### Studying original sources in mathematics education Day 3

Day 3 was in one way a very short day, in another a very long one - depending on how you look at it. There were only two talks, but there were a long walk in addition - two hours the one way and one and a half hour back. It was pleasant and the weather was great, and now everybody is probably ready for a new full day of work.

The first talk was by Costas Tzanakis, who is also the chair of the HPM group. He had three examples. The first one showed an example of using ancient Greek mathematical texts in the teaching of Euclidean geometry in the Greek Lyceum. This showed many aspects of the work they had done, but for me the most interesting part was the discussion of "why do we have to prove this" which always comes up in the classroom. This was treated by looking at the Epikureans' criticism of Euclid, and seems a fertile starting point for discussions.

His second example was on the concept of (instantaneous) speed. Here, a quote from Newton showed with all necessary clarity how confused this concept was at the time. A discussion on Newton and his immediate followers (and the criticism of him) could be very interesting. Working on Zeno's paradox is another option.

His third example was on Hamilton's quaternions, and Karin Reich followed up with a talk on "The historical roots of vector calculus: J. W. Gibbs (1839-1902)". Sadly, vector calculus is not in the Norwegian curriculum for 6-16-year-olds, so there was little in these two talks that I can take directly into my classroom. However, the point that we should some of the time look at "original sources" not as the ones that does neccessarily contain the most "original" ideas, but as some "old", authentic sources where mathematical ideas are treated, seems worth making.

The days here in Oberwolfach is making me start thinking of what I should do when I get back. One simple idea is just to use history of mathematics in my teaching at about the same level as before (or a bit more), and at the same time "tracking" the students' idea of the "value" of history of mathematics through the year. That may be an interesting starting point for a discussion. (On the other hand, I already have an ongoing interview study, and I will also do two studies on Norwegian mathematics textbooks, one on the historical contents and the other on the "family concept" in them, so perhaps I have enough to do for the next year...)

The first talk was by Costas Tzanakis, who is also the chair of the HPM group. He had three examples. The first one showed an example of using ancient Greek mathematical texts in the teaching of Euclidean geometry in the Greek Lyceum. This showed many aspects of the work they had done, but for me the most interesting part was the discussion of "why do we have to prove this" which always comes up in the classroom. This was treated by looking at the Epikureans' criticism of Euclid, and seems a fertile starting point for discussions.

His second example was on the concept of (instantaneous) speed. Here, a quote from Newton showed with all necessary clarity how confused this concept was at the time. A discussion on Newton and his immediate followers (and the criticism of him) could be very interesting. Working on Zeno's paradox is another option.

His third example was on Hamilton's quaternions, and Karin Reich followed up with a talk on "The historical roots of vector calculus: J. W. Gibbs (1839-1902)". Sadly, vector calculus is not in the Norwegian curriculum for 6-16-year-olds, so there was little in these two talks that I can take directly into my classroom. However, the point that we should some of the time look at "original sources" not as the ones that does neccessarily contain the most "original" ideas, but as some "old", authentic sources where mathematical ideas are treated, seems worth making.

The days here in Oberwolfach is making me start thinking of what I should do when I get back. One simple idea is just to use history of mathematics in my teaching at about the same level as before (or a bit more), and at the same time "tracking" the students' idea of the "value" of history of mathematics through the year. That may be an interesting starting point for a discussion. (On the other hand, I already have an ongoing interview study, and I will also do two studies on Norwegian mathematics textbooks, one on the historical contents and the other on the "family concept" in them, so perhaps I have enough to do for the next year...)

## 1 Comments:

Quite good question

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