The origins of discussions about the teaching of mathematics are lost in time. However, it is possible to evoke the creation of the International Mathematical Instruction Commission ICMI, in 1908, as an important mark: a turning point. At that point, it was characterized that mathematics and mathematics education are not of the same ilk and should hence not be confused one with the other. If the age of research in mathematics education is, at least, centennial, the area of studies called “history of mathematics education” is, in all indications, very recent indeed.

Seeking to build a research space of their own, studies about the history of mathematics education have been trying to show that they cannot be considered under the same lens as studies of the history of mathematics: the history of mathematics and the history of mathematics education do not overlap. Once we admit the specificity of the field of the history of mathematics education, the question of what kind of contribution this area can make to mathematics education arises. Pragmatically speaking, we can ask: what does the history of mathematics education offer? Answers to these interrogations can be related to a more general one: What is history for?

For what it is worth, in this text, the job of the historian is considered to be directly connected to our need to build understandings of our world and, given this perspective, its task is that of producing knowledge, through a specific project, in which the researcher is characterized as a historian. What does it mean to consider the historian’s work – the result of that which he or she produces – as knowledge? An epistemological starting point becomes necessary: all human practices represent a consortium –maybe it would be better to say dialectic– between innovation and heritage.

Thus, for example, the pedagogical practices of mathematics teachers always contain a dimension of the past and another which looks towards the future. Both contribute to the realization of original actions. This leads to the conclusion that, without historical knowledge of mathematics education, the possibility of a better understanding of the practices used by mathematics teachers in their daily work is lost.

It is usual that innovative proposals, at least those receiving social recognition, tend to come from outside of the schools for which they are intended. They originate, for example, within specialized research, that may (or may not) result in sustainable educational reforms. Without knowledge of the historical dimension contained in teachers’ actions, such proposals, generally speaking, are left somewhat fragile.

Moreover, an observation, to which we shall return later in different terms, is pertinent here: knowledge of the history behind only the political policies and educational projects adopted at different moments in time can never represent an adequate picture of what happened in the past. Historical knowledge of various other factors including, for example, teacher's pedagogic practices and knowledge of how the job of being a mathematics teacher has been modified over time are also critical.

This brings to the scope of mathematics education the challenge emphasized in the writings of Roger Chartier and which occupied the intellectual life of Michel Foucault, Michel de Certeau and Louis Marin: how to conceptualize the relationships that maintain discursive productions within social practices? The reflections to be outlined in this lecture are intended to contribute to this problematic. What did mathematics teachers do with the prescribed curriculums and with innovative proposals for the teaching of their discipline in their classrooms in times past?

The presentation will seek to discuss this theme, not so much with the purpose to respond to these questions, but to explore what kind of theoretical and methodological considerations are most appropriate for this task. So as to avoid exaggerating the amplitude of the theme, two important contexts for mathematics education will be considered: the educational reforms in the beginning of the 20th century, where the creation of ICMI is emblematic; and what became known as the Modern Mathematics Movement, in the middle of the past century. Both served as key moments in attempts to internationalize the mathematics curriculum. Above all, it will be argued that the production of knowledge related to the theme of internationalization in the domain of mathematics education calls for a historical comparative approach.