### HPM 2008 Day 2

The second day of HPM 2008 started with Evelyne Barbin (the new chair of HPM) and a talk titled “Dialogism in mathematical writing: historical, philosophical and pedagogical issues”. She gave a quick introduction to some aspects of Bakhtine’s work, and in particular the three “bullet points” active responsive attitude of the listener, addressivity and speech genres. I see that Bakhtine can indeed be interesting in the context of HPM, and need to make sure to learn more about him.

I skipped the next plenary lecture (as I had to check my email) but then went to Edel M. Reilly’s talk “Mathematics Apart: Examining the History of Subject Isolation and Its Implications for Mathematics Education”. According to her abstract (and title) this should be a historical talk, but her actual talk focussed on the present and future. I will have to read the paper to see if the historical element is there… Anyway, it was interesting to hear to which degree the US school system has chosen to compartmentalize mathematics (in most of the rest of the world, students take “mathematics courses”, not “algebra” and “geometry” without connections between them…)

Mala Saraswathy Nataraj talked about “Using history of mathematics to develop student understanding of number system structure. She described ways in working with pupils to get them aquainted with our numeral system through work with “toothpicks”. It also had a very interesting idea: that the work on writing large numbers (using powers of 10) is a useful prerequisite for later understanding the notation in algebra. It seems very reasonable, I just hadn’t thought about it like that before.

Chorlay Renaud and Anne Michel-Pajus presented the paper “The multiplicity of viewpoints in elementary function theory: historical and didactical perspectives.” This was quite fascinating. One major point was that functions could be presented in “two different worlds”: the world of quantity and the world of sets. Each of these worlds have semiotic and conceptual coherence – however, mixing them may confuse the students. In France, it is obviously the “world of sets” which is the “correct” one – functions are seen as a relation between sets. In Norway, I guess we cling to the “world of quantity” almost until university, although some definitions or ways of formulating things from “the world of sets” may creep in here and there. It would have been interesting to look at this…

Staffan Rodhe talked about “Emanuel Swedenborg’s work on differential calculus” with a few more details than last time I heard his talk (four years ago).

In the lunch break, there was a meeting of the “advisory board” of HPM – there’s never any rest…

After lunch, George W. Heine talked about “Euler’s Contributions to Mathematical Cartography”. The first part of the talk was particularly fascinating, in which Heine discussed Nicolas Delisle’s attempts (?) to make maps of Sibiria. Although given huge resources, Delisle never succeeded, and he stubbornly denied seeking help from Euler – which may be a sign that he was actually a spy in Moscow, just trying to keep the resources flowing in while at the same time shipping maps out of the country (which he apparently did).

Then today’s highlight: Peter Ransom’s act as a seafarer in the workshop “Yo Ho Ho-ratio: some mathematics of Trafalgar (How Lord Nelson inspired curriculum development in mathematics)”. Peter’s workshops are always good, so obviously we had a good time – while making things, doing calculations, learning about history… And not only had Peter put all the resources onto a CD which we got for free – he had also made pencils with the name of the workshop on it… That’s what I call dedication…

In the evening there was a very nice private social gathering, and then – on Wednesday – we had a “free day”, on which I joined many of the others to Teotihuacán – but I should write about that in another blog…

I skipped the next plenary lecture (as I had to check my email) but then went to Edel M. Reilly’s talk “Mathematics Apart: Examining the History of Subject Isolation and Its Implications for Mathematics Education”. According to her abstract (and title) this should be a historical talk, but her actual talk focussed on the present and future. I will have to read the paper to see if the historical element is there… Anyway, it was interesting to hear to which degree the US school system has chosen to compartmentalize mathematics (in most of the rest of the world, students take “mathematics courses”, not “algebra” and “geometry” without connections between them…)

Mala Saraswathy Nataraj talked about “Using history of mathematics to develop student understanding of number system structure. She described ways in working with pupils to get them aquainted with our numeral system through work with “toothpicks”. It also had a very interesting idea: that the work on writing large numbers (using powers of 10) is a useful prerequisite for later understanding the notation in algebra. It seems very reasonable, I just hadn’t thought about it like that before.

Chorlay Renaud and Anne Michel-Pajus presented the paper “The multiplicity of viewpoints in elementary function theory: historical and didactical perspectives.” This was quite fascinating. One major point was that functions could be presented in “two different worlds”: the world of quantity and the world of sets. Each of these worlds have semiotic and conceptual coherence – however, mixing them may confuse the students. In France, it is obviously the “world of sets” which is the “correct” one – functions are seen as a relation between sets. In Norway, I guess we cling to the “world of quantity” almost until university, although some definitions or ways of formulating things from “the world of sets” may creep in here and there. It would have been interesting to look at this…

Staffan Rodhe talked about “Emanuel Swedenborg’s work on differential calculus” with a few more details than last time I heard his talk (four years ago).

In the lunch break, there was a meeting of the “advisory board” of HPM – there’s never any rest…

After lunch, George W. Heine talked about “Euler’s Contributions to Mathematical Cartography”. The first part of the talk was particularly fascinating, in which Heine discussed Nicolas Delisle’s attempts (?) to make maps of Sibiria. Although given huge resources, Delisle never succeeded, and he stubbornly denied seeking help from Euler – which may be a sign that he was actually a spy in Moscow, just trying to keep the resources flowing in while at the same time shipping maps out of the country (which he apparently did).

Then today’s highlight: Peter Ransom’s act as a seafarer in the workshop “Yo Ho Ho-ratio: some mathematics of Trafalgar (How Lord Nelson inspired curriculum development in mathematics)”. Peter’s workshops are always good, so obviously we had a good time – while making things, doing calculations, learning about history… And not only had Peter put all the resources onto a CD which we got for free – he had also made pencils with the name of the workshop on it… That’s what I call dedication…

In the evening there was a very nice private social gathering, and then – on Wednesday – we had a “free day”, on which I joined many of the others to Teotihuacán – but I should write about that in another blog…

Labels: conference, history, HPM, mathematics

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