ICME14 Day 2 Part 1

The first item on the agenda was the first session of the Topic Study Groups. While usually going to the "The role of history of mathematics in mathematics education" TSG, but this year I joined TSG55, which is in the history of mathematics education. (The names seem alike, but the difference should be obvious...)

Alexander Karp welcomed us and mentioned that the field of history of mathematics education is getting recognition, for instance there are two series on history of mathematics education on Springer now, and Gert Schubring of course received a prestigious prize yesterday. The format of this TSG is talks of at most 10 minutes, followed by five minutes of discussion.

Vasily Busev and Alexander Karp: "Pafnuty Chebyshev and the mathematics education of his time". Chebysev was of course a major Russian mathematician who was also interested in mathematics education. Vasily Busev will publish a complete publication of Chebyshev's educational notes, which will give an interesting view of mathematics education at Chebyshev's time. For instance, he reviewed textbooks, and he was arguing that if a mathematical result can't be proved rigorously within the capabilities of the students, then students should be told so directly, instead of giving an almost rigorous proof.

Dirk De Bock: "Frédérique Papy-Lenger, the mother of modern mathematics in Belgium". De Bock has written an impressive book on New Math in Belgium, and this is especially interesting to me as I am doing some work on New Math in the Nordic countries currently. The talk is based on Lenger's collected writings and the reactions to these. Lenger vas part of the CIEAEM community. Already in the mid-50s, she thought that the focus on relations and structures in modern research mathematics could be a model for mathematics in school. She married the mathematician Papy in 1960, and became an important researcher in New Math in Belgium. Among her most important work was "Les Enfants et la Mathematique". She also worked with the Comprehensive School Mathematics Project in the US. Later, she worked on mathematics education for disabled children. Her work was important, but she did not get the recognition that she deserved. One possible reason was that she focused on the development, not on theory (which is an usual way to get overlooked). Also, she was overshadowed by her husband. Moreover, she was so connected to New Math that when New Math lost its position, so did many of its proponents.

Ildar Safuanov: "The history of mathematics education of Tartar nation". Safuanov discussed the history from medieval times until the 20th century. (As I know little about this in advance, it is difficult to give even a short summary of its history.)

Maria José Madrid, Carmen León-Mantero, Alexander Maz-Machado: "Mathematics and mathematics education in the 18th century Spanish journal "Semanario de Salamanca". The study of journals is an interesting supplement to studies of textbooks and other books. The journal in question was published twice a week, including both scientific articles and news from the city. For instance, it included mathematical problems, book reviews and job offers. Thus, we see how the study of journals can give an insight into the history of mathematics (including the role of mathematics in society). 

Maja Cindric: "Arithmetic textbooks in Croatia in the premodern period". Cindric talked about the history of Croatia and how it relates to neighbouring countries. In the period in question (in the 18th century), schools were run by Jesuits, not compulsory. There was no compulsory secular education until 1774. She looked at two arithmetics textbooks, from 1758 (by Mihajl Šilobold) and 1766 (by Mate Zoričić). Cindric gave details on differences between these books (which I am unable to detail here). As far as I understood, Šilobold's book was more focused on what we would call "problem solving". Cindric stressed how misconceptions in school can often be collected to terminology, and that the etymology of terminology can be traced by studying textbooks.

Karolina Karpińska: "Gnomonics in mathematics secondary school education on the territories of Poland in the 17th-20th century". Gnomonics is the theory behind the constriction of sundials. (I cannot think of sundials without thinking of my wonderful colleague Peter Ransom, who has often talked on sundials in lectures and outside of lectures.) She discussed the basic theory behind sundials, combining astronomy and mathematics. She discussed how gnomonics was taught in Poland - including different kinds of sundials and of course also whether they were treated generally (regardless of geometrical position). From 1812, gnomonics was introduced as an obligatory part of mathematics in 5th grade (in physics and chemistry). Later, it was part of geography lessons.

