PME37 Day 5 #pme37

Tim Rowland's talk on "Developing one-to-one teacher-student interaction in post-16 mathematics research" started the fifth day of PME37. He talked about the work of Clarissa Grandi. Her research was motivated by a feeling of mismatch between her intentions and her practice, where she felt she helped the students "too much", instead of scaffoldig. Rowland noted that "teaching by telling" is very prevalent, has been widely critizised but that there are not necessarily easily available and easily implementable alternatives for a teacher who wants to do something else.

Grandi analysed the form and function of her utterances during one-to-one interviews with students (and she had a few other data sources as well). It is an interesting choice to do this in the form of interviews instead of "real" classroom situations. I can see how the analysis of her utterances in interviews can give insights that are transferable to her work in the classroom. In the end, she had 12 codes showing different functions.

In the first cycle, there was a preponderance of "telling". Grandi was not happy with this. She used "telling" to demonstrate, direct, explain and funnel, not only to confirm, discuss conventions or "parallell model" (involving the solution of a related, but often simpler, example), in which cases telling was more meaningful, according to her. In the second cycle, she demonstrated and explained considerably less.

Through the research, Grandi realized that telling is sometimes consistent with a social constructivist agenda, but that she had also been able to modify her behaviour in the direction she wanted to.

Of course, some of the discussion afterwards was on the problem of doing research on oneself, and the problems you then have of distancing yourself from the situations.

In short oral presentations afterwards, first Jajaluxmi Naidoo presented a study on pre-service teachers' understanding of effective teaching strategies. The study showed that students with no teaching experience thought they should use the same strategies as their teachers had used in school. They did not have much belief in the more learner-centered strategies - it wouldn't work in real life. Which may be correct, South African classes often have more than 90 pupils, often with more ages in the same class and with many of the children hungry and unconcentrated. Of course, this is also relevant for other countries, although not as extreme- many students regard the strategies that teacher education advocates as unrealistic in that they do not take into account all the difficulties present in a classroom. This is a significant challenge for teacher education. We cannot include all the complexities of the classroom all the time in our discussions, but neither should we disregard them completely.

Charlotte Krog Skott gave a talk on "Lesson study in teacher education". This is based on an attempt to adopt the Japanese practice of lesson study to teacher education, where teacher students experiment with and discuss teaching. In analysis, they used cathegories from the knowledge quartet and others, and also used elements from the theories of communities of practice and situated learning. The pre-service students guided the students in a certain direction, in spite of their intentions. It also became obvious that the pre-service teachers didn't discuss the mathematics in the lesson study, instead focusing on how they could have asked questions to have the students think instead. They also gave a good example where PSTs designed a lesson where students should rotate to see four different tasks, and the PSTs were very good at picking different representations and making varied activities, that sadly did not connect to each other mathematically. Another result was that there is a potential to develop a community of practice around lesson study.

In just a few weeks' time, there is the ECER conference in Istanbul. As we would have to leave Kiel Friday morning, we spent the rest of Thursday planning the presentation in Istanbul. We had a very productive meeting at the hotel balcony, and now feel (almost) ready for ECER...

It was nice to be at PME - it was a lot friendlier than I thought it would be, and Germany is a very nice country (I'm already looking forward to ICME in 2016). I will always remember this conference for my struggles with Norwegian authorities during the conference, I'm afraid, but the conference as such was quite good.