ICME14 Day 6

The sixth day started with the final session of TSG12 (on statistics education). The first talk of the day was Saleha Naghmi Habibullah, with the title "Implementation of a course on Tidyverse in Pakistan under the ASA Educational Ambassarod Program". She discussed a course in the in Tidyverse - preparation, implementation and experiences. The workshop was based on the UN Sustainable Development Goals, using Tidyverse to study MICS data, and was done in a competitive manner, with teams presenting their data analyses in the end.

Michal Dvir and Dani Ben-Zvi: "Young learners' reasoning with informal statistical models and modeling". They define an Informal Statistical Model (ISM) as a "purposeful, not necessarily mathematical, representation of the process by which the observed variability was generated and includes both deterministic and stochastic components". Dvir went on to define "The Integrating Modeling Approach" (which I cannot summarize here, but had to do with switching between the real world and the probabilistic model). When student generated several samples, it spurred them to compare between multiple samples and make predictions. (Very interesting - I need to read their article(s) to get more detail than I did from a 20-minute talk. Here's one: Dvir, M., & Ben-Zvi, D. (2021). Informal statistical models and modeling. Mathematical Thinking and Learning. https://doi.org/10.1080/10986065.2021.1925842)

Von Bing Yap: "The binomial model: coin tosses or clay pots?" Two different models for binomial distribution: making n coin tosses (the number of heads has a binomial distribution) and removal of clay pots (which are high-grade and low-grade) from the kiln (not binomial, as there is lots of dependence). Many real populations are more like clay pots than coin tosses. We need to introduce simple random sampling. He gave examples of exam tasks where the binomial model is not correct, for instance when it is stated that "80 % of people..." and it is then assumed that the probability for each person is 0.8. Usually, people have different probabilities, he argued.

Orlando González: "Variability modeling and data-driven decision-making using socially open-ended problems: a comparative study of high school students in Thailand, Brunei and Zambia". The starting point of the talk was a "Darts game" - students got the dart boards of two teams competing, and were asked who were the winners. Students had many (six) different ways of scoring the dart games, implicitly creating their own rules. Most created a scoring function based on all shots, while there were also some who considered only some of the shots. (It seems like an interesting task, but it is not clear to me which important part of statistics knowledge in particular is worked on. Rather, I imagine using it to have a discussion for more general purposes.)

(Mara Magdalena Gea, Jocelyn D. Pallauta, Pedro Arteaga, Carmen Batanero: "Algebraization levels of statistical tables in secondary textbooks". Here, I was distracted by some other work for a moment, and can not reasonably give an idea of the contents.)

Stine Gerster Johansen: "Data modelling with young learners as experiences of allgemeinbildung". Johansen first discussed the concept allgemeinbildung and Lehrer&English's model for datamodelling with young learners. Modelling can contribute to bildung, but is demanding. Here, she discussed work with a Danish 3rd grade class (ages 9-10), 4 sessions, 90 minutes each. She gave examples of how children were discussing parents' quarreling, and the potential for bildung, including discussing what the use of this statistics work could be for other children.

The next item on the agenda was invited lectures, and I went for Reidar Mosvold: "Trends, Emphases, and Potential Shifts in Research on Discussion in Mathematics Teaching". His talk was based on a review of the literature. He discussed the concept of discussion, stressing that it needs a subject ("a question of common concern") and that it concerns reaching a decision or exchange ideas (based on the OED definition and on Dillon (1994)), in contrast to idle talk. He also discussed the concept "teaching", leaning, among others, on "work of teaching" (Ball & Forzani, 2009), where core components can be described as problems (Lambert, 2001), predicaments (Cohen, 2011) and tasks (Ball, Thames, & Phelps, 2008). He discussed the problem of having systematic searches for "discussion" (which after all is a quite usual word), and the rest of the review issues. He ended up with a total of 72 studies; empirical articles on discussion and mathematics.

