Thursday, July 31, 2008

ICME Day 3

The third day of the ICME started with José Antonio de la Peña’s talk on “Current trends in mathematics”. This seems as an almost impossible topic to cover in one hour, but la Peña had chosen to focus on just a few highlights, and to take a “light” approach. I think this was wise. He also pointed to the Mathematics in the movies site, which features video clips from movies. I’ll check it out…

Next, I heard an excellent talk by Jeremy Kilpatrick titled “A Higher Standpoint”. The point of departure was Felix Klein’s “Elementary Mathematics from a Higher Standpoint”, published in the first decade of the 20th century. Klein’s object was to “bring to the attention of secondary school teachers the significance for their professional work of their academic studies”. He pointed to a “double discontinuity”, whereas the student who goes on from school to higher education, feels that the mathematics is completely different, and at the same time the teacher who has finished his higher education and goes back to school to teach, does not see the connection either. Klein wanted to remedy this by updating the school curriculum and by revising the university instruction to take into account the needs of the school teacher. The talk went on to discuss the books in more detail, and also discussed Pólya and Freudenthal in the connection with Klein’s ideas.

Kilpatrick’s talk made me want to read Klein’s textbooks, which was certainly one of his objects. It also gave lots of food for thought.

At about this time in the conference, there was distributed a leaflet giving information on the 12th ICME, taking place in Seoul July 8th-15th, 2012. I’m already looking forward to it! The website is:

The next thing I attended was the TSG23. Louis Charbonneau talked about “Astronomical and mathematical instruments as pedagogical tools”, putting emphasis on the emotional aspects of being able to touch instruments that have been used to measure heaven and Earth… It was a very interesting and enthusiastic talk. Snezana Lawrence gave the answer to my concluding question in Saturday’s talk (which means I have to update my talk a little…) My question is what we can do to make teachers able to include history of mathematics in their teaching. Lawrence has used history of mathematics as the focus of a teacher development program that seemed very good. I really need to get to know more about this project (and I guess I can find out more on her website,

Liliana Milericich read the paper “The teaching and learning of integral calculus from a historical perspective”, which pointed to some pitfalls in the teaching of integral calculus. As this is not part of what I teach, I didn’t note down particular things that I need to remember from that talk.

Later in the day, I attended the SEG (Sharing Experiences Group) on interactive whiteboards (IWBs). This was incredibly interesting to me, as I’m just starting out in this area, and having written a paper for a conference just before leaving for Mexico. There were lots of interesting thoughts there, and seeing the webpage of these people was also very interesting. Moreover, I was pointed to an interesting conference in Cambridge in June 2009, which I will consider going to.

That ended day 3 of the conference. As day 4 was an excursion day, I will go on with this blog with day 5 later…

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ICME Day 2 (part 2)

The first ASG meeting of the HPM group consisted of two interesting talks. Gert Schubring’s talk was titled “Researching into the History of Mathematics Education – an HPM perspective”. He discussed how teachers were educated in different states from the middle of the 18th century. (Before that, states took little interest in this.) The talk was packed with information, and I can obviously not repeat it here. However, it was interesting to hear how there was a huge effort after the French revolution to teach teacher educators, while in France in 1763, it was argued that it was needless to educate teachers, as good textbooks would make sure that the teachers could educate themselves.

Fulvia Furinghetti talked on “The emergence of women in the international arena of mathematics education – Just so stories”. Although it was a talk about the women who has played a role, the main picture is of course that there have been very few women who has been prominent in the field until recently. Lately, that has luckily changed.

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Monday, July 28, 2008

ICME Day 2 (part 1)

Today's plenary speaker was Celia Hoyles, and the topic was "Technology and mathematics education: Transforming the mathematical practices of learners and teachers through digital technology". To me, it was a great talk, as it functioned as an introduction into a field in which I will work more in the coming years. She described six areas in which ICT is transforming mathematics education:

  • dynamic and visual tools to explore in shared space
  • tools to outsource processing power
  • new representational infrastructures
  • connections between school and learner's culture
  • connectivity
  • intelligent support for the teacher.

She had examples in all of these areas, and her talk certainly made me eager to get hold of the forthcoming ICMI Study on these topics.

She also referred to the National Centre for Excellence in the Teaching of Mathematics website, and in particular the Mathemapedia - a Wikipedia for mathematics, apparently. I haven't had the time to look at it yet, but should certainly check how this site compares to my plans for a teacher education wiki locally in Norway. Maybe there will be common areas of interest.

The next lecturer was Anna Sfard. Her talk was titled "Learning mathematics as developing a discourse". Her talk was - unsurprisingly - well attended, so the room was far too small, as was her time. Anyway, I found it most interesting. She discussed what she terms as a transition from the metaphor of "aquisition" to a metaphor of "participation" as far as learning is concerned - moving from a Piagetian world to a Vygotskyan. This has far-reaching consequences. She looks at mathematics as a discourse, and a number as a "discursive construct". This has far-reaching implications when it comes to interpreting children's approach to mathematical problems.

