The developments in mathematics in the decades around mid-19th century led some professors of mathematics and science from the University of Padua to ask themselves significant questions about the teaching and learning methods of their disciplines. The scholars of the « Studio Padovano », name of the faculty of philosophy and mathematics at the University of Padua, to which we will refer, are: Giovanni Santini, Giusto Bellavitis, Domenico Turazza, and some others. They worked on developing ideas and hypotheses on a new legislation related to teaching and on finding the most appropriate ways to influence decisions about those matters at the institutional level. They also worked on drafting educational projects for original approaches to their teaching subjects and their actual implementation during lectures with students. From the pedagogical-educational point of view, the steps to obtain a good transmission of knowledge to the new generations were the subject of a debate (through an exchange of correspondence) and also were the motivation for the production of appropriate publications on the subject. The analysis of this material, still partly handwritten and unpublished, illustrates a complex moment in which these scholars already acted as if they belonged to the very same state, although still under the Austro-Hungarian legislative sphere. The study of this material can also provide interesting points of comparison with the problems that characterized the scientific activities of subsequent periods.