ESU6 Day 5

The last day of the ESU was also the shortest. I skipped the plenary lecture to secure more time for packing, checking out of the hotel and so on. The lecture I missed was Fulvia Furinghetti and Livia Giacardini’s “From Rome to Rome: Events, People, and Numbers during ICMI’s First Century”.

I did, however, take part in Snezana Lawrence’s workshop “Digitising the past mathematics by the future mathematicians”. It concerned how working on earlier textbooks may be interesting for today’s schoolkids. For instance, they may be interested to see that earlier textbooks (based on Euclid), actually gave definitions in a way that are almost gone now. Nowadays, textbooks give explanations with pictures and words, perhaps making it less clear what is the core definition and what is examples or illustrations. The workshop did not, however, give a very clear idea of what Snezana thinks that the role of “digitising” should be in this. While I do see that students could learn from scanning and transcribing short portions of text and then making it publicly available, I’m not convinced that it is worth the time. (And the other members of my group in this workshop was rather convinced it was not worth the time.) However, the work we did in the workshop was a good illustration of some of the points Michael Glaubitz made in his plenary lecture.



That marks the end of the conference. It was hard work. I leave the conference inspired and with a wish to continue working on history of mathematics. However, I also think that I was a bit too busy at this conference. In the end, I got to choose five of the workshops, but none of the oral presentations (I was always either speaking or being a chair). Having presentations on three of the days (one oral presentation, one workshop and one panel) is a bit too much also, both in the weeks ahead of the conference and in the conference itself.

I look forward to the HPM Meeting in Korea in 2012 and the ESU7 in Spain (maybe) in 2014.

ESU6 Day 4

Michael Glaubitz’ plenary lecture, which marked the start of the fourth day of the conference, was titled “The Use of Original Sources in the Classroom – Empirical Research Findings”. He set up a teaching experiment using original sources in two different ways: a genetic approach and a hermeneutic approach. Then he also had a “conventional” approach.

While a genetic approach is usually considered a means of introducing a topic (the pupils will meet the topic in the same order as it was developed in history), a hermeneutic approach (as suggested by Jahnke) concerns reading original sources when already having pre-knowledge about the topic concerned.





Glaubitz set up three teaching sequences of equal length which were then taught in different groups of students by different teachers. The genetic approach failed miserably, while the hermeneutic approach did significantly better than the conventional approach. Of course, such an experiment can never be a proof of the non-feasibility of an idea, so the results for the genetic approach are not the most interesting ones. However, it is a bit impressive that teachers used to the conventional approach can be guided into teaching successfully with original sources (using the hermeneutic approach) in such a short time. (Although we may of course, as always, have the effect of trying something new.)

To me, this is very promising results. The genetic approach seems too ambitious to me – in a way, you need to take into account all the history of mathematics at the same time, which puts enormous demands on the teachers’ knowledge. The hermeneutic approach delves into one particular point of time and one particular context. While that is certainly also demanding, it seems more like something many teachers could be willing to try – given the right materials.

The second plenary lecture was Raffaele Pisano’s “Which is the cultural and interdisciplinary role played by physical and mathematical sciences? Epistemological Reflections”. This talk concerned the connections between physics and mathematics. To be perfectly honest, I have never had a physics course in my life, and therefore found most of the lecture too advanced for me. (Which doesn’t say much, of course.)



Then there was another panel. The title was “The role of the history and epistemology of mathematics in pre-service teachers training”. The panelists were Evelyne Barbin, Fulvia Furinghetti, Snezana Lawrence and myself. I did not take notes during this panel (except notes on what I was going to say), so I’m not the right person to try to summarize it. However, for me personally, the main outcome of the panel itself and the preparations for it was a realization that it is time that I do something a bit more substantial when it comes to making history of mathematics available to teachers. It’s been ten years since my first HPM conference (in which I complained about the quality of Norwegian textbooks), six years since my second HPM conference (and first ESU) (in which I complained about the quality and quantity of history of mathematics in the TIMSS Video Study materials), three years since my second ESU (in which I did not complain actually – but showed examples of history of mathematics I’ve used in teacher training) and two years since my third HPM (in which I discussed teachers’ conceptions of history of mathematics). Isn’t it time for me to come to a HPM or ESU with a textbook or webpage and discuss why I have created this wonderful book/webpage in this way? Maybe in 2014?

