### Studying original sources in mathematics education Day 5

The week in Oberwolfach is drawing to a close. Today was the last day of the academic programme, and there is just one breakfast left of the great food here. It will soon be the time to go home and try to keep up the motivation which has been building this week.

Today's first talk was by Hans Niels Jahnke. He talked about working with Bernoulli's lectures on the differentual calculus (1692) with 16/17-year olds. Halfway through the talk we were ourselves faced with trying to understand the mathematical ideas. Remember that an important idea was that of infinitely small quantities - and then even infinitely smaller quantities. This was the "foundation" for calculus for lots of years, even though a shaky one. (I wrote a Master thesis on part of the British side of this story.) It is always funny to try to understand the way these people were thinking on these things, and the students seem to have though so as well. I would certainly have tried to copy Jahnke in this if I had students in calculus.

The second talk was by Jan van Maanen. He was, with Jahnke and Fulvia Furinghetti, the organizers of this conference. His talk was titled "Original sources, projects, lessons and lectures". He has (as I knew before) a soft spot for original sources as in the real thing - he thinks the experience of actually handling a 1700th century book is an important part of the whole thing. That is of course good as far as it goes, but if studying original sources is to become something that the average pupil in Norway does, we will have to loosen the definition of "original sources" a bit (as van Maanen is fully aware of, of course).

van Maanen first gave a couple of examples of his own teaching through the years. Then he went on to talk about Iris van Gulik-Gulikers' PhD thesis, consisting of (among other things) teaching experiments on the history of similarity (similar triangles) and on non-Euclidean geometry. Both sounded fascinating, and I promptly mentioned that I would really want a copy of the thesis... The study was a fairly large one, being tested on about 800 pupils. I find it good to see that such solid, large-scale studies are now being done.

The rest of the day consisted of some round-table discussions and of some participants presenting things that they had not had time for earlier in the week. Among other things, I was reminded of a 1654 letter from Pascal to Fermat about a dice problem that I should really try to incorporate in my own teaching, and I was also forced to try to understand the algorithm for extracting cube roots. I think I got the main point of it in the end.

I think that I now should end these writings from Oberwolfach. The first four days are treated here:

Day 1

Day 2

Day 3

Day 4

Today's first talk was by Hans Niels Jahnke. He talked about working with Bernoulli's lectures on the differentual calculus (1692) with 16/17-year olds. Halfway through the talk we were ourselves faced with trying to understand the mathematical ideas. Remember that an important idea was that of infinitely small quantities - and then even infinitely smaller quantities. This was the "foundation" for calculus for lots of years, even though a shaky one. (I wrote a Master thesis on part of the British side of this story.) It is always funny to try to understand the way these people were thinking on these things, and the students seem to have though so as well. I would certainly have tried to copy Jahnke in this if I had students in calculus.

The second talk was by Jan van Maanen. He was, with Jahnke and Fulvia Furinghetti, the organizers of this conference. His talk was titled "Original sources, projects, lessons and lectures". He has (as I knew before) a soft spot for original sources as in the real thing - he thinks the experience of actually handling a 1700th century book is an important part of the whole thing. That is of course good as far as it goes, but if studying original sources is to become something that the average pupil in Norway does, we will have to loosen the definition of "original sources" a bit (as van Maanen is fully aware of, of course).

van Maanen first gave a couple of examples of his own teaching through the years. Then he went on to talk about Iris van Gulik-Gulikers' PhD thesis, consisting of (among other things) teaching experiments on the history of similarity (similar triangles) and on non-Euclidean geometry. Both sounded fascinating, and I promptly mentioned that I would really want a copy of the thesis... The study was a fairly large one, being tested on about 800 pupils. I find it good to see that such solid, large-scale studies are now being done.

The rest of the day consisted of some round-table discussions and of some participants presenting things that they had not had time for earlier in the week. Among other things, I was reminded of a 1654 letter from Pascal to Fermat about a dice problem that I should really try to incorporate in my own teaching, and I was also forced to try to understand the algorithm for extracting cube roots. I think I got the main point of it in the end.

I think that I now should end these writings from Oberwolfach. The first four days are treated here:

Day 1

Day 2

Day 3

Day 4

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