MathFest 2013: Hartford

Yeah, Hartford was not that exciting, but I still had a good experience at MathFest 2013. It was a very full week, so I have lots of things to share—way too much to fit in one post. I’ll pick out one thing or another and try to write a little bit for the next few days as I process.

The first thing on my mind is my Math 1100: Math in Decision Making course for the coming fall. I had a few discussions with people about this course during the conference. In particular, David Pengelley encouraged me to make the course more tactile. This seems a good idea. I have no doubts that with some work I can realize this for my unit on topological ideas.

Also, I got to thinking that a major problem isn’t so much what my students know, but rather what they “know” that isn’t true. This is especially acute during the probability and statistics unit. I am reminded of the approach taken by Derek Mueller in his Veritasium series. He points out the importance of confronting misconceptions in order to encourage genuine learning. In fact, watch this TEDx Sydney talk he gave.

So, I want to design some sort of hands on probability & statistics unit that puts common misconceptions front and center. Now I just have to figure out what those are.

I have attempted to teach this course 3 times, and I have had classes with enrollment between 30 and 40. This is large for a “presentation based” IBL style, but I adapted some group work. I figured for this coming semester I would try out a version of Dana Ernst’s felt tip pens structure. But today, I checked my enrollment.

I will have 68 students.

I emailed my comrade Doug Shaw. We have embarked upon this experiment of teaching Math in Decision Making in parallel. (I’d say together, but we don’t talk often enough. Seriously, Doug. We should chat more.) His two sections are 72 students each.

Time for rethinking.

Robert Talbert and Matthew Jones dropped some tips over on Google+. I’m going to investigate some peer instruction ideas, some details about using classroom response technologies, and even more group work flavors of Inquiry Based Learning. I have to design something that will work.

If you have ideas, I am happy to hear them.

IBL and Flipped Classrooms compared


Last weekend I went to the MAA Michigan meeting to participate in a discussion of “innovative teaching techniques.” The session was organized by Robert Talbert from Grand Valley State University, and the other presenter was Dana Ernst from Northern Arizona University. This was a long trip, but I enjoyed going. It was especially nice to meet Robert in person (as we had only interacted on the internet before) and also to make the acquaintance of his colleague Matt Boelkins. (Dana and Matthew had planned a breakfast to discuss Matt’s open source book Active Calculus, and they graciously allowed me to sit in.)

Earlier today, Robert posted to his blog at the Chronicle some musings on the following question:

Is the modified Moore method an instance of the flipped classroom?

You should probably go read that post for context. Read it: Robert’s blog is good stuff.

I have been thinking about this all day. I am still uncertain about my feelings, partly because I don’t know enough about the “flipped classroom” approach. Anyway, here is my take on the essential similarity.

It seems to me there are great differences between IBL and the flipped classroom, but they have an essential nugget of commonality: to be effective, switch things around to make the students focus their energies on sense-making activities. Certainly, many IBL teachers do this as Moore did, by minimizing the amount of time spent on raw information dissemination from instructor to students. At least, that goes for class time. An important component of running a successful Modified Moore Method/IBL class is getting the sequence of tasks or activities structured _just so_. A great deal of the information transfer is actually buried in the class script. In fact, I want the important ideas to come out of the students work, so I must structure my questions so that
  1. students are eventually led to the ideas they need and come to a full understanding, but
  2. students really do have the experience of having those ideas for themselves.
It feels like a fancy magic trick. You want to give each student exactly what he or she needs to do it for himself or herself, and no more. The first run at this is communicated to the students through the careful choice of questions to answer and conjectures to prove or disprove.
Of course, even in a really strict traditionalist Moore Method style there is time for conversation and discussion, and any time that an instructor participates in this it serves as a vehicle for more information transfer. It is not quite the “this is a fact” kind of transfer, but still that is how it is done.
One Other Thought:

It seems that proponents of flipping a class think about things this way: move the routine information transfer stuff out of the classroom and take class time for rich mathematical activity.

As an IBL instructor, I strive for something a little different: move almost all of the student work out of the classroom, and use class time for discussion. Now, this is a rich mathematical activity. I see it as different, because I hope students spend their time “figuring things out” outside of the classroom, and I use class time for formative assessment and feedback. The whole class takes part in that process, in the open. Students explain and defend their ideas, and we all work on evaluating them and giving constructive feedback. It is a very particular flavor of mathematical activity.