ICME Day 5

I have kept boasting that this is the fourth time that I've taken part in both the ICME and the HPM conferences. Among the things I've learned is that you should not feel bad about taking breaks - having a full programme of talks from morning to evening for two full weeks, simply does not make sense. The brain needs some spare time to think about something else - or maybe process what it's alteady learned...

So I took the morning of the fifth day off, sleeping late, even though Thursday (day 4) was excursion day. In fact, I was perhaps even more tired after the excursion day than after any other day - it was a day of many thoughts as we crossed the line to North Korea, if only for a few minutes...

Thus, day 5 started, for me, with Marja van den Heuvel-Panhuizen's talk, named "Freudenthal's work continues". She has been a big influence to Norwegian mathematics education lately, and I keep seeing her name, so it was about time I heard her "live".

She has worked at the Freudenthal Institute for 25 years, and started by talking about the history of this important research institute. It has a history going back to 1971. In November 2010, it was decided that primary mathematics education was not a part of the core goals of the science faculty, so the FI was divided. 

She talked on three projects connected to primary school: the didactical use of picture books, mathematical potential of students in special education, and textbook analyses.

First, the project on the didactical use of picture books in kindergartens. Freudenthal himself was sceptical to limited and isolated worksheets, and wanted to give children context-rich experiences in which the children could discover mathematical connections. Picturebooks can give rise to meaningful activities, offer cognitive hooks (Lovitt and Clarke) and give opportunities for practice. In a 2008 paper, van den Heuvel-Panhuizen showed that almost half of children's utterances when read a particular book, was mathematics-related. Among the other subprojects, they also found significant improvement in the children's Score on a PICO test (whatever that is). 

Then she went on to the project on special education, with work on subtraction and combinatorics. The project was motivated by policies claiming that weak students should not discover strategies by themselves, but be told how to do things. Of course, to accept this would mean that weak students can never appreciate mathematics as a creative field of knowledge.

van den Heuvel-Panhuizen presented a model with 12 (3x4) different methods for subtracting, and studied whether special education students could, on their own, use indirect addition to solve problems suited to that method (without being taught it first).  It turned out that the students could do that.

The third project was the textbook analysis project. Textbook analyses give us a first inside view of how mathematics is taught, and is therefore relevant to teacher educators. It focussed on content, learning facilitators and knowledge presupposed. Among the clear findings is that realistic textbooks have more didactical support - like the use of context, models, textual instruction etc.

Then there was the third session of the TSG20. First, Mustafa Alpaslan talked on “"History of mathematics” course for pre-service mathematics teachers: A case study", a paper written with Cigdem Haser. HM got mentioned in the curriculum of 2005. Textbooks had small snippets of historical information. For pre-service teachers, a course on HM was introduced by the government. In his masters thesis, Alpaslan showed an improved knowledge of HM in teacher students. In the present project, he and his colleague wanted to study such a course for students who will teach ages 12-14. The data collection included classroom observation for 5 weeks, examination of materials and semi-structured interviews.

The course was partly presentations by the teacher and then by the students, who had by then done small "projects". The course had nothing about the use of HM in maths education. Students found that doing mathematics "within its history" was enjoyable. But students wanted to know how to transfer this to the students. 

The course was based on group work, but this was not effective - they did not receive sufficient help on where to look for reliable sources, for instance.  Students were also busy studying for the general examination at the end of their teacher education.  The study suggested changes in the courses, and his doctoral work now will be dedicated to try to create a better course. I will be very interested in hearing more about this as it progresses.

Xuhua Sun was supposed to be the third speaker, but as the second speaker did not turn up, she was up next. The topic was "The systematic model Lu of JiuZhangSuanShu and its educational implication in fractional computation". She pointed out the two different traditions, the proof-based (of for instance Euclid) and the "problem-based" (of many civilizations), where solutions are given without proof. She then went on to show how 3/4 : 3/8 can be done in two ways: "flip and multiply" and transforming to the same denominator. She then connected this to the idea of Lu in Chinese mathematics. In Chinese mathematics one used different methods of multiplying with the common denominator to solve the problems in fractions.

Then there was the HPM group meeting. Evelyne Barbin talked first, on "Reading of original texts and 'dépaysement': from the teachers to the classroom". She referred to her article in For the learning of mathematics, 11, 1991 for the aims of the work on original sources. A key word for Barbin is 'dépaysement', or reorientation. By meeting an unusual take on something familiar, we will reconsider it. Barbin used the method of tangents by Roberval as her example. His idea of a tangent was the line which a point would follow if it detatched from its curve (which it was moving along). This idea was used to establish the tangent to the parabola and to the cycloid. 

