### HPM 2008 Day 1

The first day of the HPM 2008 was very good. It takes place in a very nice building in the very centre of Mexico City. The first talk was David Pengelley's "The use of original sources in the teaching of mathematics pupils at all levels". He discussed his dream: that pupils at all levels should learn all of their mathematics from primary sources. I surely do not share that dream, but I certainly think that primary sources has their place in the mathematics classrooms, just as pupils in Norway will never be allowed to go through 10 years of education without reading Ibsen (instead of just short summaries of his works). David also came up with the idea of having the HPM maintain a bibliography of the HPM field. That is certainly both an incredibly big task, but it would also be very useful. Just imagine an online bibliography where you could search for particular mathematicians, levels (in school), type of paper (empirical research, ideas from the classroom...), language. It could certainly not be the work of one person, but still some person must start and dedicate a significant amount of time to it...

The next plenary lecture was Rosa María Fanfár, who talked on "Matemática educativa. La convergencia de series infinitas". I must admit that this area of mathematics is one I do not usually work on, so that it was a bit of an overload on my brain to try to understand all of the mathematical examples based on the simultanous translation into English - it didn't help that I hadn't made sure to sit close enough to the screens to actually see them. Luckily, the paper is in the proceedings.

Then it was time for parallell sessions, and I was chairing one of them. The talks there was good: Maria Christina Araújo de Oliveira and Ruy Pietropaoplo talked about a magazine for uneducated school teachers in Brazil in the 1950s and 1960s. Ildikó Pelczer gave "A historical overview of analysis exams in Rumania", which showed patterns that I suspect would also be found in Norwegian teacher education exams of today. Hans-Stefan Siller discussed the emergence of Informatics as a subject in his talk "Informatics - A subject developing out of mathematics", while Flávia Soares discussed examinations for teachers in the 1800s in Brazil.

In the second parallell session, Funda Gonulates discussed a project which she has done, where she tried to measure whether working on history of mathematics did change the students' attitudes to history of mathematics and their knowledge of how to include it in teaching. However, she did not find significant increases. This does point to one of the problems of doing empirical research in the HPM field - the number of students involved needs to be high, and even if there were significant results, critical voices would certainly demand a control group. And given a control group, some would also question if the teaching given to the control group was "good enough". While this kind of research is certainly useful, for the individual teacher who wants to try to include history of mathematics, I think it is even more useful to get examples which can motivate him. "The proof is in the pudding": if the teacher thinks that the students are benefitting from the history, he will keep including it. On the other hand, no teacher will include anything based only on research papers telling him that something works for some faraway students.

Bjørn Smestad (who - again - happens to be me) talked about an interview study he has done trying to find out things about teachers' conceptions on history of mathematics. This talk went much better than the talk in Monterrey - maybe because it was much better prepared. There were interesting questions afterwards as well.

Robert Peard gave interesting ideas of courses he has had for teacher students in which he did not try to teach them the "basics" which they had failed to learn through 12 years of schooling, but instead focused on a few examples in which mathematics is important for understanding the world around us - for instance the calendar.

Beverly M. Reed talked about "The effects of studying the history of the concept of function on student understanding of the concept". Her theoretical basis was APOS theory, based on Piaget's theories. Her approach was qualitative, and she had promising conclusions, although I guess critics would still argue that her results could also have been obtained without history of mathematics.

That concluded the formal part of day 1. A very good day indeed. And now I'm free to do "whatever I want" for the rest of my stay in Mexico, as my talks are finished...

The next plenary lecture was Rosa María Fanfár, who talked on "Matemática educativa. La convergencia de series infinitas". I must admit that this area of mathematics is one I do not usually work on, so that it was a bit of an overload on my brain to try to understand all of the mathematical examples based on the simultanous translation into English - it didn't help that I hadn't made sure to sit close enough to the screens to actually see them. Luckily, the paper is in the proceedings.

Then it was time for parallell sessions, and I was chairing one of them. The talks there was good: Maria Christina Araújo de Oliveira and Ruy Pietropaoplo talked about a magazine for uneducated school teachers in Brazil in the 1950s and 1960s. Ildikó Pelczer gave "A historical overview of analysis exams in Rumania", which showed patterns that I suspect would also be found in Norwegian teacher education exams of today. Hans-Stefan Siller discussed the emergence of Informatics as a subject in his talk "Informatics - A subject developing out of mathematics", while Flávia Soares discussed examinations for teachers in the 1800s in Brazil.

In the second parallell session, Funda Gonulates discussed a project which she has done, where she tried to measure whether working on history of mathematics did change the students' attitudes to history of mathematics and their knowledge of how to include it in teaching. However, she did not find significant increases. This does point to one of the problems of doing empirical research in the HPM field - the number of students involved needs to be high, and even if there were significant results, critical voices would certainly demand a control group. And given a control group, some would also question if the teaching given to the control group was "good enough". While this kind of research is certainly useful, for the individual teacher who wants to try to include history of mathematics, I think it is even more useful to get examples which can motivate him. "The proof is in the pudding": if the teacher thinks that the students are benefitting from the history, he will keep including it. On the other hand, no teacher will include anything based only on research papers telling him that something works for some faraway students.

Bjørn Smestad (who - again - happens to be me) talked about an interview study he has done trying to find out things about teachers' conceptions on history of mathematics. This talk went much better than the talk in Monterrey - maybe because it was much better prepared. There were interesting questions afterwards as well.

Robert Peard gave interesting ideas of courses he has had for teacher students in which he did not try to teach them the "basics" which they had failed to learn through 12 years of schooling, but instead focused on a few examples in which mathematics is important for understanding the world around us - for instance the calendar.

Beverly M. Reed talked about "The effects of studying the history of the concept of function on student understanding of the concept". Her theoretical basis was APOS theory, based on Piaget's theories. Her approach was qualitative, and she had promising conclusions, although I guess critics would still argue that her results could also have been obtained without history of mathematics.

That concluded the formal part of day 1. A very good day indeed. And now I'm free to do "whatever I want" for the rest of my stay in Mexico, as my talks are finished...

Labels: conference, history, HPM, mathematics

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