The so-called Movement of Modern Mathematics (MMM) was constituted in a set of actions occurred in a great part of the world, originated by the mismatch between the development of the Mathematical discipline and the teaching. which in general aimed to modernize the teaching of Mathematics, changing and updating the contents and methods, encouraging the participation of teachers in events where the theme was discussed, especially in the 1960s. To a great extent, in the initial grades, curriculum and programs were influenced by the studies of the Hungarian mathematical educator named Zoltan Dienes (1916 - 2014), who disseminated his studies in Brazil through a group of studies, mainly the Grupo de Estudos do Ensino da Matemática (GEEM). In this scenario, the present work is linked to the broader Project Mathematics and the first school years: processes of internationalization, institutionalization, professionalization and circulation (1880-1970), developed by the Mathematical Education History Research Group in Brazil (GHEMAT). This major research is based on studies about knowledge involved in teacher education by the Research Team on History of Educational Sciences (ERHISE) of the University of Geneva in Switzerland that distinguishes the knowledge to teach from the knowledge to be taught, treated from the point of view Historical, as products of school culture and therefore as consumption of a culture of "outside", as an attempt at emancipation. In our text, we deal with the processes of emancipation, professionalization and circulation of mathematics to teach, applied at the School Vera Cruz of São Paulo (from 1965 to 1975), an institution that during the 1970s acted as a training center for teachers in new methodologies. We have as main objective to analyze the mathematical knowledge present in the set of notebooks of the initial series. Anchored in studies of the history of education and cultural history, this analysis has as its guide the question: what do the set of notebooks on mathematics taught in the initial series of the Vera Cruz School (1965-1975) reveal?

We conclude that, influenced by Cognitive Psychology and Structuralism, the education started to explore the Mathematics as a unique structure, with an emphasis on functions and relationships, seeking to develop a new methodology and consequently another organization of school mathematics based on the exploration of simple mathematical structures, the student participation, the use of structured manipulable material and the respect to the times and spaces necessary for the construction of axiomatization. Therefore, it was necessary for the teacher to understand the new approach, to elaborate a methodology appropriate to the specificity of the teaching in the initial grades, with more attention to the activities that preceded the abstractions aiming the emancipation of the student.