This paper aims at making theoretical-methodological contributions to investigations that analyze the production and systematization of knowledge about teacher training and teaching by experts in education. To do so, we consider studies in the fields of History of Education and History of Mathematics Education. Our research work is justified, in the historiographical field, through the nature of the knowledge we intend to analyze, that is, the knowledge systematized by experts in regulations, decrees, teaching manuals, textbooks, school notebooks, etc. The study of such knowledge is interested in 1) enabling the understanding of the processes and dynamics of the constitution of knowledge in training and in teaching from a historical perspective; and in 2) highlight on the education expert`s role in the production process of such knowledge, which are considered here as “mathematics to teach” and “mathematics for teaching”, which are, respectively, a teacher’s object of work and working tools. Our investigation supports the hypothesis that “the different types of mathematics” change over time, and that education experts are the bringers of such change.
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