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 To answer this question, I first present an unpublished survey with secondary school mathematics teachers (pupils from 10- to 18 years old) about the introduction of the history of mathematics in their classes.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.