*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.