Something I am proud of: an IBL Geometry Course

Originally Posted 08-22-2012

[Part Two of the Math Blogger Initiation.]

So, this rambling, introspective blog often focuses on negative things. (Or at least challenging things.) This is only natural, as I am trying to reflect on my progress as a teacher and find ways to improve.

I want to take a minute and share a success story. I got hired to teach geometry courses at UNI. That means things like

  • Euclidean Geometry for preservice teachers (now on 8th time)
  • Introduction to Modern Geometries for a mix of teachers and math majors (twice)
  • Geometric Transformations for a mix of teachers and MA math students (five times)
  • Differential Geometry for math majors and MA students (just once)

I have taught a lot of geometry in my 5+ years at UNI. The most important course is Euclidean Geometry. The reason is that this is the class I have used to turn myself into an “Inquiry Based Learning” teacher.

Over the last five years, I have developed a set of course notes for an IBL version of a Euclidean Geometry class. I am very proud of them. I am even more proud of the effect that using those notes has had on my students, and on the culture of the department.

Here is a link to the student version of the notes. This blog is rather bare-bones, so I can’t embed it. And this is just the first handout, because the whole thing is too big for the casual reader.

Right now I am teaching the class again. We have just had our fourth meeting and the 18 students in this section have handled everything on here except for 1.2 (which is really hard) and 1.3 (which is not bad, and I suspect will be done early next time.) They have also made a list of four of their own conjectures and questions extending the material, three of which have been handled. So, Things are Going Swimmingly (with apologies to A.A. Milne).

Some context: My students have all had a geometry course in high school. For the most part, they didn’t really learn it. I don’t want to insult/bore them by going back and re-doing that bit again, or pretending it didn’t happen. Also, I want them to get a sense of Euclid’s work. I really love Robin Hartshorne’s book Geometry: Euclid and Beyond, but it is too challenging for my audience. The solution I settled on was to use Euclid’s Elements as a text/reference, but design my own problems around it. I started by stealing problems from the end of Ch1 of Hartshorne’s book. That grew slowly into what I use now. It took four or five semesters to get this in a shape that I liked.

The notes have been accepted at the Journal for Inquiry Based Learning in Mathematics. But I have extensive rewrites to do on the instructor’s version before it can appear. There is just so much to say to help a novice IBL person use these effectively, and I have to say it carefully.

So, more will be made “public” at a point in the near future. In the mean time, I am happy to share with anyone who wants to talk about IBL or geometry teaching.