The third item on my agenda today was the TSG23 - the topic study group on history of mathematics in education (not to be confused with the topic study group on the history of mathematics education, of course). Due to some technical difficulties, one of the talks were postponed to tomorrow's session, and only Costas Tzanakis had his talk. This was a very interesting talk on how history of mathematics may throw light on the problems pupils face when trying to learn the variance concept. One particularly striking point (to me) was how educators have tried to make the topic "soft" by including examples from social sciences instead of from physics and geometry, but have ended up making it harder. This is because the terms mean - and even variance - have clear, concrete interpretations in certain examples from physics and geometry, and because they offer the possibility of experiments.

Now, I'm having lunch break, but will go to the ASG meeting for the HPM group later this evening. But it has already been a very interesting day. (And I've also had the time to look at my own talk, which will be on Saturday. I think it will be ok.)

(As mentioned before, these posts are delayed by 20 days.)

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ICME Day 1

The ICME 11 has started today - the main conference for mathematics educators worldwide. As always, the first day is mainly spent on formalities and on setting the stage for things to come.

The opening consisted of a whole series of speeches - inevitable, I guess - and the distribution of the Felix Klein Awards and the Hans Freudenthal Awards for 2005 and 2007. This was a nice thing to see - both that everybody took the time to listen to praise for the lifetime achievements of some of our most wonderful colleagues, and that the prize winners showed that the prizes were actually quite important to them as a recognition of a lot of heavy work.

The winners were:
Felix Klein Award 2005: Ubitaran d'Ambrosio
Hans Freudenthal Award 2005: Paul Cobb
Felix Klein Award 2007: Jeremy Kilpatrick
Hans Freudenthal 2007: Anna Sfard

Although all four are well-known names, personally, I know the work of Ubi best, and found it particularly touching to see him thanking his wife for all her patience for 50 years...

The first two plenary lectures were on what has happened for the previous ten years and what should happen in the future. The venue for the plenary parts of the program is not very good - there is too much background noise, and it's difficult to see the screens from many positions. The solutions in the previous two ICMEs (which involved using actual buildings instead of a "tent") worked better. However, I thought that the first lecture (by Artigue and Kilpatrick) was quite inspiring and interesting. They tried to summarized the main trends in mathematics education over the previous ten years. Some keywords: more systemic approaches, a look at constraints, semiotic perspectives.

The panel on what we need to know, which was supposed to summarize the answers of educators around the globe, however, did not manage to inspire me. Well, Paul Kobb's interpretations of the (mainly US) answers from North America, were meaningful. The other three also discussed important questions, but in a way that made it look less like a panel than separate lectures. The format of plenary activities for thousands of listeners is a difficult one, indeed.

The highlight of the day was undoubtedly the workshop by one of my favorite colleagues, Peter Ransom. He and a colleague had a workshop on using sundials in the classroom. Peter is so enthusiastic that it's hard not to start loving sundials, and the activities were fun as well. I should try to find a way to include sundials in my teaching in Oslo...

That was the first day already. In between were coffee, lunches etcetera, of course. And lots of meetings with colleagues who I haven't met for 1, 4 or even 8 years. A nice start to the conference.

(As mentioned before, these posts are written during the conference, but posted afterwards.)

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Thursday, July 24, 2008

Mexico 2008 – and lovely randomness

This summer, I will be staying in Mexico for 20 days. I will be attending both the ICME (International conference on mathematics education) in Monterrey, and the HPM (the meeting of The International Study Group on the Relations between History and Pedagogy of Mathematics) in Mexico City.

The trip here went well. However, I met two different approaches to randomness which were interesting. In Chicago, I was pulled aside for a routine random check of my luggage. Of course, I knew that nothing was wrong, so my only thought was “Why did they pick me?” I was stressed, since I didn’t have much time, and didn’t know exactly how much time all the procedures in transit in Chicago would take.

In Monterrey, much the same happened to my colleague – she was picked randomly to be checked. How? It was simple: every passenger picking the green line (Nothing to declare) had to press a big button. Then someone (probably a computer) decided if you should get a green or a red light – if you got a red light, you were chosen for random check.

The difference is not so large, but for the passenger, it does feel better, and the people working there will be able to defend themselves against the charges of racial profiling and all such charges that are usually impossible to defend yourself against. (However, they should still be able to check people who they found particularly suspicious…)

Then we were to take a taxi to town. We went to a counter and was presented by a screen. The woman behind the counter told us that we could pick any taxi company we wanted – or press the big “random” button. We chose to press “random”, paid our taxi ride and went out to find the company. An altogether better solution than to have every single taxi company having their own counter in the arrivals area – and the alternative would have been that we had walked out of the airport and chosen a taxi at random outside.

So already on the first day: two nice ways to use randomness to solve problems.

(Written 4th of June 2008.)

(The blog posts from Mexico will be posted with a delay of 20 days. This is simply because it is not considered advisable to advertise to the world that you are staying away from your apartment for weeks…)

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