PME37 Day 4 #pme37

The first talk of Wednesday (one I also chaired) was Shin-Yi Lee's talk on metacognitive strategies for improving problem solving abilities in probability. She had done an experiment in which 9th grade students were encouraged to use a metacognitive-strategy worksheet while working on probabilities. The most striking result to me was that the control group, getting traditional instruction, had a significant decrease in their results from the pre-test to the post-test. But in the discussion we concluded that this may often be the case: if students use their common sense, they may go a long way in simple probability tasks, but if they are given a few formulas, they will try putting everything into them, leaving their common sense. The study had its limitation in that we knew little about the experimental group and the control group, and many ideas for further studies popped up in the discussion.

Then I went to Gert Schubring's talk "From 'armchair pedagogy' to experimental research and to case studies". He discussed the history of empirical research in mathematics education. At an early stage, teaching was considered as a treatment with learning as an effect, and research was done to show the effect. There were many small-scale studies with little connection to theory. Around 1960, large-scale studies were made possible by grants from science funds. In 1969, at ICME1, Begle called out for more empirical research, less research based on opinions. He repeated his criticism in 1979.

Later, case studies got more prominent and the interest was more in qualitative than quantitative studies, although TIMSS and PISA have been important exceptions. Schubring claimed, however, that these studies perhaps grew more from outside the mathematics education research community than from within. Of course, as anyone who has ever attended a talk by Schubring will understand, this short note is nowhere near doing justice to Schubring's talk, full of information as they always are. The best thing I can hope is to have given a sense of what the topic was...

By the way, the term "armchair pedagogy" reminded me of an earlier discussion within the HPM community (where Gert Schubring is of course a prominent member) about "armchair research". There, I have argued that the field of HPM needs both research and development (in Norwegian: FoU - forskning og utviklingsarbeid). If by "armchair research" is meant the development of "good ideas" and teaching sequences by experienced educators with an interest in the history of mathematics, this is an invaluable part of the development of the HPM field, making it possible for teachers to take up HPM practices as well as providing materials that researchers can research. To do research on education, you need someone to provide the actual education you want to study, and it is not necessarily the best researcher who has these ideas...

Then, C. Miguel Ribeiro talked on "Characterizing prospective teachers' knowledge in/for interpreting students' solutions". In the programme, Arne Jacobsen was given as the presenting author, but there was evidently a change. Of course, an important part of being a mathematics teacher is to interpret and try to make sense of students' solutions. This project used Ball's MKT "ball" as a starting point, here looking particularly at common content knowledge and specialized content knowledge. They see the ability to make sense of students' knowledge as part of special content knowledge. In their materials, which concern fractions, they do see a tendency that teachers mostly see as correct those of students' solutions that are similar to the teachers' own solutions, which suggests a need to focus on this in pre-service teacher education. One strength of e study, by the way, was that it involved three different countries.

As so often happens in these cases, there was a lot of discussion on the quality of the tasks and how they should be interpreted. One comment was on the concept of "babbling", where the language of pupils is interpreted as the unqualified use of language in a context where the pupil is busy working out the mathematics, so that some of their utterances are not well thought through. Another comment was that the correct answer to the question "What amount of chocolate would 6 children get if we divide the 5 bars equally among them?" is 5...

Then it was time for the conference's excursion. I had chosen to go to Lübeck. I did not expect this excursion to be as fascinating as the North Korea border excursion at ICME, but it would still be a welcome diversion, both from mathematics education and from private problems...