ICME Day 1

The first day of ICME was a light one. It started with a two-hour opening ceremony, with a combination of welcome addresses and cultural performances, which was an eclectic combination of Korean and Western style, just as modern-day Korea. It is always nice to attend these opening ceremonies, as they try to convince us of the importance of our work in general and the conference in particular. This time, there was a recorded address from the president of S. Korea. Thereafter, the Felix Klein and the Hans Freudenthal awards for the last four years were awarded. Of course, I was particularly pleased to see Luis Radford get his well-deserved prize.

The first plenary lecture was by Don Hee Lee. She spoke on the topic "Mathematics education in the national curriculum system". She discussed the place of mathematics in the educational system, taking Plato as her starting point. Is mathematics taught mainly for the intellectual development of "the liberal man" (learning for its own sake) or for the development of society?

She quoted a Korean professor of mathematics (without necessarily agreeing) claiming that there is no mathematics that is both easy and interesting at the same time. Mathematics is based on thousands of years of intellectual work, and therefore advanced. While this is an interesting point of view to share with pupils who have unrealistic ideas of the amount of work (or lack thereof) necessary to learn mathematics, it should probably not be a credo for a mathematics teacher. 

For regular lecture today, I chose Alan Schoenfeld's "How we think: A theory of human decision-making, with a focus on teaching". Alan Schoenfeld received his Felix Klein Award in the morning, and the lecture hall was so crowded that the organizers immediately decided to ask him for a rerun later in the week. 

The starting point of the talk was the question "If I know enough about you, can I explain every action you do and every decision you make?" He claimed that the answer was yes, with the important caveat that he is talking about situations where you are an expert. Thus, it holds for the cooking of a chef, the teaching of a teacher and the setting of diagnoses of a doctor. So what do you need to know about a person to be able to explain his actions? You need to know about his knowledge/resources, his goals and his orientations (beliefs/values...)

The word "explain" is not meant as a mere verbal explanation, but the ability to set up a model which can - to a degree - predict the actions.

Why look at teaching? As he put it: "If you can model teaching, you can model just about everything." Teaching is highly complex; it is highly social and it is ever-changing.

He gave a few examples of how he has worked with teachers to model their behaviour. He gave one example of teacher who believes that he cannot tell students anything unless it's based on something the students already have said - and therefore is lost when the whole class agrees on a wrong answer. His actions were to a large degree explained by this belief. Another example - a teacher who teaches by raises issues, asks for student suggestions, clarifies and then moves on. He transitions to the next issue when goals are met. So what does he do when things don't go as he wants ? According to Schoenfeld, he "doesn't have a choice" - he will still build on the students' questions/input and discuss them with the class. His beliefs determines his actions.

His third example was on Deborah Ball teaching a 3rd grade class. She did some surprising things, including at one point asking a question that many would consider a mistake, as it derailed the discussion with the class. Schoenfeld didn't understand what Deborah was doing. Could it be modelled? And what about Deborah's "mistake"? After years of studying it and discussing it, he came up with a model here as well. Yes, her behaviour was consistent with a model. Within the model, her "mistake" was based on a need to understand her students' thinking before going on to the next topic.

So what's the point? Why are models important? I would ess that they are not, but that they serve to point out the importance of a teacher's resources, goals and beliefs (etc). If two experienced teachers do things very differently, we should not assume that it is because of some insignificant chance. It may very well be because of some fundamental difference. And of course it doesn't help much to give teacher students the necessary knowledge and skills to teach well, if we don't also consider their beliefs. As Schoenfled put it: a teacher who believes that only the best students can do problem solving, will not even try to give his poorer students problems to solve.

Schoenfeld's way of thinking seems highly relevant to the research project I'm currently involved in, and I will keep it in mind...

The rest of the day,  I got prepared for Tuesday - the day of my little talk.