really excited to present the ideas to others.The other section of geometry has had a more fractious take on everything.
A personal challenge has been the unevenness of learning in the IBL setting. While I expected this as part of the change to IBL and a more realistic learning process, it can be very emotionally draining to help students through this process. This is especially difficult when students are not being respectful of others. Sometimes this means that they use tone of “How do you not know this?”, other times they speak over each other (or me). One day I feel like students make great steps in both understanding the material and their approach to mathematics in general, and the next feels like a totally different experience. The daily mechanics of class are the same but the emotional response of the students seem to be very different. This is one of those benefits, and difficulties, with connecting to students more than just being in the same room a few times a week. In particular, I am working to try to engage specific students before they get too frustrated in order to try to keep productive work going and to encourage respectful explanations and discussion.
In the future, I am looking to build in more opportunities for students to get help when they are stuck. One thing that has been helpful is to remind students that it only takes a few seconds of talking to me or other students to become unstuck. This happens at the start of every class as they prepare in small groups to present homework. I am trying to get them to come by to get this push before the next class meeting as well. We will see how much of this I can affect.
My linear algebra class is a more traditional approach to IBL with students working through a problem set, presenting in class and discussing difficult ideas. They turn in homework each class. The non-proof problems are graded as a set out of 3 points. I have given a rubric for students to understand what each level means as more than a 0, 33%, 66%, or 100%. I find that it is useful to give regular reminders to students about this process driven grading and the inclusion of points for meaningful presentations. I also grade proofs on a 0-2 scale and allow as many resubmissions as are needed.
About 80% of students regularly attend class meetings and are making progress on my meta-goals of careful thought and communication. Content has progressed slowly but students are appreciating the great increase in individual feedback compared to previous courses. In fact, this week students took their first exam, which caused several students to come talk to me about how they are doing. All of these conversations were focused on the bigger picture of how to change students into effective thinkers and communicators. The students almost never brought up ideas of content. They talked about how to be better at the other stuff. It was just the lift I needed after some of the difficulties in Geometry.