Barbin showed two ways of using this in the classroom. The first is based on Frederic Vivien, who chose to translate it into the language of vectors. Then the pupils are asked to translate Robertval's reasoning in some examples into vectors. Barbin seemed very sceptical of this approach - it's not clear what you will learn about Roberval from this, as his context is disregarded, and what you learn about vectors, you could probably learn as well in another way. (this is my interpretation, not Evelyne's words, of course). The second is based on André Stoll, who used it with students who already knew how to find vectors. The ideas of Roberval can then be used to introduce the differensiation of vectors. He also uses this method to work on the cycloid.

Thus, an original text can be used both to read something known or to understand something else. But it is not necessary to read the text of Roberval to learn about vectors - for that, the examples could be used without the original source. To get good use of the original sources, it is interesting to discuss the context of the sources.

Then Fulvia Furinghetti talked on the history of mathematics in teacher training. She stressed that in teacher education, it is important to challenge teacher's existing beliefs. The aim is to make teachers reflective practitioners.

She agreed with Evelyne about the importance of replacement and reorientation, making the familiar unfamiliar, building cultural understanding. Finally, working on history of mathematics contributes to a construction of meaning of mathematical objects.

Fulvia then went on to describe a course on history of mathematics, consisting of theory and laboratory. The course is parallel with a course on mathematics education. It aims to create a community of practice, and is based on work on original sources: Fermat, Roberval, Barrow.

For me, it is interesting to see different ways of designing history of mathematics courses presented at ICME. Many of the courses presented would be utterly inappropriate in Norway, because of Norwegian students' lack of knowledge in mathematics. But there are also other differences between the courses than what can be ascribed to knowledge of the different knowledge levels of the students, of course. It would be very interesting to try to analyse different courses in relation to the designers' knowledge/resources, beliefs and goals (referring to Schoenfeld's talk on Monday). For instance, I'm concerned with showing students a variety of ways of including history of mathematics, while there are other courses that does not include that at all. 

Then there was the new chair of the HPM, Luis Radford. It was a rather informal talk, describing his path into the HPM group. At the end, he talked about how to use epistemology (based on Artigue) as a prism to critically observe and understand the objects of knowledge in the curriculum, and as a means to understand the development of the objects of knowledge. Radford is concerned with epistemological obstacles (both within mathematics and as related to the social, cultural and historical circumstances). His talk will hopefully appear somewhere.

ICME Day 3

Etienne Ghys held the most mathematical plenary at this ICME, with the subject "The Butterfly Effect". I will not try to summarize his popularization of chaos theory, but his underlying point was that mathematicians have a duty to popularize mathematics - and that the popularization of chaos theory has so far failed, in that it has been oversimplified in the popular culture. In particular, Ghys claims that chaos theory has often been painted as a purely negative "theory", saying that the future is impossible to predict, instead of as a positive theory making a contribution to our understanding. He showed how chaos theory often gives quite accurate prediction of the long-term behaviour of a phenomena, even though the behaviour at a particular moment can not be predicted.

It is interesting to notice that Ghys' talk was actually on the history of mathematics - the history of chaos theory, including Maxwell, Hadamard, Poincare, Lorenz, Smale. It should also be mentioned that Ghy's talk was the most beautiful and visually impressive so far at the conference, with great animations included.

After the talk, I wondered if teachers' behaviours are chaotic or, as Schoenfeld seemed to suggest, deterministic. I would guess that it is chaotic - that a slight change in the mood of the teacher or of the answer of a student can lead to a very different outcome in a particular case, even if the set of possible outcomes can be predicted.

Topic study group 20 continued with three talks. First, Jeffrey J. Wanko talked on "Understanding historical culture through mathematical representation". He talked on a course he has held - with students in general, not with pre-service teachers - entitled "Outside Euclid's Window", using book "Mathematics in Historical Context". The course is taught in Luxembourg, with study tour to important mathematical cities in the area. Examples of stuff covered was Gauss' calculation of the sum 1 + 2 + ... + 100, using diagrams to compute polynomials (in the US they learn about the FOIL method (first, outer, inner, last), adding and subtracting integers, understanding infinity (using Hilbert's ideas), building Platonic and Archimedean solids. The outcomes of the course were engaged students, who discovered mathematics and developed an understanding that it has evolved.