I could mention that my part of the panel discussion was taking Deborah Ball’s model of teacher competence in mathematics as a starting point. My own preparations on this – as well as a question in the discussion – made me realize that I have to revisit Ball’s articles to see what her (and her colleagues’) conception of “mathematics” is.

After lunch, I attended Kristín Bjarnadóttir’s workshop “Arithmetic textbooks in 18th century Icelandic manuscripts”. I think I would have found such a workshop painstakingly boring ten years ago, but I’ve grown to appreciate the study of textbooks as a valuable part of research on history of mathematics. Moreover, the kind of “detective work” that Kristín has been doing here and which she invited us to take part in in this workshop, is rather fascinating. Her object of study is an Icelandic manuscript, and she wants to find out as much as possible about which textbooks influenced it. The “detective work” consists partly in finding out which textbooks were known in Iceland at that time, and of comparing “her” text with these. From time to time, there are clear “hits”, when numerical examples are exactly the same in different textbooks – they must clearly have a common source.



In Norway, there has been published a book on the first Norwegian mathematics (arithmetic) textbook: Tyge Hanssøn’s “Arithmetica Danica” from 1645. While the author (Geir Botten) has done lots of work on this book, he has not done research on the influences of the textbook (as far as I know). It would surely be interesting to see the results of such a study at one point.

coffee break area

The evening program was again oral presentations. Again, I was chairing (or cheering). There were three talks: Oscar Abdounur talked about the University of Sao Paulo, and how the invitation of European scholars to the university influenced it. Andreas Christiansen (whose name was terribly mispronounced by the chair – it’s a surprise that Christiansen (not Christensen) managed to speak after such an insult) spoke about Bernt Michael Holmboe’s textbooks and in particular how the concept of irrational number was presented in different editions, compared to how mathematicians elsewhere defined irrational numbers. Thirdly, Nuno Dias talked about the Portugese mathematics education, in particular after the Jesuits (who controlled Portugese education) were expelled in 1759.

ESU6 Day 1

I am currently attending the European Summer University on the History and Epistemology of Mathematics Education. The conference takes place in Vienna, Austria. As usual at such conferences, I will blog about what I learn from it.

The conference was opened by Mannfred Kronfeller, the main organisor of the conference, and by the Vice Rector of the Technical University of Vienna, Hans Kaiser.

There were also short introductions by Evelyne Barbin, the chair of the HPM group, who outlined the history of the ESUs, and by Costas Tzanakis, who mentioned that representatives of 28 countries are present at the conference. That's not bad.

The first plenary speaker was Uffe Jankvist from Denmark. He talked about a teaching experiment that he has conducted (and which formed part of his PhD), where the history of mathematics played a major part. The topic was error-correcting codes and cryptography. But while this was the background of his talk, his real concern was to get more specific about what role history of mathematics can have in teaching. In particular, he studied whether he could see signs that the students would have meta-issue reflections on mathematics that were anchored in the mathematical in-issues that they were working on.

I find Uffe's approach very interesting. Instead of just claiming that "history of mathematics can make students reflect on the epistemology of mathematics", for instance, he sets out to study particular interpretations of this claim. It makes for a more nuanced and informed view of the part history of mathematics can play.



Uffe argues powerfully for the use of empirical studies (in this sense) in research on history of mathematics. I agree that this is one important path to follow. However, I believe that we still need the other paths as well. While studies such as this are convincing, they do too little to provide examples and materials for teachers to trz. For many teachers, successful attempts at including history of mathematics in their own classrooms are more powerful than researchers' results.

