The quality of conceptual change in mathematics – the case of number concept

In this article, the main results are presented from a number concept test in which 538 students from 24 randomly selected Finnish upper secondary schools took part. The test included identification, classification and construction problems in the domain of rational and real numbers. In addition, the students were asked to explain their answers and estimate their certainty about them. The theories of conceptual change and of mathematics concept formation were used to categorize students’ explanations into different levels. The results indicate the clearly restricted nature of students’ prior thinking of whole numbers and of their everyday experiences of counting and continuity. On the basis of the results, we claim that the problems that students have with these difficult concepts are not only due to the complexity or abstract nature of the concepts to be learned, but also to the quality of their prior knowledge, which is not sufficiently taken into account in traditional teaching.