Andre Cauty talked about "Lab work of epistemology and history of sciences: How to transform an Aztec Xihuitl (a 18 periods year) into a calendar?" The Maya and Aztek had 260 days named by a complex expression of a number from 1 to 13 (or 2 to 14) and a sign of day (20 different). He went through many details on how these were written and several other cycles in the area, and historical attempts to harmonize these into a calendar. Sadly, the "lab work" part of the title was not touched upon, thus leaving the connection to the teaching of mathematics to the audience.

Maria del Carmen Morilla's title was "Visualization of the Archimedes mechanical demonstration to find the volume of the sphere using 3D dynamic geometry". She referred to Hanna, and the distinction between mathematical proofs than prove and mathematical proofs that explain. Using dynamic geometry helped explore Archimedes' demonstration of the relation between the volume of the sphere and the volume of the cone and the cylinder. The talk illustrated how dynamic geometry software can be a useful additional tool for explaining complicated geometrical arguments, to supplement the careful step-by-step exposition in dialogue with students.

After lunch, "Adjacent schools with infinite distance - narratives from north Korean mathematics classrooms" was Jung Hang Lee's title. I knew fairly little about North Korean mathematics teaching in advance (having read just one article about it before, which happened to be written by Jung Hang Lee and his supervisor), so this was a reasonable choice (even though there were many other tempting offers as well - for instance, I missed Luis Radford's lecture for this.

The research is based on interviews with refugees from the North Korean oppressive regime, 5 teachers and 10 students, three interviews with each. The teachers had teaching experience ranging from 6 to 25 years, all had taught in secondary school.

The North Korean school system wants to homogenize the students. Schools didn't even have school identities or school songs - on their uniforms they were only allowed to have a picture of the leader. But until the 1980s, many saw the system as a good idea, with free education and free health service. Then, however, conditions worsened.

The vice principal of the school are in charge of ideology in the school, and he manages the teachers. He is obviously member of the party. Positions were partly handed out based on family background check.

They do have a system of teacher development. Every week, one of the teachers present a new topic, and then discuss pedagogy and improvements to the topic. North Korean teachers don't have school holidays, but has to attend professional development sessions.

There is only one set of textbooks in North Korea, with a note on how much time should be spent on each subtopic. Throughout secondary school, mathematics is the subject with most hours, 6-7 hours s week in theory. There was a rigid class schedule, where each mathematics lesson should include five different sections, including Reinforcing the Policy of the Party, which they were meant to spend 20% of their time on.

After the "March of Suffering", in which 10 per cent of the population died, they mostly gave up on providing education for all, and concentrated on the most gifted students. Afternoon classes were often cancelled because the teachers had to go elsewhere to try to find food. Some teachers also brought goods to school to try to sell it to their students, even though this was an immense loss of face.

Probability theory has only recently (in 2002) been introduced in North Korea's curriculum. After all, many of the uses of probability theory are not relevant to North Korea (insurance, gambling, stock markets...) It replaced "computer and programming".

Wednesday's final plenary activity was a panel discussion on "Teacher education and development study: Learning to teach mathematics (TEDS-M)", with participants Konrad Krainer (Austria, Chair), Feng-Jui Hsieh (Taiwan), Ray Peck (Australia), Maria Teresa Tatto (USA). "Panel discussions" in such conferences tend to degenerate into a series of individual lectures which are not relating to each other, so it's always interesting to see what happens. In this case, the panellists had divided the topic neatly between them, presenting a lecture divided in four parts.

Konrad Krainer started by painting a picture by mentioning Hattie, Adler and Shulman. Then he introduced TEDS-M, whoch includes 23.000 teacher students from 17 countries. Norway is among the underachieving countries if you do a regression in relation to the Human Development Index. 

Ray Peck talked on "teaching and teacher knowledge". three MPCK subdomains: curricular, planning, enacting. He also showed some items and explained the concept of "Anchor Points" (which I can certainly not repeat here).

Feng-Jui Hsieh followed with the theme "teacher education and education system". She stressed that teaching is attractive in Taiwan, because of income, working hours, job security and status. Thus, the process to become a teacher is highly competitive. Taiwan surprisingly ranked as number one - surprisingly, because Taiwanese teachers are generalists at the primary level. However, based on items where they do badly, Taiwan have already taken steps to improve the teacher education. Taiwan also has a sharp decline between secondary and tertiary education.

