Positionssystemet : Elevers möjligheter att förstå positionssystemet i årskurs 6

Sammanfattning: Swedish students are showing a continuous deterioration of knowledge about the concept of mathematical place-value and by looking at a closer analysis, made by the TIMSS, it was made even more visible that the concept of place-value, which is associated with our positional system, is very central to students' understanding of the number concept. The PISA - report further demonstrates that it is possible to discern the deteriorating knowledge of students' perceptions of digits’ place-values in calculations of standard algorithms. The study is carried out because I want to explore as well as contribute to the research on the opportunities students are given to understand the positional system. The study aims to create knowledge on students' opportunity to understand the positional system in the sixth grade. The questions the study seeks to answer are the following:  What are the different patterns of variation the students meet during the lesson about the positional system?  Which are the critical aspects that can be discerned when listening to the students' descriptions of the positional system? To get answers to these questions, and thus fulfill the purpose of the study, different teachings have been observed and students have been interviewed. The theory of this work is variation theory. This theory was chosen because it makes it possible to understand many different ways to treat a selected subject of matter as well as to relate it to students' opportunities to learn. Results of the study show that students encounter several different parts of the pattern of variation in the teaching about the positional system, including contrast, generalization and separation. By taking in the students' descriptions of the positional system, three critical aspects could be discerned. These were the place-value together with the significance of zero in multi-digit numbers, numbers properties and lastly number sence. The conclusion is that students have different opportunities to develop an understanding of the positional system in the sixth grade. The possibilities are different depending on which critical aspects that are distinguished by the students in the education of the positional system.