A number of reforms have taken place in the teaching of mathematics over the past thirty years in France, most particularly in the teaching of analysis. These reforms have attempted, apparently in vain, to reconcile two imperatives: the need for rigour, proper to all mathematics education, and a pedagogic requirement for understanding and the transmission of meaning. But since meaning concerns ideas which have to do with infinity (irrational numbers, the infinitely small, infinitely large, limits, ..) intuition, which is necessary for appreciating meaning, comes up against contradictions, and is incapable of a full appreciation of the conceptual richness of the ideas that mathematicians have developed over time in the field of analyses. The solution which seems to have been adopted in latter years has been to largely abandon the idea of teaching meaning, in favour of methods which are essentially numerical, but which give the illusion of rigour. But such rigour as there is, occurs only in dispersed islands, preventing any appreciation of a global and structured meaning, in favour of purely formal rules. Another solution seems possible, which preserves our concern with meaning, while at the same time structuring the mathematical thinking of the students in a coherent and rigorous way: this consists in setting mathematics and its teaching in a historical context. In this way, the meaning and the rigour of mathematics are no longer absolute, contradictory or inaccessible, but are interactively constructed, along with the student’s mathematical insight, by a process which is dynamic and living. (ZDM/Mathdi)