At this point, Liv Sissel Grønmo got the chance to complain that too little is happening in Norwegian teacher education in response to TEDS (a fairly unreasonable complaint as the TEDS results have just been published). She also complained about the increased place of general pedagogy in Norwegian teacher education. In the end, she said that Norwegian teacher education at times seems like it is trying to educate teachers for mathematics without them having to know much mathematics. I am certainly more optimistic than Liv Sissel, and thinks that the new 5-10 education (which I am partly responsible for implementing at my institution) is a major improvement, because students will learn mathematics and didactics more directly related to the grades they will teach - and of course many will also have double the amount of mathematics compared to before. In 1-7 education,  I think a more tailored curriculum will also help. It would surprise me greatly if this reform would not contribute to an increase in the TEDS score on the primary and secondary level if TEDS is repeated some years from now. How we will improve the results on tertiary level, I am more unsure.

Maria Teresa Tatto talked on new research in teacher education based on TEDS-M. She gave examples of anchor points, and then went on to present the results of the study.

Like TIMSS and PISA, the main contribution by TEDS is probably not the rankings, but rather results on individual items that can help us get more knowledge about our own outcomes, and inform discussions on what we would like the outcomes to be and how to get there. It helps that the databases are, apparently, available on the TEDS website.

Of course, I am interested to look for traces of for instance history of mathematics in the TEDS items. It seems, though, that the study has too limited a concept of mathematics to include the history of mathematics. Thus, there are important bits of MCK and MPCK missing - unless it is found somewhere in the material that I have not found so far.

Finally, there was a meeting of the HPM Group. Here, the activities of the HPM Group were presented, including the HPM Newsletter, of which I've been an editor for the previous eight years. This meeting will be followed up with another session on Friday.

ICME Day 2

Before going on to describe day 2, I should mention that I'm still meeting "new" Norwegians in almost every break. I think the number of Norwegians must at least have doubled since 2008. So I wonder how many will be in Hamburg in 2016...

The plenary lecture of the day was Bernard Hodgson, titled "Whither the mathmatics/didactics interconnection? Evolution and challenges of a kaleidoscopic relationship as seen from an ICMI perspective". He was concerned with the divide between mathematicians and didacticians of mathematics - a divide partly due to they being connected to different paradigms, with different sets of rules for what is valid knowledge and so on.

He described how the mathematics education field is populated with mathematicians who are also teaching mathematics, as well as didacticians who are primarily doing their research in mathematics education. Of course, there is also the complication that even many mathematicians have a limited view of mathematics - we should include historians of mathematics in the discussion, for instance, but Hodgaon did not mention this. 

Hodgson went on to talk about three mathematicians with thoughts on teaching: Archimedes (with his "Method" - with a clear idea of the difference between a proof and just a reasonable indication), Euler (with all his textbooks) and Pólya (ten commandments for teachers). 

Hyman Bass has talked about the Klein era and the Freudenthal era of the ICMI. In  the Klein era, ICMI was populated by mathematicians, while in Freudenthal's era, didactics became a subject in its own right. The Freudenthal era also saw the launching of Educational Studies in Mathematics. Also, plenary lectures at ICME has turned from mathematics (for instance fractals) to didactics.

Hodgson ended by listing some challenges for mathematicians, here only summarized in short: acknowledge education as a responsibility, career issues, presence at ICME, level of rigor. Challenges to didacticians: keep research accessible to outsiders, collaborate in mathematically-oriented fora, acknowledge importance of creative mathematical work by teachers, must know mathematics.

The divide Hodgson talked about is of course present also in the Norwegian context, to a certain degree. It is evident whenever a new course description is to be agreed upon, a conference is to be planned, and so on.

For the TSG20, Peter Ransom was presenting Snezana Lawrence's talk on a project he has been involved in himself. They are trying to make the subject engaging by providing historical background, beginning with "historical appreciative session" on a topic. They do work on historical sources and explore which could give access to 'rich' tasks in the mathematics classroom. They introduce modern technologies in relation to the historical mathematics. For instance, he gave examples from work with quadratic curves, where history and different technologies came together.

Then I had my talk, discussing teacher students' attitudes towards history of mathematics based on a questionnaire I used in connection with a teaching sequence I developed. The full paper is available in my Academia.edu account. (I will insert a link here when I get the time, of course.)

In a way it was nice that the room was too small, as it gave me the rare experience of lecturing with eager listeners sitting on the floor and standing in the hallway, listening through the open door. 

