People are very interested in Mendicant University, but there is very limited public information out there about it, even now that we've been working on the experiment for nine months aleady. From March 26th to April 8th, I'll be posting short stories daily that might give a better picture of what's inside my head, as well as what's going in the ivory tower that is our Ruby Progamming school.

As I mentioned in the previous post, my roughly three years of on-again, off-again college attendance was a mixed experience. There were certainly plenty of courses and professors who following the 'my purpose is to generate grades for transcripts' formula, but the percentage of instructors who actually gave a damn was much higher than what I found in primary school. One professor in particular exposed me to a style of teaching that has altered the way that I think about Life, the Universe, and Everything.

Leaving school for a while and then coming back, I found myself overqualified for introductory math courses, but with not enough options for advanced courses due to a lack of available open courses. Fortunately, through a stroke of luck one other student (John) was in a similar situation and our professor Dr. Uebelacker offered us an interesting alternative: An independent study in Topology (not to be confused with Topography). The course material itself sounded interesting to me and was enough to win me over, but when I heard about the way he intended to teach the course, I could not be more excited.

The style the course was taught in was a modified form of the Moore method, named after a topologist who popularized the idea by coming up with a way to teach Topology that allowed the bulk of the materials to be developed and presented by the students taking the course. In the context of our independent study, what it meant for us was that rather than reading a series of lengthy explanations about fully fleshed out proofs and listening to long lectures on the various topics, we used an exercise book which broke the materials down into manageable chunks and required us to work through developing the proofs ourselves. We then met on a weekly basis to discuss our results, along with the obstacles we ran into along the way. This basically meant that John and I would take turns making fools of ourselves on a chalk board while Dr. Uebelacker heckled us a bit and then helped us find our way. Occasionally, John and I would find errors in each other's work, or have competing proofs that solved the problems in a few different ways. This lead to lengthy discussions among the three of us about what sorts of best practices apply and what the pros and cons of each approach were, not unlike the sorts of discussions you might encounter between folks contemplating software design or pairing together to solve a particular programming challenge.

It is fairly obvious that one benefit of this approach is that if you prove something yourself, you will need to understand it much better than if you had just read a proof and made use of its results. Additionally, it's not hard to see that my earlier comment about how teaching causes you to learn something much more deeply would apply here, since every ad-hoc presentation was a teaching opportunity. However, there were many other emergent lessons to be taken from this sort of course which were a lot more subtle.

The constructive nature of the course blurred the lines between the curriculum and personalized exploration. Because you needed to generate the proofs yourself that you later built on, there was nothing in your way if you wanted to explore a side track. Taking this course offered me a formal way of understanding that if you've got a question you want to explore, that there are ways to find your answers without looking them up somewhere. Often times we turned 'I wonder if...' questions into informal proofs that would reappear later in the course as a required exercise. While most of the times these amounted to little more than footnotes in terms of their net impact, the mere notion that we could form conjectures, prove them, and make use of them was an eye opening realization that we weren't simply learning about math, we were also doing math. While we didn't have the time, resources, or environment that would facilitate us to generate genuinely new knowledge, we certainly were experiencing that sort of growth personally, which was tremendous practice for the kinds of things I'm working on now that do take me into uncharted territories.

Finally, the nature of the course baked curriculum, pedagogy, and evaluation all into one cohesive experience. We didn't hand in any written work for this course, but showing up after not doing the reading and the necessary legwork to test out and build upon the ideas we were discussing nearly guaranteed having nothing to say in a class with only two students in it. Evaluation came in the form of presenting our ideas and then discussing them, and even occasionally in the form of observing Dr. Uebelacker make a mistake in his own lines of reasoning and then allowing us to try to fix them. While the responsibility to do the work was individual, the process of evaluating it and making into something of value was a collaborative one, making it so that all those involved had an interest in helping keep things moving along.

In this course, I learned not just Topology, but a whole new way to look at the world. Dr. Uebelacker would go on to correctly point out that the format doesn't apply to everything, and in fact the next independent study we did together on Galois Theory was taught in another format. But when Moore works, it really works, and it can totally change the way you look at formal education. It did for me.

NOTE: I have a handful of other folks who really inspired me in my days at University of New Haven, in various ways. They include but are not necessarily limited to Dr. Sharma, Dr. Fischer, Dr. Eggert, Dr. Griffiths, and Dr. Daniels. However, I singled out Dr. Uebelacker because my Topology session with him has shaped the way I look at training and teaching in general, and in RMU sessions in particular.