Then there was time for workshops. Workshops form a major part of the ESUs, as the ESU is supposed to give more "hands-on-experiences" than ordinary conferences. I attended Masami Isoda's workshop on how he has used the dbook software to create digital editions of textbooks with appended interactive materials. The example given was of historical instruments (from van Schooten's book). We were also given the chance of recreating the historical instruments by means of paper (see the wonderful instrument created by the group consisting of Jan van Maanen and me - I must admit that Jan did most of the work...)




I think this is an interesting way of connecting the textbook with more interactive media.

Then I attended a three-hour workshop with Uffe Jankvist. There have been discussions during the conference of whether the three-hour format is too long. In my opinion, Uffe's workshop provides an existence proof that three hours may at times be about the right amount of time. Uffe wanted the participants to analyze some bits of transcripts with the same analytical tools that he had used in his PhD. In the beginning, the participants were quite hesistant, as both the mathematical and historical topic under consideration was unfamiliar and the analytical tools were new to us. However, by the end of the workshop, it seemed to me that everybody was participating in trying to find the "potential anchoring points" that Uffe was interested in.

As mentioned above, I think that there is great potential in getting more detailed concepts of how history of mathematics may be included in teaching, making it possible for teachers to be more conscious about exactly which effects they are trying to produce in a particular circumstance.

Oral presentations are not such a high priority at the ESUs, so on Monday they were taking place from 1830 to 2000 at night. Gerlinde Faustmann talked about "Classroom experiences with history of mathematics", following the path mentioned above of providing examples and ideas for teaching mathematics using history. Then I had my presentation on the Norwegian literature on history of mathematics, where I outlined several points of potential improvements. (I keep thinking I should write a book on the subject - but where is the time for it...) And finally, Po-Hung Liu discussed "the evolution of college students' epistemological views of mathematics in a history-based class". This was a combination of teaching ideas with a somewhat detailed look at what students did get out of it.



Of course, giving such a short summary of the first 11 hours of the conference does not allow for too many details. The proceedings of the conference will be available perhaps a year from now, so more details will be obtainable there...

I will continue with a discussion of day 2 in a later post.

European Summer University (ESU 6)

Next week, the European Summer University on the History and Epistemology in Mathematics Education (ESU6) will take place in Vienna. I will try to blog about it as it goes along, but thought I should start already...

The programme (available at the ESU6 website) has lots of interesting stuff, often with six events in parallell, so already it is time to lament all the good talks I will miss. However, such is life at big conferences. Here, I'll instead write about what I won't miss:


Uffe

The conference opens on Monday 19th of July. Uffe Jankvist will give the first plenary lecture, which seems to be based on his newly finished PhD (on historical modules in code theory). I will of course be attending this lecture. Afterwards, I will probably choose Masami Isoda's workshop on "Using historial instruments and interactive e-Textbook for experiencing the interpretation of historical textbooks" (although there are particularly many interesting workshops simultaneously). After lunsh, it seems reasonable to attend Uffe's three-hour workshop on "Students' meta-issue discussions of history of mathematics". As if that wasn't enough, there is an evening session of oral presentations, where Gerlinde Faustmann will talk about "Classroom experiences with history of mathematics", yours truly will talk about "History of mathematics in Norwegian - a literature review" (although the title in the program is "Making history of mathematics available to teachers - one page at a time"). And then Po-Hung Liu will speak about "Evolution of College Students' Eopistemological Views of Mathematics (...)". Then, finally, it's eight o'clock, and it's time to find a wiener schnitzel or something...


