The first day of ICME13 (The thirteenth international congress on mathematical education) was Monday 25th of July, 2016. This conference takes place in Hamburg, Germany. As usual, I will try to blog from the conference (as I noted yesterday).
I missed the conference opening ceremony, but got there in time for the plenary panel on "international comparative studies in mathematics: lessons for improving students' learning". (Not that difficult, as the conference was at that time 40 minutes behind schedule.) The panel participants were Jinfa Cai, Ida Mok, Vijay Reddy and Kaye Stacy. The panel was based on a paper to be published (open-access) shortly.
The panelists each talked on one lesson to be learned about international studies, defined as studies involving at least two "countries", with an intention to compare them. Such studies are good to understand ourselves and to understand different possibilities.
Lesson 1: examining the dispositions and experiences of mathematically literate students. Kaye Stacy talked about large international comparisons, PISA in particular. She showed how PISA 2012 were trying to unpack the scores by looking at the processes of doing mathematics. Different countries had different patterns - for instance, Japan had a high score on formulating, lower score on employing and interpreting. Netherlands and the UK had very different profiles. (English-culture countries were best in interpreting.) This fitted not very well with students' answers about their exposure to different kinds of tasks. She also showed graphs showing huge gaps in confidence between boys and girls in some countries (i.e. Australia, but not Shanghai). We need to draw evidence from different sources to inform policy.
Lesson 2: Understanding students' thinking. Jinfa Cai talked about small-scale studies, trying to understand students' thinking when trying to solve tasks. He showed two tasks, one where average is demanded, the other where the average is given. About a fourth of students in both countries got the first task right and not the second task. He showed some of the different errors in the second task - most concerned adding and dividing, as in the (correct) solution of the first task.
He also showed the "pizza ratio problem", where he also gave different solutions, some of which were almost only used in one of the two countries studied. Thus, comparative studies gives a broader sense of possible ways of thinking.
Lesson 3: Changing classroom instruction. Ida Ah Chee talked about TIMSS Video Study and Learner's perspective study. They have complimentary roles. TIMSS Video Study showed that teaching was a cultural activity. LPS compares lesson structures and lesson events and looks also on practitioners' thoughts about their lessons. Lesson events are as different as lesson structures. Analysing structure and events in light of teacher interviews give an even richer picture than the TIMSS Video Study did.
Lesson 4: Making Global Research Locally Meaningful: TIMSS in South Africa. Vijay Reddy talked about the sociopolitical perspectives. She stressed how big differences is a fruitful ground for research. In the Apartheid system, bad education in mathematics for large groups was explicit policy. After 1994, improved access to education has been a priority, but improvement is slow. Mathematics results is a proxy for equality. She discussed how TIMSS can be used to understand the local development. South Africa had big inequalities in the TIMSS scores, reflecting social inequalities. Finally, in 2012, results are better. TIMSS also shows that the level of violence is higher on SA than in any other country.
The "panel" did give some ideas for how to use international studies for better understanding, and there are surely lots of data out there that can be looked at, as an alternative to always collect your own data...
After lunch, I attended the talk by Emma Castelnuovo-Award awardees of 2015, Hugh Burkhardt and Malcolm Swan (in absentia). It is particularly interesting to see proponents of what we in Norway call "utviklingsarbeid" awarded and given prominence at such a conference. Their work have resulted in many beautiful tasks and sets of tasks, carefully designed to facilitate particular learning outcomes.
First he gave information on ISDDE, which has goals of building a design community, raising standards, increase influence on policy. Educational Designer is a journal and the website is isdde.org.
The talk was very inspiring, but difficult to write notes about, as many of the points mentioned were illustrated beautifully with examples of tasks and student responses. But here are a few points:
- The Shell Centre wanted impact through useful materials, with focus on design. Materials need to fit the system they aim to rearch. It doesn't help if materials are brilliant if they don't work. Therefore, engineering research involves design research and systematic development.
- Tasks can provide 'microworlds' for learning.
- They talk about novice tasks, intermediate tasks and expert tasks. Expert tasks involves complexity and unfamiliarity, which means that the technical demand cannot also be high. He gave many examples of the three levels of tasks.
- The usual role of a teacher is to manage, explain, set tasks. Certain tasks facilitates "role shifting", and role shifting changes the classroom culture.
- In general, what this team wants to achieve is technical fluency, conceptual understanding, strategies, appreciation.
- Mostly, lessons that they develop are either concept focused or problem solving focused. Concept focused lessons are developed in the "diagnostic teaching" way. He gave examples of different kinds of the two kinds of lessons.
This talk was a whole lot more inspiring than what these points suggest. He suggested making small units of lessons so that a teacher could substitute their textbook for a few weeks, without having to make a bigger commitment. I would be interested in joining such an effort...
Then there was a discussion on a survey on competences, led by Mogens Niss, joined by Regina Bruder, Nuria Planes and Ross Turner. The main issue is "What does it mean to master mathematics?" (Which also begs the question what we mean by mathematics.) We may talk about the products of mathematics or about the enactment of mathematics. Knowing and doing is not the same thing.
Classically, the answers were given in terms of content and related facts and procedural skills. Criticised in Spens report 1938, by Pólya in 1945 and so on. The first IEA study in the 1960s included several components. Also, Papert in the 1970s commented. Since the 1980s, there has been a trend focusing on enactment.
Ross Turner asked what are the relationships between mathematical literacy, numeracy, quantitative literacy, mathematical competence/competencies, mathematics. How would a Venn diagram look like? Or, if you put them in a diagram with products and applications on two axes, how would it look? (As usual, I'm trying to figure out where the history of mathematics and other integral cultural parts of mathematics fit into such a diagram - I think it shows that the concepts here are too narrow. - at least, to "products" should be added "background". Turner, however, put history into applications.)
Regina Bruder talked about two types of research: research where the construction competencies are an object and research where it is a means. One important discussion is whether it makes sense to discuss mathematical competencies without specifying which domains they are related to. Also, it is discussed if affective considerations should be included. Also, can they be detected empirically? In general, yes, but they are often overlapping and are not developed or enacted in isolation.
Mogens Niss and the others then discussed how competencies have played roles in different national curricula. Nuria Planes explained that in Spain, competencies have had a big inpact on paper but not in actual implementation and practice. In Latin America, processes have been included in curricula. Ross Turner told us that in many countries in South East Asia, doing mathematics is clearly included in curricula. But of course, the main question is how these words are implemented. Regina Bruder told much the same story for Germany. In Austria, personal and social competencies are included.
Then, challenges to implementation were discussed, but this seemed to be the usual list of points. The conclusion was that bridges between action and research is needed - which ties this panel nicely to the previous talk - research and development (in Norwegian: FoU) both are needed, and need to work together.
That concluded the first day of ICME 13. A day with a varied scientific programme, with a big delay in the morning and with serious temperature problems in the afternoon (the buildings obviously not built for full auditoriums in late July). My choice of outfit (shorts + t-shirt) will be repeated for the days to come.
And as usual, most important is what I do not mention here, lots of talk with colleagues over coffee, lunch, beer and dinner and in-between.