Then there was Tinne Kjeldsen's "Genuine history and the learning of mathematics: The use of historical sources as a means for detecting students’ meta-discursive rules in mathematics". HM is part of the curriculum in Denmark. Tinne took Anna Sfard as a startong point, and argued that HM can have a profound role in becoming a participant in a mathematical discourse; to learn the meta-discursive rules. "Commognitive conflict" can give change in meta-rules. Historical texts can play the role of discursants.

She showed an example from a teaching  module on the concept of a function, and in this talk focused on the norm that a variable should take alle values, not be restricted to an interval, looking at Euler (1748). The students first worked in groups on four worksheets, then "expert groups" (with representatives from all four of the earlier groups), which wrote a paper. Analysis of the papers and the discussions showed that there was indeed some discussion on meta-level rules. (but it is impossible to quote the transcripts here...)

She also mentioned in passing an interesting confusion by the students between Dirichlet's use of a and b and the modern textbooks' use of y= ax+ b. The students apparently saw a and b as connected to linear functions only, not thinking of a as a constant but as the slope of a linear function.

Next regular lecture was Terezinha Nunes' "Number, quantities and relations: Understanding mathematical reasoning in primary school". She claims that cultural tools are essential for thinking, and that we use quantities, numbers, operations and relations when we use mathematics. She defines operations as transformations applied to quantities or relations. Numbers have two types of meaning: formal and extrinsic. These have to be coordinated. There are also two kinds of relations: necessary relations (i.e. 5 is 2 more than 3) and contextual relations (i.e. "Per has three apples more than Nils"). She showed examples of pupil errors that were not really mathematical, but just contextual - not having understood the context fully.

Nunes' main point seemed to be that while we have spent lots of effort working on representations of quantities and operations, we have paid little attention to the representation of contextual relations to support reasoning. Problems involving relations are always more difficult than problems with only numbers and operations.

Children must learn how to use iconic models - the models are not obvious. Children's drawings will often be nice but not actually illustrate the relations, and will therefore not help in solving these problems. Numes and colleagues are now doing a study about the use of representations for relations in primary school, with three small groups (intervention group, control group and "unseen" group.  Preliminary results seem to show that the models help, but pupils obviously tried easier ways of doing it when they could, which was unhelpful for learning to use the models...

While pupils in Singapore may work so much on the models that they become very proficient, pupils n England had a hard time learning to use them, which reminds us that this is not a routine to learn, but rather a tool one can learn to master. (A teacher from Singapore in the audience confirmed that also in Singapore, learning to use the representations was very difficult.

The rest of the day was spent on Discussion Group 5, of which I was the originator. I cannot summarize that here, but I'm sure we will provide a summary of the discussions among the 20+ participants in due time.

ICME Day 1

The first day of ICME was a light one. It started with a two-hour opening ceremony, with a combination of welcome addresses and cultural performances, which was an eclectic combination of Korean and Western style, just as modern-day Korea. It is always nice to attend these opening ceremonies, as they try to convince us of the importance of our work in general and the conference in particular. This time, there was a recorded address from the president of S. Korea. Thereafter, the Felix Klein and the Hans Freudenthal awards for the last four years were awarded. Of course, I was particularly pleased to see Luis Radford get his well-deserved prize.

The first plenary lecture was by Don Hee Lee. She spoke on the topic "Mathematics education in the national curriculum system". She discussed the place of mathematics in the educational system, taking Plato as her starting point. Is mathematics taught mainly for the intellectual development of "the liberal man" (learning for its own sake) or for the development of society?

She quoted a Korean professor of mathematics (without necessarily agreeing) claiming that there is no mathematics that is both easy and interesting at the same time. Mathematics is based on thousands of years of intellectual work, and therefore advanced. While this is an interesting point of view to share with pupils who have unrealistic ideas of the amount of work (or lack thereof) necessary to learn mathematics, it should probably not be a credo for a mathematics teacher. 

For regular lecture today, I chose Alan Schoenfeld's "How we think: A theory of human decision-making, with a focus on teaching". Alan Schoenfeld received his Felix Klein Award in the morning, and the lecture hall was so crowded that the organizers immediately decided to ask him for a rerun later in the week. 

The starting point of the talk was the question "If I know enough about you, can I explain every action you do and every decision you make?" He claimed that the answer was yes, with the important caveat that he is talking about situations where you are an expert. Thus, it holds for the cooking of a chef, the teaching of a teacher and the setting of diagnoses of a doctor. So what do you need to know about a person to be able to explain his actions? You need to know about his knowledge/resources, his goals and his orientations (beliefs/values...)