Shinnosuke Narita, Naomichi Makinae, Kei Kataoka: "Approach of an early 1940s Japanese secondary mathematics textbook to teaching the fundamental theorem of calculus". Calculus was introduced into textbooks in the 1940s, in 10th grade (4th grade in junior high). Narita detailed how the textbook introduced calculus, showing that students were expected to develop their knowledge through solving problems, before giving definitions later in the textbook. (Which seems reasonable - but it must be stressed that the role of the teacher is difficult to establish, so how free students actually were to develop their calculus.)

This was a demanding start of a day - two hours of presentations and discussions without breaks, on a wide variety of topics. In addition, Zoom is for some reason more demanding than physical meetings to me, particularly for my neck - it has something to do with having to sit in front of the camera in a particular way. Nonetheless, these first two hours of TSG55 showed clearly the variety and the tensions in history on mathematics education - sometimes very focused on the mathematics, sometimes on the institutions or on the discussions on mathematics in society and so on. Some researchers are very detailed on one little piece of a large puzzle, without including the context very much, while others give a lot of attention to context and less to detail. Of course this is also a matter of the limits imposed: four-page papers and 7 or 10-minute presentations. This is not conductive to including both detail and context sufficiently. But even disregarding these limits, I believe still researchers have different leanings, and that is fine. For instance: detailed accounts of a series of textbooks can be very valuable to another researcher, who can build upon them further.

The second item of the day was the plenary lecture by Lingyuan Gu: "45 Years: An Experiment on Mathmeatics Teaching Reform." This detailed mathematics reforms near Shanghai from 1977 to 2022. Giving just the highlights will seem like a string of buzzwords: from 1977 to 1992, the stress was on "affection, progression, attempt and feedback", from 1992 to 2007, the stress was on "comprehension" and "experiencing variation", while from 2007 to 2022, the focus was on "inquiry and creativity". This may seem silly, as everyone in mathematics education - from 1977 till today - will surely agree that affection, progression, attempt, feedback, comprehension, variation, inquiry and creativity are important factors. So the point is obviously not to jump from one to another of these (or to pretend - as Norwegian directorate of education tends to do - that every new curriculum includes some new focus that has never been thought about before). Instead, the point is to do a careful analysis of the current situation and try to establish what part of this mix of "buzzwords" (which are, after all, important concepts) need to be prioritized for a period of time going forward.  Such an approach, with careful research, testing and so on, has been followed in Shanghai. They combined macro studies with quantitative means, with micro studies with observations of low-scoring students and their interactions with their teachers.

I did enjoy his example of introducing parallell lines. Some teachers will just give a definition and many students will be able to resite it when asked. Other teachers give students an example ("are like two tracks of train"), thereafter opening up to a discussion about what else is or is not parallell lines ("Are they still parallel lines if the train makes a turn?". In this process, both what is and what is not (but are "nearly") will be included in that process. That's a nice close-up of some of the principles at work in a classroom.

It was interesting to see that even though inquiry had been an underlying principle for most of the time, results were not good by 2007. Therefore, inquiry was one of the main foci after 2007. That is perhaps not very surprising, I think - it is hard to break the habits of minds in classrooms, where everyone expects that no matter what the teacher says, the teacher still has the a script of what is supposed to be thought in a classroom. (Yes, I mean "thought", not just "taught"...) Results now are promising. 

One of the interesting points of going to international conferences is seeing that the problems people struggle with on one continent is often the same as on other continents, even though contexts are very different. Gu's talk was impressive while the main concepts were familiar. Lastly, he stressed the importance of video in educating teachers, to make available the analysis of classroom occurences in detail - with the teachers or teacher students. (Of course, then we start getting into the Lesson Study field, which I remember hearing a lot about at the 2000 ICME and which has been worked on a lot also in Norway, but has still not - as far as I know - become a normal part of education for all teacher students.) I also liked that Gu stressed that the point of this line of research is not to write "the perfect paper" but to improve teaching, which means that there will always be mistakes and wrong turns, but still, in the long run, improvement.

Already, this blog post is getting rather long, so I think I will end it here, and have the rest of the day in a brand new blog post...