The construction of the National Common Curricular Base (NCCB) for the area of Mathematics and its High School Technologies in Brazil and the last update of the Mathematics Program for High School in Paraguay are prescribed curriculum documents in force for the teaching of Mathematics in these countries. The construction of each one of them exposed intense political elements and has been a constant target of conflicts and tensions in these countries. The policy cycle approach, established by sociologist Stephen J. Ball and collaborators, has usually been applied by curriculum policy researchers, as well as from other sectors. Therefore, it has been configured in an important methodological bias for the understanding of the documents’ approval processes from the contexts of production and influence, as well as the standards that guided this construction and the ideological constraints that emanate from the involvement of multilateral organisms. In order to achieve this objective, this article presents a comparative analysis of documents in specific circumstances during the processes of the recent reforms of the prescribed documents for mathematical learning in Brazil and Paraguay. It starts from the methodological phases of Comparative Education, summarized by Pilz (2012), by which it reflected on the vertical models and the reductionism and emptying of the area, as well as the contents as instruments of management and performance to meet the varied demands of the globalized world. The theoretical hybridization carried out in the study also pointed to a greater number of specific competences prescribed for the teaching of Mathematics in Brazil, and in Paraguay, a curriculum that prioritizes more functional Mathematics.