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Many international studies focus empirically on integrating the history of mathematics in mathematics education. Over the last 2 decades, some studies also revealed theoretical elements concerning the implementation of learning sessions and/or their didactical analysis and effectiveness. This paper has the aim of complementing these empirical studies with a more systematic approach in the French context. Defended for decades within the IREM (Institut de recherche sur l’enseignement des mathématiques), the history of mathematics is now officially introduced in the French curriculum. Nevertheless, is it really sufficient for teachers to change their habits by implementing the history of mathematics in their practices? To answer this question, I first present an unpublished survey with secondary school mathematics teachers (pupils from 10- to 18 years old) about the introduction of the history of mathematics in their classes. This survey allows the comparison of teachers’ desires (‘history of mathematics in potentiality ’) and realities in classrooms (‘history of mathematics in actuality ’). Then I focus on French mathematics textbooks (for pupils from 15- to 18 years old) in order to question their effectiveness as tools for the introduction of a historical perspective. I describe the historical/mathematical tasks available in these textbooks focusing on their reference to Fibonacci. Finally, I present a proposition to implement the history of mathematics in mathematics education starting from the textbooks, aiming to help mathematics teachers to redesign the tasks of their textbooks so as to be more relevant.

Les traductions arabo-latines, et particulièrement celles réalisées en Andalus au xiie siècle, nourrissent l’Europe latine de nouveaux savoirs et méthodes. Ici, nous nous intéressons à l’art mathématique de la résolution de problèmes, qu’ils soient géométriques ou arithmétiques. Nous avons isolé, dans plusieurs codices datés entre le xiiie et le xve siècle, un corpus de textes techniques et didactiques dont la stabilité, dans l’histoire des copies, interroge l’historien des mathématiques. Son étude nous permet non seulement de dévoiler la forme et le contenu d’un tel corpus mais aussi de montrer la cohérence entre l’entreprise probable du traducteur tolédan Gérard de Crémone et le devenir de ce corpus en termes de circulation et d’appropriation. Arabic-Latin translations, particularly those made in Al-Andalus in the twelfth century, provide Latin Europe with new knowledge and methods. In this contribution, we focus on the mathematical art of problem solving, both in geometric and arithmetic fields. We have isolated, in several codices dated from the thirteenth to the fifteenth century, a corpus of technical and didactic texts, the stability of which, in the history of copies, challenges the historian of mathematics. Studying it allows us not only to reveal the form and content of such a corpus but also to show the coherence between the probable work of the Toledan translator Gerard of Cremona and the future of this corpus in terms of circulation and appropriation.

Les traductions arabo-latines, et particulièrement celles réalisées en Andalus au xiie siècle, nourrissent l’Europe latine de nouveaux savoirs et méthodes. Ici, nous nous intéressons à l’art mathématique de la résolution de problèmes, qu’ils soient géométriques ou arithmétiques. Nous avons isolé, dans plusieurs codices datés entre le xiiie et le xve siècle, un corpus de textes techniques et didactiques dont la stabilité, dans l’histoire des copies, interroge l’historien des mathématiques. Son étude nous permet non seulement de dévoiler la forme et le contenu d’un tel corpus mais aussi de montrer la cohérence entre l’entreprise probable du traducteur tolédan Gérard de Crémone et le devenir de ce corpus en termes de circulation et d’appropriation.