Inquiry-based mathematics and science education have been promoted to address the declining interest of young people for mathematics and science. In my thesis, I conduct an analysis of the International Baccalaureate (IB) using the Anthropological theory of the didactic (ATD) to understand the conditions and constraints behind the implementation of inquiry-based education in mathematics. I also question the beliefs, convictions and attitudes of the IB mathematics teachers towards inquiry. In the field, I analyze the practices of two mathematics teachers and the work of two students on the Mathematical exploration – a research activity involving investigating an area of mathematics. The main result shows that despite the existence of favorable conditions fostering the implementation of inquiry, the identified constraints constitute a significant break and reduce the inquiry potential of the Mathematical exploration. An important contribution is the operationalization of the ATD tools to conduct a posteriori analysis of an inquiry-based activity.