Abstract
The teaching of Mathematics must respond to two different demands. The first intends that its theoretical constructs serve to understand the teaching-learning processes of Mathematics, and the second serves to guide the improvement of these processes. The first demand requires tools for a descriptive and explanatory approach to teaching that serves to answer what has happened here? How and why? The second demand needs tools for a valuation of the teaching that serves to answer the question: What could be improved? These are different, but closely related, demands. This paper reflects on the constructive criteria of pedagogical suitability within the framework of the problem of the role that assessments and normative principles should play in teacher practice (second demand). More generally, a theoretical development work of the pedagogical suitability construct is carried out: how it originated, what it leads us to and how it can affect the practice of the Mathematics teacher.