Kostas and me in Greece last year


Man Keung Siu (with Peter Ransom)

Tuesday will begin with a plenary lecture by Michael N. Fried ("History of Mathematics in Mathematics Education: Problems and Prospects"). Right thereafter, Costas Nikolantonakis and yours truly will have a two-hour workshop on "Historical methods of multiplication". After lunch I will be relieved to be finished with the main part of my obligations at this conference. I will go to Man Keung Siu's three-hour workshop on "Inscribed square in a right triangle". Then, I'll have no choice, as I am the assigned chair of one of the sessions: I will chair three talks on "The use of periodic property through history (...)" (Gabriela Buendía Abalos), a study of a paper by George Boole (Adriana Cesar de Mattos) and "The geometric representation of complex numbers and education" (Gerard E. Grimberg). And as if that was not enough food for thought for one day, I will take part in the meeting of the HPM Advisory Board from 8 o'clock - hopefully accompanied with dinner.

Wednesday will feel like a day off after these 11 hour days. There will be a plenary lecture by Marc Moyon on "Practical Geometries in Islamic Countries" and a panel discussion on "The history of mathematics in school textbooks". The rest of the day is put aside for lunsh and excursions - as well as a cocktail reception in the evening.


Kristín Bjarnadóttir

Then there's Thursday. Michael Glaubitz will give a plenary lecture on "The Use of Original Sources in the classroom - Empirical Research Findings". Michael was one of the editor of the proceedings from the Oberwolfach meeting on original sources some years ago, and it will be interesting to hear him again. The next plenary lecture, by Raffaele Pisano, will contain epistemological reflections on "the cultural and interdisciplinary role played by physical and mathematical sciences", according to the program. My mind will probably be with the next thing on the agenda: the panel discussion on "The role of the history and epistemology of mathematics in pre-service teachers training". I will be one of the participants of the panel, and this will also be my debut in the plenary of such a conference. After that - and lunch - I will attend Kristín Bjarnadóttir's three-hour workshop on "Arithmetic textbooks in 18th century Icelandic manuscripts". I last heard her at the HPM in Mexico City two years ago, and she is always interesting. And finally, I believe I'll listen to José Manuel Matos and Mária Almeida on "Shaping a modern mathematics pedagogical content knowledge: the case of Telescola in Portugal in the middle 1960s" as well as Catarina Mota's "The concept of tangent line: historical and didactical points in its teaching in Portugal".

Which leaves Friday. I may want to skip the plenary lecture on ICMI's first century, as I've heard Fulvia lecture on the topic before. Then I will probably choose Michael Glaubitz's workshop on "Teaching methods for the use of original sources in the classroom". Then I will consider if I want to hang around for the closing ceremony or if I should run to the train that will take me to holiday in Salzburg...

During the conference, I will also try to take lots and lots of photos - they tend to become useful in the context of the HPM Newsletter...

So that's my plans for next week. It will be fun. And interesting. And I will need the holiday afterwards...


(Update: Just for fun, a few days ago I had a look at what countries are participating in this conference. Here's the list:
Algeria (1)
Austria (9)
Belgium (3)
Brazil (9)
Canada (2)
China (1)
Cyprus (1)
Czech Republic (3)
Denmark (3)
France (18)
Germany (13)
Greece (14)
Hungary (1)
Iceland (1)
Iran (1)
Ireland (3)
Israel (5)
Italy (10)
Japan (2)
Morocco (1)
Mexico (2)
Netherlands (5)
Norway (2)
Poland (1)
Portugal (13)
Slovakia (4)
South Korea (2)
Spain (8)
Taiwan (1)
Uganda (1)
United Kingdom (2)
USA (3)
And then there are a few people who are on the programme but not on the list yet - such as the first plenary speaker...)

ESU 6

I have received notice that ESU 6 (European Summer University on the history and epistemology of mathematics education) will be in Vienna (Austria) from 19 to 23 July 2010. (More information will be available in the next HPM Newsletter.)

Personally, I have enjoyed taking part in the ESU 4 in Uppsala and the ESU 5 in Prague, and am looking forward to going to Vienna for this conference.