Introduction To share educational materials across national or cultural boundaries is becoming more and more common. Sometimes researchers and/or teachers enjoy the idea to share educational resources across borders for a variety of reasons. In the European project Developing Quality in Mathematics Educations II (DQME II) we decided to do it because the project has several common goals across national and cultural borders. The same modelling project will be taught in Denmark, Hungary, Romania and Sweden. Teaching and learning as a national mirror Teaching and learning is not conducted or organized in exactly the same way around the globe. In fact there are huge differences also between countries in Europe. In November 2007 I had the opportunity to experience mathematics teaching in an ordinary gymnasium in Bratislava, Slovakia. We, the observers, were all seated in the back of the classroom. The about 15 students came in and sat down at their desks, silent small talk could be heard. When the teacher arrived, they all raised into an almost military “attention”, standing silently beside their desk, all staring straight forward. The teacher walked up to her desk and called out: "God morning, students". The students were about 18 years old and in a natural science program, and they answered in chorus: "God morning, teacher!" After that the lesson started with carefully, well prepared exercises -- the content were geometrical series, both finite and infinite. The teacher set the agenda and the students immediately reacted when the teachers gave them a sign to step up front and do some calculations at the black board. No discussions among students were heard. The students were allowed to borrow fairly modern calculators from a mutual cabinet, but no student used the calculator. Compare that to a "normal" lesson at a Swedish gymnasium I visited two weeks later, with students at the same age and also in a natural science program. The teacher went in first in the classroom to make sure that everything was in order. Then she opened the door to hallway outside the classroom, allowed the students to come in, looking them in their eyes and exchanging some small talk to each and every one when they passed her. When the class was in order after some five minutes, they almost started to negotiate. What should we discuss today? What did we do the last time we met? Is everybody satisfied about what they know about geometrical series? (The content was more or less the same as in the school in Bratislava). After some discussions, the teacher clarified some basic concepts in the theory of geometrical series on the black board before the students started to work on a small project task, organized in small groups. The teacher walked around in the classroom, assisting the groups when they asked for help, but not really teaching. She seemed to be listening more than talking. All students had their own calculator, which they used regularly together with paper and pencil techniques. The level of discussion was sometimes very high. Is it self evident that I saw the facilitation of the same mathematical learning taking place in these two classrooms? Is it possible to use exactly the same tasks in the two classroom situations? Research questions: • What can pass as a suitable mathematical modeling project in four different countries? • How will mathematics teachers in four different countries actually teach the same mathematical modeling project? • What will the students in these four countries learn and how will it be assessed? • What will be different in students' learning outcomes between the four countries?

Comparative studies, Assessment of mathematical modeling (see reference list)

That the schools in Sweden and Denmark and their way to teach is more suitable for project work, but that Hungary and Romania will benefit from more mathematical students. The main challenge will be to convince the Hungarian and Romanian teachers.