Canada – professionally

Seeing as I wasn’t in Canada more than 2 months and the purpose of following 2 courses at a francophone university was comparing how math is taught in French to how it is taught at a Danish university, I’ll concentrate on the way the teaching was performed.

I followed a course in non-linear statistical modelling and a course in math didactics for high school. The latter was offered  by the faculty of math in cooperation with the faculty of education.

A lesson at a university in Canada lasts for 75 minutes (it lasts for 45 minutes in Denmark). Then you have a 15 minute break before the next class starts. The statistics course I took had lessons Mondays and Fridays, but just one 75 minute lesson at a time (in Denmark you always have at least two 45 minute lessons no matter which subject, one after another, with a 15 minute break in between), after which the students had to hurry off to their next lesson. This isn’t optimal in terms of coming from afar and wanting to get to know your fellow students. The math didactics course was Tuesday evenings from 6 pm to about 8:45 pm, with a 15 minute break after about 75 minutes.

The way an actual math course is taught at a francophone university doesn’t differ much from the way it is taught at a Danish university. The teacher is very traditionally standing next to the blackboard, speaking and writing the most important details at the blackboard, while the students try to follow and take notes. Sometimes questions are posed to the class, but the teacher will answer them in case the students can’t, and this is as far as student involvement goes. Our teacher did make a bit of an effort to see if we could follow him, but didn’t feel obliged to stick to the chronology of the notes and normally he wouldn’t say how far in the notes he’d get in a specific class. However, he would normally say so in the beginning of a class if he expected to finish a chapter of the notes during that lesson.

Homework is given in a more spontaneous and irregular way than I am used to from the University of Copenhagen. The course didn’t have a web page, we didn’t get any weekly plans, and homework was given without prior warning at the end of a class, usually for the next class. Seeing as classes were Mondays and Fridays, it would often happen that the homework was given to be done over the weekend, which is something that everybody makes an effort to avoid at the University of Copenhagen. At the University of Copenhagen there’s a lot of group work, but this wasn’t done here. We were not asked to form groups and do the homework together, actually it didn’t seem as if the idea of group work even occurred. Nobody asked about it.

Apart from an exam in the end of the course, there were 2 tests during the course. You sit such a test during one 75 minute lesson, and you’ll get the result at the next class or the class after that.

The way the math didactics course was taught was more interesting. Even the tables were set up so that you were forced to form groups, and typically a class started by a discussion of the articles or chapters that we had read for that class, after which the rest of the class would be devoted to group work and presentations of the group work. The group work could be anything from making a poster explaining a certain theory within math didactics through solving the problem: “how does one find the area of a regular pentagram?” to improvising short plays on different angles on math teaching. Apart from this we had a visit from an employee in New Brunswick’s department of education, who took us through that province’s educational plan for math in high school.

In some classes we were supposed to get acquainted with CASMI, which is an interactive math education site on the internet. The school pupils log on to this, solve some math problems of increasing difficulty, of which you get new ones every week, and get feedback from the math teacher students. There is a very long online form to fill in in order to give feedback, containing parts dealing with everything from the quality of the solution of the problem through the pupil’s understanding of the problem to the correctness of the French grammar the pupil used in his or her solution. I was quite surprised by the latter as grammar doesn’t make much difference one way or the other in a typical Danish math situation. When I commented on this, I was asked by my group mates if we don’t have grammar in Danish at all?

The purpose of this was to train the students in giving proper feedback. This was also discussed a lot and in much detail in the course books. The desired angle is to support and help the pupil find the solution him- or herself by connecting known phenomena with a thorough understanding of a new problem. Repetitive, unvaried work is regarded as a counterproductive and undesirable way of learning math, seeing as the student in most circumstances won’t be able to use the gained knowledge to solve similar problems in which the learned-by-rote method can’t be applied uncritically.

Mathematical problems should always be represented as “problem-situations” in which the actual mathematical problem is camouflaged as an everyday situation. For instance: “the florist of Moncton makes bouquets. Each bouquet must contain 15 flowers and any one bouquet can’t cost more than 20 dollars. He has 2 kinds of flowers, roses and irises. A rose costs 2 dollars, and an iris costs 1 dollar. Can he make a bouquet with 8 roses and 4 irises?”. This specific problem-situation is interesting, because most students are likely to say yes, because the bouquet is exactly 20 dollars, though the correct answer is no, because this bouquet only has 12 flowers as opposed to 15. It was taken from a French survey into the level of actual mathematical understanding of French school pupils.

“Modern” teaching with as much student involvement as possible was presented as the best and most desirable way of teaching. This entails, among other things, that the students can decide for themselves which themes they want to work with and which angles of approach, they want to take.

This way of teaching was obviously strictly adhered to in the math didactics course, while the actual math course I also followed, was taught in a way that included more or less all the things the math didactics course books say you shouldn’t do in teaching math. There’s a bit of way from theory to practise, both in a francophone university in Canada and in a Danish one in Copenhagen.