On the role and scope of historical knowledge in using the history of mathematics in education

The aim of this paper is to gain a better understanding of the role and scope of historical knowledge in work on using history of mathematics in education. This work can come from three types of actors, namely, teachers, teacher trainers, and educational researchers. The texts written by these actors show that their objectives and practices can be different, as is the historical knowledge they deploy. We can read writings of teachers who seek to 'give meaning' to school knowledge, by integrating original texts into their teaching progression. We also can read writings of educational researchers who prepare 'history capsules' for teachers, which can be introduced into teaching from time to time. To carry out this research, I focus on analyzing the complex relationships between the following three poles: objectives, pedagogical practices, and historical knowledge. To this end, I use the notion of ideal types introduced and developed by the sociologist Max Weber. Section 1 is devoted to the construction of ideal types corresponding to my aim. Based on these ideal types, in Sect. 2, I elaborate on the role and scope of historical knowledge in concrete situations where the history of mathematics is used; specifically, on the one hand during the reading of original texts in an educational context, and on the other hand, in the particular context of teachers education. Some further comments are made in the third and last section.