For the very beginning I have to say that this was one of the first courses on didactical mathematics that I have ever taken part, or any other pedagogical courses as a matter of fact, so I'm having some serious trouble comparing this course to anything. Which, I think, would be beneficial for both myself and whoever else is interested in reading this report.

First thing that comes to my mind about the course is of course the inspiring way that professor Dubinsky was presenting his stuff. To be honest, from the papers about the subject that I read beforehand, I could not get a clear picture of what was going on in this thing. I do know that the reason for it was purely my own lack of understanding professional text about pedagogy. Anyway, I believe I got the picture during this course.

The idea of learning mostly in groups was definitely a new one to me, at least in mathematics. But it didn't sound too far out, in fact, it made sense in many ways. Thinking about the way mathematics is being taught in my university (it's a pity I do not have any knowledge of other universities), and the way that I think that the usual mathematics students are, that means quiet and not very social, I truly believe that this would make learning much easier in many ways. Not only would it create an opportunity or even a must to make social contacts, which in my opinion increases your activeness otherwise too, but it would make the situation more secure for the department of mathematics of maybe not losing so many students. Because, in constant group work it doesn't feel like you're left alone, unless of course the characters of the group don't mix, and I think that one quite big reason for quitting mathematical studies in the university is the feeling that nobody can help you with the studies, or the inability of asking for help from people you don't know.

One thing that must be said about the course, and to which I think most of the students there would agree on, is the fact that even though the ISETL language was comparatively easy to use for somebody who has been studying mathematics for several years, and even easier for those who have some experience in computer languages, the programming part was really a pain in the butt. For us participants that already knew or at least should have known the mathematical part of it, the method seemed maybe a little bit of a waste of time, especially when the course was taking all day and we were tired in the afternoon. But maybe for the student that haven't got the knowledge that we do, the method would make things clearer. Thins bring in mind the tables about the results of the courses that this method has been tried out with. At least to me the percentages and other scorings did not look very impressive, because the results, compared to the usual method, did not differ a great deal, mostly not even significantly. I have a feeling that this could be because of the fact that the method of teaching was so new to the students, that they couldn't benefit from it completely. It would be interesting to see a long-term research about this, for example, if the same students would get the same sort of teaching throughout their studies, what would the result be?

One truly interesting part of the whole thing was Asuman's story about the practise course she had taught using the videoconferencing equipment or something similar, I don't remember the correct name for it. The use of the e-mail mailing list with the teacher's role as its moderator was especially interesting, and it seemed to work out quite well.

Even though up to this I haven't really critisized this course or this method of teaching much, I'm not all the way buying this just like that. The question that has been puzzling me after this course is, is this just another way of trying to keep the students happy by letting them play nice games? By this I mean the programming part or other stuff done with the computer. In school everybody at least in my class were always more relaxed and more exited, when in maths or any other subject we had something to do with computers or otherwise something that was not just the usual sort of teaching. And on this course, too, it felt really fresh to try out something new to yourself. But if the use of programming in teaching becomes routine, will the students be able to stay as exited about it and stay more willing to learn as with the classic methods? Will they remember things better like this, will they maybe be able to adapt themselves quicker to problems that are new to them?

In my opinion also it would have been more fruitful, if we had thought more carefully about what the exercises really teach to the students. Now it was just like finding a list of words that first come to your mind when you see the exercise sheets, and this left me somewhat cold, so to say. Of course we were in a hurry, but maybe we wouldn't have needed so many exercises with basically similar content.

All in all, I'm very glad to have participated in this course because of the new ideas it gave me about teaching and of course it is always refreshing to meet mathematics teachers from foreign countries, as well. Which, I hope, will happen more often in our university.