Large-scale evaluations have played a relevant role in the contemporary field of education, not only because of their importance in providing a more precise assessment of the proficiency of large numbers of students, but also because of their use as a means of producing more reliable elements that are used in the improvement of educational policies. The proficiency scales adopted in these evaluation programs are a very important part of this process, for they are employed by educational evaluators and decision-makers as an instrument able to gauge and interpret the students` levels of proficiency in the many different abilities that compose the knowledge domains under investigation. The object of this thesis is precisely the proficiency scales used in large scale evaluation systems, which are treated according to three different approaches: First an investigation is made about the relative merit of different methods of association between the items that make up a test and the significant points or levels of proficiency in several scales that have been employed by different evaluation programs. Then, by using a 4th-grade Mathematics proficiency scale, an alternative approach to characterize levels that are representative of a proficiency scale is developed. This is done by the use of a cluster analysis method aimed at choosing a subset of items that characterize each proficiency level. Finally, a pedagogical interpretation of the clusters formed along the proficiency scale is obtained through the consideration of teaching and learning of Mathematics education basic skills, related to the beginning series of the fundamental level. The methodology used in this process is the analysis of the nature of mental operations that characterize each one of the competencies and skills that are typical of each cluster, by adopting references to Mathematics learning processes as basic assumptions.