ESU7 Day 3

The first of Wednesday's talks was Cécile de Hosson's on "Promoting interdisciplinary teaching through the use of elements of Greek and Chinese early cosmologies." Her talk discussed the connections between physics and mathematics, and how the history of physics could be used as part of physics education. She gave examples, for instance Eratosthenes' calculation of the circumference of the Earth, which is of course a good example that should be part of mathematics education. She noted that students had trouble accepting that the sun's rays are "nearly parallell" - mathematically, "nearly parallell" is quite different from "parallell"! This is of course a central part of the tension between mathematics and physics. The talk was one of several at the conference highlighting not just that the use of history will have to be different for different target groups, but also how it will have to be different.

Then there was the first panel; "Computational Technology: Historical and philosophical approaches to technics and technology in mathematics and mathematics education". I'm always very sceptical of panels, as they tend to disintegrate into four or five small talks that does not neccessarily connect very much to the professed theme of the panel and very rarely touch upon what the others have said. This, however, was beautifully organized, in that each panelist gave just a short talk (5 minutes?), followed by an answer by one of the other panelists before going on to the next short talk. All panelists were in active dialogue with the others and the theme of the panel.

Mario Sánchez Aguilar discussed how computer technology changes the way pupils and teachers work on mathematics. One way is through the use of non-traditional sources for help in working on the mathematics - nowadays, students can get so much help in different websites, for instance. For teachers, there is the possibility to enrich the instructional techniques, bringing videos into the classroom (YouTube) and by bringing the teaching into pupils' homes.

In response to this, Per Jönsson asked what much of mathematics needs to be internalized and how much can be outside you for you to know mathematics. He also asked if the teacher is needed at all in this system.

Per then went on to discuss "what is mathematics?" Computing have changed problem solving dramatically (in the research on mathematics). Mathematics should now be learned with more focus on problem solving and computing.

Mikkel Willum Johansen reacted by pointing out that the role computers play is as a tool for mathematicians.

Mirko Maracci: computers are used for educational purposes. Two ways of looking at it is that they mediate learning processes or that they embody knowledge. When they're seen as mediating, it can be either that the artifact may permit the transformation of the object and/or permit the subject's concious-raising of the object.

Morten reaction to Mirko: important to be critical - tool also changes and transforms mathematics. When a tool is used, it can change things in different ways. Important to study of the whole ecosystem.

Mikkel pointed put that mathematics is impossible without the right tools - it is a tool-driven practice. Tools have consequences, however. So even though computers are "just another tool", they have an impact on the content of mathematics. Computer-assisted proofs, mass cooperation and experimental mathematics are examples of how mathematics is changing.

Morten said that in teaching, computers challenge the existing mathematics education practices, for instance in something so basic as "what is a good task?" Mathematics education is squeezed between research mathematics, school traditions, the applications in specialized domains and children's everyday domains. New tools will change all four of these domains.

Evelyne raised the obvious question of gender (in this all-male panel). What are the gender aspects of the influences computers have? There was quite a bit of discussion on this, although mostly anecdotal in nature.

Another comment from the audience: we have to decide what we are going to teach - we cannot go on teaching what we have done. And we have been in this situation before through history.

It was nice to have a panel about computers in mathematics education without focusing all the time on the problems they bring by stealing students' attention. Of course Facebook was mentioned, but I was on Facebook at the time, so I didn't hear the complaints so well... (I had just blogged about yesterday's experiences at the conference, and noticed that a Swedish colleague who took part in HPM in Daejon but couldn't be here, thanked me for these updates...)

After this panel, the academic program was over, but the day had just begun. We had a bus ride to Nyhavn, a boat trip on the canals (with lunch), a guided tour of Christiania, a couple of hours on our own and finally a dinner which transformed into a party and lasted into the small hours of the night. There were no presentations during all that time, but I had more academic conversations than for the rest of the conference combined. I had interesting chats with people from France, Norway, China, Italy, Sweden, Denmark, Germany and probably many others that I have forgotten by now. The programme is usually too tight to have long conversations in the breaks, so this day was welcome also for giving us time to discuss. And of course we managed to squeeze in some non-academic discussions as well...