A history of the graduation of knowledge: elements for the analysis of mathematics for teaching

This article was developed within a collective research project whose theme involves historical investigations on the constitution of the professional knowledge of the teacher who teaches mathematics. Based on the theme of this project, this text initially focuses on differentiating “mathematics teaching” from “mathematics for teaching”. Under this perspective of analysis, the objective of the study is to build the graduation of teaching as a research object, from a historical analysis. To this end, the problem to be dealt with in this work can be summarized in the following question: How to historically characterize the graduation of teaching mathematics for teaching? The results of the work show that the graduation is presented as progression, programming, sequence and march of teaching, depending on the scale of observation in which it is treated.