Matematikundervisning i internationella miljöer : En studie av arbetet med att överbrygga skillnader i matematikundervisningen

Sammanfattning: This study investigates the difficulties that may arise for students as a consequence of differences that exist in mathematics education between different educational systems. The questions asked are when and why difficulties as a consequence of differences in writing or types of student problems may arise and in which way teachers and students attend to these difficulties. The focus is thus on the written parts of mathematics education and the questions are asked within the frame of general upper secondary education.In order to answer these questions, a sociocultural perspective based mainly on Sfard’s (2006) participationist theories together with Vygotsky’s (1999) general theories on development and learning is used. An important analytic tool is the discourse concept which in this context means a type of communication that brings some people together while excluding others from the communication. From this perspective the different rules that govern the way student problems are formulated and the ways of writing that will be accepted, may be described as parts of a specific discourse in the mathematics education rather than universally accepted truths.The study has been based on a qualitative research method and has included observations of lessons and semi-structured interviews with teachers and students. In order to give a global picture, four schools have participated in the study and one week has been spent at each school. The selection has consisted of one international school with IB education, two schools abroad (from different countries) and one Swedish upper secondary school.The study shows that difficulties occur for students and that these are mainly due to differences in the mathematics education between the different educational systems. Partly, the student problems have proved to differ in crucial ways and therefore it is difficult for students to interpret and find solutions to unknown student problems. Besides, the mathematical writing differs in many fields such as text editing, use of mathematical notation and algorithms, and this also causes difficulties. In order to overcome these difficulties, teachers and students use methods which aim at creating habits for the new way of working by showing the practices to the students who then repeat them on their own accord.Apart from the direct answers to the research questions, another great problem for students who start studying mathematics in a new educational system appeared to be lacking basic knowledge, which means that they lack certain essential knowledge and calculation proficiencies that are necessary prerequisites. This problem is specifically preponderant for students with Swedish educational background. Furthermore, it appears that the teachers at the international schools are much conscious of the fact that there exist differences in mathematics education and in general they consider it inspiring to be able to learn more from the knowledge of their students.By interpreting the differences in the mathematics education as representative for different discourses, it has been possible to understand that the difficulties that arise are due to the fact that the student has not yet individualized the new discourse. This means that the student is only able to carry out the discursive routines collectively, with aid from the teacher or the group, which explains the routine creating practices used by teachers and students. When the student has worked within the new discourse it will be individualized and the student will be able to work within the discourse in a deliberate and independent way. For the education, thisimplies that the students will first be able to perform certain routines within the discourse before a comprehension of the rules that govern them will be achieved.Since the problem of lacking basic knowledge is due to a total lack of the students’ necessary prerequisites, it is possible to interpret this problem with help of Vygotsky’s (1999) reasoning. The knowledge assumed by the new discourse does not lie within the zone of proximal development and therefore the conditions for learning are not fulfilled. The positive and reflective attitude of the teachers with respect to differences in the mathematics education differs in a decisive sense from the literature and appears to influence the possibilities to overcome the difficulties in a positive way.