Teaching through variation has been proved to be an effective way of teaching mathematics in China, but has also a profound theoretical foundation both in China and France. Developing my PhD with two co-supervisors, in China and France, I construct a model of “teaching mathematics through variation” by trying to integrate these two theoretical approaches with the Documentational Approach to Didactics focusing on teachers/resources interactions. This model distinguishes potential, actual and practical variation and is based on the process of transforming potential variation into actual variation, and of using practical variation for rethinking potential and actual variation. This thesis is situated in between China and France of two traditions and cultural contexts, aiming to think fruitful interactions between them and improve the effectiveness of mathematics teaching by understanding the role and evolution of variation in teacher’s documentation work.

Three research questions are explored: 1) What are the potential variations in the upper secondary school mathematics textbooks and other curriculum resources in China and France? 2) What are the actual variations in the Chinese and French cases to achieve the teaching goal? 3) What are the practical variations in Chinese and French cases? How does the case teachers respond to the practical variations?

We followed in both countries the available resources and the documentation work of two experienced mathematics teachers of upper secondary schools, focusing on the topic of function. This study allows to enlighten our questions of research and to refine our initial model. It opens new perspectives for taking variation into account variation not only for a given task, but also for the enrichment of teachers’ resource systems, and for their professional development.