Some of the results he mentioned in his talk was that the studies varied in focus, surprisingly few define what they mean by discussion, and a majority were small scale studies. The problems of studies for instance were about teachers' or students' actions, experiences, learning, demands. Key issues were orchestration (more than half), talk moves, norms, demands... For instance, only two or three articles had any significant discussion of norms. (This is surprising to me, as norms seem to be so central these days. I have more than three articles on norms on the reading list for a course I'm teaching, but obviously they do not all fill the criteria of Mosvold's search.) He also found that there was a surprising variety of literature refernced. Of course, Lampert (1990), Yackel/Cobb, Ball and Stein/Grover/Henningsen, were referenced by many (but only 5-10 references to each, which is surprising). Also, surprisingly few referenced studies on discussion outside of mathematics education. 

One of his takeaways from the review, was that there should be more investigations on what might be involved in establishing a classroom climate for discussion. (Personally, I use Makar/Bakker/Ben-Zvi (2015) with my students. It's title is "Scaffolding norms of argumentation‑based inquiry in a primary
mathematics classroom" and would not be included in Mosvold's survey, as the word argumentation is used, instead of discussion. However, it is an overlap between norms of argumentation and norms of discussion, I would think.) In the discussion, he was asked about other terms such as "discourse", and he argued that it was necessary to limit the number of articles and at the same time "discussion" is an often used word. I asked my question ("I believe that the literature on argumentation, norms of argumentation and so on, would partly also be about discussions without actually using that word. Any comments on that?"), but Mosvold actually already answered that before the question was posted (one of the problems of sending questions in the chat without the possibility of withdrawing it...)

The final part of the sixth day was the final part of the TSG55 (The history of the teaching and the learning of mathematics). 

Sian E. Zelbo: "Building an American mathematical community from the ground up: Artemas Martin and the Mathematical Visitor". This talk is on Artemas Martin (1835-1918) from the US and his journal "Mathematical Visitor", which also included contributions from leading mathematicians of the time. Zelbo stressed that the aims were different than the Journal of Mathematics, to which it has been described as simply a precursor. The aim was to reach young people, and also teachers and administrators contributed.

Elisabete Zardo Búrigo: "The discarding of the rule of three in the 1960s: changes in elementary education in France and Brazil". The rule of three was discarded in the elementary school in the late 1960s, but was later reinstated. The rule of three was taught both for use in life and for use on entrance exams to post-elementary schools. However, as compulsory schooling was expanded, entrance exams were abolished and "New Math" targeted the rule of three as "too mechanical", rule of three was removed about 1970, in both countries. In France, a functional approach replaced the rule of three, while in Brazil, the study of proportions were delayed until later grades. The rule of three was reintroduced in France in 1985 (and was still there in many places from 1995), while in Brazil, it was mentioned in the 1997-8 plans, but from 2017 it was explicitly discouraged.

Yana Shvartsberg: "Mathematics education for young women during progressive era: historical overview". Her period was 1890-1920 and her geographical focus was the US. High school curricula were differentiated, according to the kind of industry/position the students were planning to go to. Mathematics became an elective topic for many students. Shvartsberg's research is looking at how this influenced women. There was a belief that women did not need the same education as boys, but at the same time, and many high schools for girls did not offer the same courses as high schools for boys, and more boys than girls selected mathematics courses. However, some educators argued that the same opportunities should be available for women.

Alexei Volkov and Viktor Freiman: "David Eugene Smith (1860-1944) and his work on mathematics education". Here's yet another talk on the US, but Smith also had international consequences, of course, being one of the founders of ICMI. This talk focused on his early didactical works. Of course, I will not try to summarize his life and works. In the talk, the connections and reactions to different European theorists (for instance Busse, Pestalozzi, Gruber, Tanck, Knilling...), were pointed out.

Alexander Karp: "College entrance exams in mathematics in Russia before the second world war: development, role, objectives". He stressed the importance of exams, also in terms of dictating an unofficial curriculum and thereby influencing how the subject is taught in schools. He gave rich examples of how the entrance exams were regarded through contemporary sources. Critics argued that the entrance exams should just include mathematics that is actually included in the secondary curriculum and not "extremely artificial techniques". In the discussion, it was mentioned that this situation, of entrance exams taking priority over the actual curriculum of lower school levels.

That concludes the 6th day of the ICME. One day to go.