ICME14 Day 7

Seven days - that's too much. Of course, it makes sense to make the most out of it when thousands of mathematics educators come from all over the world and assemble in one city once every four years, and then, also there's the added value of experiencing a new city. When instead sitting in an office at home, a whole week is a lot. Another conference I went to this year solved this by expanding the conference from one to two weeks - with shorter days (which automatically meant that when things did not interest you, you suddenly had a whole day for other work. 

And still, I should not complain, as ICME is arranged in a way that means most items on the agenda is between 8.30 AM and 5 PM. People in other parts of the world have more difficult time problems. 

There are some issues that need to be thought about after such a hybrid event:

- Video recorded talks work fine - but why are we all watching them at the same time? There is no real reason to include the plenary talks in the time table: they could be posted and seen at the viewers' own discretion. With a time slot at the end of the conference for interaction with plenary speakers, communication would still be taken care of. In CERME, most working groups have the rule that everybody should read everybody else's papers before the sessions. We could then have a more compact conference and more dialogue.

- Zoom meetings (with 10-30 participants) work fine. The dialogue is possible to arrange. Webinars are more challenging - the dialogue via questions in the chat is problematic, it never turns into a real discussion. 

- The hybrid mode works better than expected, but it does not work well. There are far too many problems with the sound and so on.

For the future, I guess there will still be huge international (and local) conferences where you will meet people in person and start collaborations that would not be possible online only. But I think we will see a lot more short conferences that will be online only. If all talks are prerecorded and you can see all talks (and/or read papers) in advance, two or three days of 3-4 hours of actual dialogue, could be really valuable and time well spent. (I'm excited that the MES conference this autumn has chosen a format where the time table is 22PM-01AM, 6AM-9AM and 3PM-6PM (Norwegian time). The idea is that everybody should be able to attend to at least two of the three time slots. For Norway, it is possible to choose between the 22-01 or the 6-9 time slots (in addition to the perfectly acceptable 3-6PM time slot), but I do not advice to attend both the 22-01 and the 6-9 for days on end. Sleep is important.)

Oh, and I miss the social events and the excursions, of course. I have fond memories of the border between North and South Korea, the pyramids of Mexico, and then, partly as a result of the excursions and programmed social events; dinners with new and old friends. Of course, I cannot say I have any new friends after this ICME - although I certainly have a few more names and faces which will make it easier to get in touch either by email or in person in future.

Enough of that. Today's first item was invited lectures, and I chose Susanne Prediger: "Enhancing Language as a Catalyst for Developing Robust Understanding – A Topic-specific Research Approach". When I did an overview of the research on language and mathematics exam tasks a few years ago, Prediger's name was everywhere, so I wanted a chance to connect a face and a voice to the words - and of course to hear of recent developments. 

She talked about 12 years of projects in the research group MuM - Mathematics learning under conditions of language diversity" (as always my notes here can not possibly convey the content of the talk, but may inspire someone to look up the relevant articles). We see, all over the world, that schools fail to provide equitable access to mathematics for students with low academic language proficiency. This can be multilingual students, but also monomingual students, for instance with low socioeconomic background. This is mainly concerned with conceptual understanding, which has to do with rich relationships between concepts. It is also important that in school, academic language proficiency is needed, not just everyday language, and it is important that children get opportunities to learn this. Of course, stress on language in mathematics teaching and working on different representation is important.

She discussed design principles for topic-specific design research. She gave examples from two Grade 6 boys in work on fraction, where the boys' language hinders the explication of (and development of) meaning. Academic language demand mediating between the other registers. Thus, one important point is to have students connect language registers and representations (not just to talk and write much). She gave a series of examples on how traditional learning trajectorys for concept learning can be tweaked into developing discoursive practices. (Or rather: to combine a conceptual learning trajectory with a language learning trajectory.)

She went on to describe a large-scale (38 classes, 655 seventh graders), with language-responsive intervention, with pre-test and post-test (with control group). The language-responsive intervention group learned significantly more than the control group. The results held also (and were even higher) for students with high language proficiency. And they were largest for non-routine items. Thus, it works for all students. But there was a huge variation between classes. She pointed out that it is needed to look at teachers' enactment. (I would argue that one should also look at the norms of the classrooms.) In looking at teachers' enactment, they used the TRU Framework, slightly adapted. (See Prediger et al, in ZDM 2021.) 18 classrooms were video-recorded, and quality dimensions were rated every 5 minutes. They found high variance in Use of Contributions, Equitable Access and Discursive Demand, and these were related to the results. 

It is quite amazing to see top researchers reflect on their research journeys and how their findings have spurred new questions and how these new questions build on other parts of mathematics education research and use multiple methods to get even further. She actually shared a link to her video to the participants at the end, and I think this will be really interesting to discuss with colleagues when the holiday is over.

Final reflections

As often happens at week-long conferences, I run out of steam and can't keep up the blogging throughout the last day. I have already given some reflections on the form of the conference at the top of today's post. Now I will try to summarize for myself some of the key points to keep thinking of. 

From TSG55, I am intrigued by the great variety in the papers. I did note Alexander Karp's repeated calls for contextualization and to get beyond doing studies of one textbook at a time in isolation, but in my opinion, sometimes the smaller pieces that will later fit in a larger puzzle, can be valuable research projects in themselves. I see this particularly in working with New Math in the Nordic countries, that there are so many detailed investigations that have to be done to better be able to compare and contrast different periods and/or different countries. Some of these detailed investigations can possibly fit into the rather insane four-page limit of ICME, but not if they are also to include enough of the context and research background and implications...

Being a novice to TSG12 (statistics), it was interesting to get a quick idea of where the research front is; what are the issues being discussed and what are seminal works that everybody refer to, and what are the key competencies that students are able to understand at different age levels. I was particularly impressed by some of the work on the youngest students in school. I now have several tools to look into and several articles to read to get a clearer understanding of this. In the same way, attending the discussion group on algorithmic thinking gave me an insight into where the problems are. They were not altogether surprising.

The plenary panel on the collaboration and conflict between mathematicians and mathematics (teacher) educators was interesting, although in my context, I believe the division between mathematicians and mathematics teacher educators is rather fuzzy, and the collaboration and conflicts with other actors (pedagogues, politicians, administrators) are rather more frustrating and time consuming.

I did enjoy the HPM session, although I've taken part in quite a number of such sessions through the years. I also enjoyed getting an overview of Gert Schubring's research through his awardee lecture. In fact, there were a number of lectures like this (including Prediger's lecture today), with a prominent researcher reflecting on many years of research, which is a nice occation to see people's work as a whole instead of reading one article at a time. (However, one does wonder how many twists and turns are left out - from my own experience, as a quite non-prominent researchers - I know that I happen to take part in many research projects that does not fit neatly into an overall story. But that may be one reason why I am so non-prominent.)

Perhaps I should now reflect on my own contribution to the conference. Blogging is one way for me to keep alert and to actively process what is happening. Even in physical conferences, my contribution in terms of questions and comments are not that frequent (although before I've always had one presentation, and I've also contributed to the HPM session some times, and also led a discussion group once). This time, I think I contributed with just two or three questions during the whole week. But in normal circumstances, we also discuss what we have heard during lunches and dinners, and during walks around the town and so on. I miss that. 

This is the end of my ICME blogging this time. I hope to be back for ICME in 2024 (and of course for many other conferences before that). (Oh, I notice that next ICME will be in Sydney, Australia, from July 7th to July 14th, 2024. As I was originally planning to skip this ICME because I want to cut down on flying, it seems unlikely that I will be going to the ICME in Sydney. So perhaps I'll rather go to the 2028 one.)