On day 6 (Saturday) of ICME13, the plenary lecture was by Deborah Loewenberg Ball, whose work I have referred to a lot in my own articles lately. She talked on "Uncovering the special mathematical practices of teaching". As usual, I was eager to get signs of her definition of "mathematical" (see yesterday's blog). She organised her story in three parts: a journey, getting lost, finding the way. At some point, many years ago, there was a movement from wondering what mathematics teachers need in teaching to what they use. The "getting lost" part was building tools to "measure" teacher knowledge. On the positive side, ways of studying outcomes of teacher education and professional development were developed, but on the negative side we fell back from understanding practice to looking at knowledge. Also, it may have contributed to separating aspects of teaching, for instance equity. So in a way, we got microscope images of many aspects, but not understanding it from the inside. She argued that we have to work on the "mathematical work of teaching" mathematics. (Still not defining "mathematical" or "mathematics", but at least referring to previous talks this week.)
The work of teaching is taking responsibility for maximising the quality of the interactions in a classroom in ways that maximize the probability that learners learn. (This fits quite well with Biesta, doesn't it?) Using "work" is to focus on what the teacher DOES, not on the curriculum, what students are doing etc. "Mathematical" listening, speaking, interacting, acting... are part of the work of teaching. A fundamental part of the work is attuning to other people and being oriented to others' ideas and ways of thinking and being.
She then showed us examples from a grade 5 classroom with 29 pupils in a low-income community. Showing us different sequences, she asked us to pinpoint what the teacher was doing. (What I saw: Getting people to come up. Classroom management. Monitoring. Steering discussion (sociocultural norms), respond to question, saying " it doesn't have to be right") She pointed out how the teacher had walked around the classroom, reading nearly 30 student answers, choosing which to look into) Then Ball mentioned concepts from Cohen and Lohan(?) on assigning mathematical competence, including developing competence. The work of the teacher is partly noticing everything that is not the wrong answer. Translation from learning goals to meaningful language for children. The work of teaching is discursively intensive work: talking while monitoring if anyone understands what you're saying and understanding the answers.
I liked the talk very much. As I saw it, it was a step away from "the ball", which has worked to privilege some kinds of knowledge and hide away others, not to mention skills. The criticism of testing for MKT is also welcome. What comes instead, though, is not clear. I'm afraid "the ball" is too simple and pretty to be replaced by anything messier or more filled with doubt and judgements...
The first invited lecture I chose today was Ansie Harding's talk entitled "The role of storytelling in teaching mathematics". Her talk was geared towards tertary education, which is interesting, but I also hoped to learn things for primary education. Of course, storytelling is also an important way of including history of mathematics in primary school (re discussion group at previous ICME), so also from that point of view it should be interesting, as well as for my cooperation with the L1 teacher of my students is next academic year.
Harding teaches 400-500 students at a time at the University of Pretoria. Here, she first gave the story of storytelling, from about 50.000 BC. (Already at that point someone challenged the veracity of the story, which raises the question of the role of truth in storytelling - which is also part of the discussion concerning history of mathematics in teaching; which role does myths have in teaching?) In her story, she included movies, TV and the internet (not including games) - but the examples she used did not include movies - she stressed the value of low-tech storytelling. Instead, her first story example was the story of the length of a year, leap years and so on. (It is a bit difficult to see the difference between her story and normal lecturing, so maybe normal lecturing should be defined as well.) Features of storytelling: are essy to remember, are compelling, are for all ages, embed value, travel, fuel conversation. A story often has a character, ambition, problem, outcome as well as an emotional connection.
The value of storytelling in education is to entertain, inspire and educate. With tertary students, stories can be used as an intro (but is a bit like having the dessert before the main course), as a "by the way", as a commercial break, as a reward (which is how she uses it). You need to get everyone involved and create a "class feeling".
Ingredients: maths connection, human element, tale (start, flow, end), humour. Her second example was "How mathematics burned down the houses of parliament".
With engineering students, she uses the last ten minutes every week (which contains 200 minutes a week) for story telling. She showed a list of examples, much of which the usual history of mathematics "stories". Telling stories takes some effort (you must make it your own), it is a culture that you foster, there are unexpected rewards.
5-10 students leave before the stories all the time. She asked students for comments, and 30 students responded. Categories: emotional impact, reward, motivation, subject impact, appreciation (more approachable), bigger picture (more to maths than this course).
She ended her talk with two stories, one on De Moivre and one called "The story of one, five, seven" on van Gogh's sunflowers.
For me, this talk was an inspiration to dare telling stories more in my own teaching, and to put stress on them, not to tell them apologetically and quickly. However, "making it my own" will probably mean making sure they are relevant to the mathematics and often the history of mathematics that we are working on.
After a break, I was back to TSG47, where there were three talks:
Caroline Lajoie talked on "Learning to act in-the-moment: prospective elementary teachers' roleplaying on numbers". The observation was made in one lesson in teacher education. Her key concept was knowing to act in-the-moment. (See Mason and Spence 1999.) in this context students take role of the teacher and 1-3...students, in front of the whole class. Role play involves introduction time, preparation time (everybody prepares all roles), play time and discussion time. She gave examples on how students, even though prepared, need to improvise. One took a risk in a situation where she was not certain of the answer, while another chose to switch to an explaining mode when he saw that he didn't know what would happen. This came up in the discussion, but that was because students were willing to discuss and "criticize" each other.
Pere Ivars on "The role of writing narratives in developing pre-service primary teachers noticing". "Narratives" in this talk refers to stories about classroom interactions. The hypothesis is that writing narratives will help noticing. Students wrote two narratives, with feedback after the first narrative (and some detail of the feedback given were provided here). The development from the first to the second narrative was more evidence of students understanding in more detail (it is important also to notice that students wrote the first narrative based on observation, the other based on what they themselves taught).
Lara Dick on "Noticing and deciding the "next steps" for teaching: "a cross-university study with elementary pre-service teachers." Noticing is a skill teachers need and that they need to develop. Much work have been done with using video to work on noticing, but little on use of student work (such as the previous one). The current project was a three-hour lesson on multiplication. The students saw student examples and analyzed one each and made posters. The students were asked to attend to the mathematics, interpret what they see and make an instructional decision - based on looking at all the posters. Four major themes: gravitation towards traditional teaching ideas, vague decisions, desire for written number sentences, focus on strategy progression. (This seems like a lesson it would be useful to try to copy with my students as well.)
(About TSG proceedings: there is a format suggestion from the ICME , but it is unclear how much flexibility there is. The suggestion was few but extended papers, while the TSG organizers would prefer shorter but more papers.)
These talks remind me that key concepts to meet for new teacher students are noticing and building on what students know instead of figuring out what they don't know.
After an extended break, I attended, of course, the HPM meeting. Luis Radford gave an introduction to the HPM group, its research and publications, while Fulvia Furinghetti presented the history of the group. Then, Kathy Clark, the new chair of the HPM, gave a presentations with her own background and some views on the HPM. She mentioned two projects: ÜberPro project (Germany; Übergangsproblematik) and TRIUMPHS (US; transforming instruction in undergraduate mathematics primary historical sources).
(The proceedings of the 2016 HPM conference are online here: http://www.mathunion.org/fileadmin/ICMI/files/Digital_Library/History_and_Pedagogy_of_Mathematics_Proceedings_of_2016_ICME_Satellite_Meeting.pdf )
This concluded the last whole day of the conference. However, discussions on mathematics education and other interesting topics continued for many more hours...