The main aim of this paper is theoretical and methodological: to show how The Antropological Theory of the Didactics – in particular, the construction of a praxeological reference model – can be used as a foundation for developing a diagnostic test tool which examines students technical and theoretical knowledge of basic algebra (and related arithmetical knowledge on which initial algebra is based). The point is to provide explicit control on what is being tested, for instance, in relation to a given national curriculum, and in relation to teaching interventions.