Students' difficulties dealing with number line: a qualitative analysis of a question from national standardized assessment

In this paper we analyse some peculiar students’ mistakes in a task selected from the Italian National Mathematics Standardized Tests. In particular we show different types of errors identified in the solutions of grade 6 students who faced an item that involved the management of the number line. We use both the statistical results of the national sample and the qualitative analysis of answers in a smaller sample of 181 students. Our study draws on previous research on difficulties that students face placing rational numbers on the number line. We use an intertwinement of different theoretical lenses to explain the possible causes of failure. We show how some students’ answers can be interpreted as results of different misconceptions. The identified mistakes are related both to the management of the rational numbers representations (i.e. decimal representation and fraction) and to the manipulation of the graduate scale of the number line.