The word "explain" is not meant as a mere verbal explanation, but the ability to set up a model which can - to a degree - predict the actions.

Why look at teaching? As he put it: "If you can model teaching, you can model just about everything." Teaching is highly complex; it is highly social and it is ever-changing.

He gave a few examples of how he has worked with teachers to model their behaviour. He gave one example of teacher who believes that he cannot tell students anything unless it's based on something the students already have said - and therefore is lost when the whole class agrees on a wrong answer. His actions were to a large degree explained by this belief. Another example - a teacher who teaches by raises issues, asks for student suggestions, clarifies and then moves on. He transitions to the next issue when goals are met. So what does he do when things don't go as he wants ? According to Schoenfeld, he "doesn't have a choice" - he will still build on the students' questions/input and discuss them with the class. His beliefs determines his actions.

His third example was on Deborah Ball teaching a 3rd grade class. She did some surprising things, including at one point asking a question that many would consider a mistake, as it derailed the discussion with the class. Schoenfeld didn't understand what Deborah was doing. Could it be modelled? And what about Deborah's "mistake"? After years of studying it and discussing it, he came up with a model here as well. Yes, her behaviour was consistent with a model. Within the model, her "mistake" was based on a need to understand her students' thinking before going on to the next topic.

So what's the point? Why are models important? I would ess that they are not, but that they serve to point out the importance of a teacher's resources, goals and beliefs (etc). If two experienced teachers do things very differently, we should not assume that it is because of some insignificant chance. It may very well be because of some fundamental difference. And of course it doesn't help much to give teacher students the necessary knowledge and skills to teach well, if we don't also consider their beliefs. As Schoenfled put it: a teacher who believes that only the best students can do problem solving, will not even try to give his poorer students problems to solve.

Schoenfeld's way of thinking seems highly relevant to the research project I'm currently involved in, and I will keep it in mind...

The rest of the day,  I got prepared for Tuesday - the day of my little talk.

ICME Day 0

This will be my fourth ICME (International Conference on Mathematics Education), after Tokyo, Copenhagen and Monterrey. As always, I arrived a few days early. It's nice to get used to the temperature and the time before the conference starts. Seoul reminds me of Taipei (a city I've spent some time in). There are the same smells, a similar mix of local and US stores and culture, similar traffic and so on. The subway system is comprehensive and easy to use - like in Taipei. So I immediately took a liking to the city.

It's also nice to meet up with old colleagues. On the day before the conference, I met lots of Norwegians; Andreas, Marianne (with husband), Torgeir, Liv Sissel, Odd Helge, Kristin (with husband), Ole Einar and more. And still, I have met only perhaps half of the Norwegians. In Tokyo in 2000, I don't believe I met anyone else from Norway.

My expectations this time are diverse. I'm looking forward to hearing some of the "big names" - people that I've read but never seen. And the Topic Study Group will be interesting, I'm sure. But I must admit that at the moment I'm thinking most of my own contributions - a talk on Tuesday, leading a Discussion Group on Tuesday and Saturday and saying some words on the HPM Newsletter on Wednesday. I never stop being nervous, even after all these years, and even if the groups I'm talking to are rather small. What if I don't get my points across? What if I mess everything up? Well, I'll do my best not to...

After ICME, I am, again for the fourth time, going on to the HPM conference, which is in Daejeon this time. I'm looking forward to that, partly because I have fewer responsibilities there (just a workshop), but mostly because the scale is smaller and it is (therefore?) friendlier. At ICME, you can meet and get to know someone on the first day and then never see them again - it's that big. (Or they may be consciously avoiding you, of course.)

It will be two interesting weeks, for sure.

HPM Newsletter - February edition

A surprising treat for people interesting in the connection between the history and the pedagogy of mathematics (HPM): The HPM Newsletter website has published a few articles which will be included in the March paper/pdf issue of the newsletter. This is the start of a new habit, in which we hope to publish new materials every month, to be collected in the paper/pdf version three times a year.

New on the website today is for instance an article on BSHM Bulletin number 3/2010, including a link to the full papers of that issue of the Bulletin.

Enjoy!

HPM Newsletter 75

The newest issue of HPM Newsletter (no 75!) is now available at the HPM website.

It can also be read online at HPM Newsletter's website, which is currently in a test phase.