In this article, we discuss the potential of a critical approach to standardized tests and their results. In particular, we explore and discuss this potential not only for the assessment of students' mathematical competence, but also for teachers' professional development. We identify and describe two kinds of potential: the Informational Potential (IP) and the Developmental Potential (DP). The IP refers to the information that can actually be obtained by interpreting students' performance results on standardized tests, while the DP refers to the educational opportunities offered by a critical approach to standardized tests and by a re-elaboration of the informational potential.