Friday, September 20, 2013

The Calculus of (Instructional) Variation

As a professor, I take a lot of professional pride in my teaching. As part of that professionalism, I am always looking for ways to improve the learning experience for my students. In this post I am going to describe how some small changes have made a really noticeable impact in one of my classes. (That's where this post title comes from: a little variation has added up to a big change.)

Before I can describe what I did, I should give a little background about what happens in my classes. For now, I am going to focus on my Transition to Proof course. I teach via inquiry-based learning (IBL). As part of that approach, I use student presenters a lot. This means that students come to class having worked on problems (mostly proofs) at home, and they come to class knowing that for most of the problems, someone will have an opportunity to present their proof attempt in front of the class.

This semester, one of my goals is to improve the quality of the discussions that follow a student's presentation. To achieve this goal, I made a couple of changes. In the past, I collected work from everyone at the beginning of class. Then, a presentation proceeded through the following steps:
  1. A student wrote their work on the board 
  2. The student explained their work.
  3. The class proceeded through a Think-Pair-Share: They were asked to look at the work in silence, then share ideas with a partner, and finally ask questions or make comments to the presenter. 
  4. During this entire time, the presenter remained standing to answer questions about their work. 
This term, I started in a small classroom with a small chalkboard and a projector screen fixed in place in front of the chalkboard, so that using (most of) the chalkboard was only possible if I unhooked the screen from the wall and set it on the floor. This was part of the inspiration for a new presentation procedure:
  1. I photograph student work and upload it to NotesPlus, and project the student work via iPad. 
  2. The student explains their work, but sits down immediately, rather than waiting for questions. 
  3. The class proceeds through a Think-Pair-Share: They look at the work in silence, then share ideas with a partner, and finally ask questions or make comments, BUT now the presenter is not on the spot during the discussion, as he or she is sitting down.
In addition, I have changed from collecting work at the beginning of class to collecting at the end of class. During class, students used colored pens (Thanks Clark Dollard and Dana Ernst!) to annotate their work, so that I know what was completed before class. Therefore, students are able to compare their work to the work being presented.

These changes are minor, just changing the medium of the presentation, letting the presenter sit during Q&A, and letting students keep their work in front of them for comparison. But the discussions have been stronger for the four weeks of this semester than in years past. My hypothesis is that the students feel more comfortable asking questions with me at the front, even though I am still directing questions back to the class or to the presenter. The class no longer feels like it is putting the presenter on the spot when they raise issues.  Moreover, they are able to ask questions based on their own efforts that they now have in front of them. I am sure there are other factors involved in the improved discussions, including the fact that cohorts of students vary, and this group seems to have a number of people willing to share. Still, it is amazing how small changes can have such a visible impact. 


  1. Have you noticed a difference in how students feel about their accomplishments?

    For me, the key part about the student taking questions at the front is that the student has to take ownership and defend their work. That way, when it comes off well, they completely own the success.

    I wonder if your experience is the same (from previous iterations of the course), and if that sense of ownership and pride in success remains now that things have shifted a little?

    Just curious

    1. TJ,
      Good question. I don't have a strong reading on this yet, but I am going to speculate that the sense of ownership is probably a bit less. The students do still have to defend their work at times, or they answer questions of the "What did you mean?" or "Why did you do that?" variety, so ownership of the problem is not completely lost. But I imagine it is reduced.

      At the same time, there is no longer that dynamic where no one has questions for the presenter and then I end up in a dialogue with the presenter about this or that. Discussions have been really strong. Maybe some of it is that my attention is more on the room than the presenter now, so students feel more obligated to take up the questions or to raise issues.

      Finally, I just graded the first quiz, and I was pleased overall. No problems were left blank, and no one gave answers that were totally irrelevant to the problem. So I'm willing to sacrifice a little of the good of the one for the good of the many.

  2. Good stuff! It's a small change on the surface, but it's really about shifting the discussion from it being about the person's proof to about the proof. I can see that if everyone sits down and looks at it, then there is just math at the front. Also when there is someone at the front of the room, it may be the case that subconsciously people revert to "sit in a lecture class mode." Interesting. There could even be a psychology dissertation imbedded in this. ha!

  3. I am always amazed that such small changes in teaching inputs can lead to such large changes in learning outputs. It makes me wish that I could hire a coach to watch me teach and ask me to make adjustments in all of the little things that I am doing wrong.

    I couldn't get funding for this, though.

    1. Bret,
      Have you tried videotaping your class? If your institution has a teaching and learning center, or maybe even if not, you could probably scare up someone to take a video of your class. You would have to tell them what you want to have in the video (how much focus on students vs. the front of the room, etc.). Still, it might give you some insights, and you would probably learn a lot. And then you are not bound by finding a colleague who is local and willing to visit your class.