Learning about "Cool Things"

Written by: Christine von Renesse

Think of and then write down the 5 coolest things you know in mathematics. Did you ever think about including them in your MLA course? You can, and perhaps should.

What are “Cool Things”?

“Cool things” are short “mini presentations or activities” about a mathematical topic that is exciting to us and usually different from the math content that we are currently working on in class. For example: how are 17 dimensional flag manifolds connected to the honeybee dance?

I learned about “cool things” when I taught our Math for Liberal Arts class using Julian’s book (The Infinite) and realized that there was something I was missing. His students were much more excited about math in general than mine. After many conversations I finally realized that he showed his students “cool things” on a regular basis.

I am a hard-core IBL teacher and don’t lecture at all. Other than administrative issues, I spend less that 5% of class time talking about mathematics with the students assembled as a whole. I only facilitate and try to stay out of the way of my students so they can do the math. Visit a typical class of mine in the following video clip.

I am currently working on finding and including "cool things" in my classes.

Only if I take the risk of learning myself will my students be willing and able to do the same.

Let's look at an example. In the following video clip Julian shares his excitement about the above mentioned honey bees.

Why do “Cool Things”?

  • Showing cool things is one way to relate to the audience of a math for liberal arts class (link to audience blog). The students see something that I find cool and that they hopefully find cool as well. Or at least they get to see how someone else is truly passionate about mathematics.
  • I do it to break things up – it is a change of pace. My students have been working hard (and well) but now they really need a break from the current topic. You can do this by switching topics entirely. But it is often enough of a change of pace to take part of a class to do something.
  • I do it because I want them to see that there is incredible breadth in the beauty and surprise in mathematics. I don't ever teach this course without beauty and surprise. But it only occurs in the one area we are currently studying.
  • By showing cool things in other areas in mathematics I hope that I am encouraging them, in the long run, to be more open minded about exploring these things, reading about mathematics when they come across it, finding their own cool things (sometimes an assignment I give), and in general being more curious/accepting about mathematics that is not a specific part of the immediate curriculum that they are responsible for.

Here is our current (and evolving) List of "Cool Things".

Things to consider:

  • While Cool Things are a teacher-led component of the course which is important, its time-frame is quite small. With success in IBL it has to be, once students have become actively invested in inquiry they will not relinquish for very much longer than a few minutes at a time to see some teacher-led fireworks. They're too interested in their own discoveries.
  • The “cool things” that I am doing as part of the course are not really cool to all of the students. It is important to have a diversity of “cool things” (even if they are not all studied deeply) to reach the diversity of the tastes/interests/majors of our diverse students.
  • What’s cool depends on the instructor. When I asked Julian to share a few of his cool things with me so I could use them as well I still did not get the same response as he did! The problem was that I needed to find things that I was personally excited and passionate about. Julian’s cool things worked for him (and some worked for me) but really I needed to create my own list of cool things.
  • I find it personally much easier to be passionate about something that relates math and art or math and teaching than about some application of mathematics or even a new discovery in pure mathematics. I think it has to do with my personal feelings of feeling ridiculous when I am showing passion for something my students might not relate to. It is powerful to recognize these places of shame and to work on taking bigger risks in my classes. Can you relate to this?