### Studying original sources in mathematics education Day 2

Another interesting day at the mini-workshop at the MFO. The day started with a talk by Peter Rasfeld, where he told us about a project he has done on the problem of points (the famous problem worked on by lots of mathematicians, for instance Luca Pacioli, Girolamo Cardano, Niccolo Tartaglia, Blaise Pascal and Pierre de Fermat). He described a four-week project with his pupils aged 16, where the pupils worked on original sources much of the time - after initially trying to solve the problem themselves.

I am very happy to be able to hear this kind of presentations, as I have on previous conferences and meetings of this kind had an impression that most people have more interest in things for older students. For me, who is teaching teachers-to-be for 6-16-year-olds, it is important that the mathematics is at a reasonably low level...

The second talk was my talk. I would have liked to be able to say that it was absolutely brilliant, but I am in no position to know that. However, I think I managed to get the point across that including history of mathematics in the average classroom takes a lot more than just putting it into the curriculum. I used a study on the TIMSS 1999 Video Study material, a study on the Norwegian textbooks in elementary and secondary school, and a study that I am doing at the moment where I interview teachers about their attitudes to history of mathematics.

The third talk was by Adriano Dematte (with a sign over the last "e" that I am unable to conjure up on this computer). He talked on a new collection of materials for secondary school students (12 to 18) that is coming out in Italy in a few months. I'm looking forward to getting hold of a copy and considering what I could do to get this kind of material available in Norwegian for Norwegian teachers. Together with the Historical Modules from the US and with a book I just heard of today, this new book certainly will give me some ideas (although things will certainly have to be adjusted to fit the (not too impressive) level of the Norwegian mathematical curriculum.

The fourth talk (after lunch) was by Caroline Bardini and Luis Radford, with the title "Unknown, Variables and Parameters". I think I have tended to think that the difference between these should not be stressed too much to the students, but I believe that I should think it over more thoroughly. It is obvious from the discussion in the lecture hall and outside that there are important questions to be answered here. The video segments from classrooms were also interesting.

The fifth talk was Evelyn Barbin's talk titled "The different readings of original sources: an experience in pre-service teaching". The talk included an amazing number of ideas for historical sources that can be used in a mathematics course - her own present experience was from a course for pre-service teachers who were aiming for primary school. (French primary schools, that is, which is at another level altogether than Norwegian ones.) Maybe the most important part of her lecture, however (which was exemplified throughout the rest of the lecture), was an attempt to cathegorize the different ways students can engage with a historical source - from "interpret in our mathematical language" at the one extreme to "interpret in its own historical context" at the other.

My main decisions coming out of this day were these:

- I will put more effort into making available for Norwegian teachers materials on history of mathematics (for use in the classroom) in Norwegian.

- I will look again at my own teaching to think of how history of mathematics could enhance it more than presently, and think of the different ways students could engage with the materials.

In addition to this, there has been wonderful weather, good food, a nice walk and lots of friendly people. I'm looking forward to the next three days. And I'm glad I've had my presentation, so I don't have to think of that any more...

I am very happy to be able to hear this kind of presentations, as I have on previous conferences and meetings of this kind had an impression that most people have more interest in things for older students. For me, who is teaching teachers-to-be for 6-16-year-olds, it is important that the mathematics is at a reasonably low level...

The second talk was my talk. I would have liked to be able to say that it was absolutely brilliant, but I am in no position to know that. However, I think I managed to get the point across that including history of mathematics in the average classroom takes a lot more than just putting it into the curriculum. I used a study on the TIMSS 1999 Video Study material, a study on the Norwegian textbooks in elementary and secondary school, and a study that I am doing at the moment where I interview teachers about their attitudes to history of mathematics.

The third talk was by Adriano Dematte (with a sign over the last "e" that I am unable to conjure up on this computer). He talked on a new collection of materials for secondary school students (12 to 18) that is coming out in Italy in a few months. I'm looking forward to getting hold of a copy and considering what I could do to get this kind of material available in Norwegian for Norwegian teachers. Together with the Historical Modules from the US and with a book I just heard of today, this new book certainly will give me some ideas (although things will certainly have to be adjusted to fit the (not too impressive) level of the Norwegian mathematical curriculum.

The fourth talk (after lunch) was by Caroline Bardini and Luis Radford, with the title "Unknown, Variables and Parameters". I think I have tended to think that the difference between these should not be stressed too much to the students, but I believe that I should think it over more thoroughly. It is obvious from the discussion in the lecture hall and outside that there are important questions to be answered here. The video segments from classrooms were also interesting.

The fifth talk was Evelyn Barbin's talk titled "The different readings of original sources: an experience in pre-service teaching". The talk included an amazing number of ideas for historical sources that can be used in a mathematics course - her own present experience was from a course for pre-service teachers who were aiming for primary school. (French primary schools, that is, which is at another level altogether than Norwegian ones.) Maybe the most important part of her lecture, however (which was exemplified throughout the rest of the lecture), was an attempt to cathegorize the different ways students can engage with a historical source - from "interpret in our mathematical language" at the one extreme to "interpret in its own historical context" at the other.

My main decisions coming out of this day were these:

- I will put more effort into making available for Norwegian teachers materials on history of mathematics (for use in the classroom) in Norwegian.

- I will look again at my own teaching to think of how history of mathematics could enhance it more than presently, and think of the different ways students could engage with the materials.

In addition to this, there has been wonderful weather, good food, a nice walk and lots of friendly people. I'm looking forward to the next three days. And I'm glad I've had my presentation, so I don't have to think of that any more...

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