Yesterday, a friend and fellow mathematician said that he was (and still is) drawn to mathematics due to the remarkable experience that very often a mathematical result will connect two properties that at first seem utterly different and disconnected. Of course, he added, the result itself can be virtually meaningless and not attractive at all. Instead what is attractive to him is the following: if you are able to fully understand the proof of the result, those two completely different things will suddenly appear clearly indivisible and naturally connected to you. And this change of mind is the most thrilling and pleasing thing about being an active mathematician -- the only thing to top that is proving such connections for the first time and sharing that wonderful insight with the world (ah well, at least with your fellow experts...).

However, this makes it very hard to communicate mathematics to a wider audience. Something that is incredibly difficult to understand wil...

(more)

Since my last entry I have had the chance to experiment a little bit more. Right now, I am quite happy how things progress. The students are generally getting better (with the occasional hickup, of course) and as far as I can tell they make the ideas behind my tutorial work (for them).

The scores in their written homework appear stable on an acceptable level. As I described in my other posts my main didactic goal lies in the interaction between them during the tutorial session. This is why I mysels -- as teaching assistant -- try to move into the background as much as possible. Instead the students work through the solution of one student together, hopefully to find errors and clear misunderstandings and help those students who did not solve the problem fully understand their solution.

I must admit that at times I am not prepared well enough to prevent serious errors from happening since I often focus more on the presentation and interaction then the actu...

(more)

My last blog entry ended in too much of a rant; sorry about that. The reason was primarily that it had gotten too long and I had to stop. So this post is about the first few ideas I tried to implement and the problems that arose.

The primary problem that I have encountered among the students is lethargy.

So I asked myself what one wants to achieve in teaching a (set theory) course. The following are some basic observations.

1) Identify what kind of mathematical problems this field deals with

2) Identify the tools developed to approach these problems

3) Teach the students to analyze the new kinds of problems, identify their core and show how the tools of the lecture can solve them

4) Get the students to communicate their own approach, ideas and intuitions

The first two issues can be dealt with by good preparation on the part of the lecturer and TA.

The third and fourth...

(more)

Being a "Doktorand" ("PhD student", grad student) at the Freie Universität, Berlin, I volunteered to be the TA for a lecture on set theory this semester. This lead me to reflect a little on university level teaching in mathematics in Germany and my own position on teaching.

Now, during my time as a student the tutorials that I suffered through and then forced others to suffer through are basically done as follows. Every week the students of a lecture have to hand in the solutions to (usually around) 4 exercises. Those exercises would be marked by something like a GSI or TA (depending on the size of the class). Additionally there would be a 90 minute tutorial with a presentation of a standard solution for each exercise.

Depending on the GSI/TA, the marked exercise you were handed back would be more or less helpful in figuring out where you went wrong (or right, for that matter). Similarly, the tutorial might be done with more or less interact...

(more)

Hm, it seems I never published this blog properly... Well, here you are -- this was written in August.

Recently, the olympic games are the hottest topic on the news. I don't want to talk about the games as such, rather I want to start my blog by talking about a parallel I noticed yesterday while listening to the German public radio station Deutschlandfunk (www.dradio.de).

They aired a feature on financial support for German athletes. Apparantly, one major factor is the support offered by the German olympic sports union (DOSB). The feature criticized that the DOSB's support focuses too much on high level athletes and too little on low-level sports, i.e. local clubs, regional networks etc. Even without an understanding of the latter, special part of German culture I think the problem is easy to understand: The lack of support for everday, John Doe kind of sports clubs of all inclinations (think kayaking, gymnastics, archery, curling) can reduce the amount of...

(more)