On the assessment of mathematical competence: keys in moving towards an interpretive approach

In this paper we discuss the problem of the interpretation of mathematical competence
in the classroom. In order to overcome some of the controversies affecting the approach by competencies, we intend to move towards an interpretative approach of mathematical competence in which the mathematical knowledge and their understanding are more significant. The potentiality of our proposal is shown through an example of interpretation of mathematical competence of a secondary student in solving a specific algebraic task. The uses of mathematical knowledge provide evidences on how the traces of mathematical competence and understanding of different nature emerge and they relate to each other.