Within the theoretical framework proposed by the Anthropological Theory of Didactics (ATD), this text deals with two issues that have in common to come from works about problem solving in mathematics. The first one focuses on the praxeological developments students have to carry out in order to use with some efficiency their mathematical theoretical knowledge in the problems they faced to all along the secondary and tertiary curriculum. Students' personal work appears to play a decisive part in these developments which are mostly ignored by the didactical systems. Students are supposed to take on more and more responsibility within the studying and learning process, with special speeding-up of the process at the institutional changes between junior high school, high school, college and university. This issue is presented in the first two chapters. The second issue deals with mathematical knowledge' and more generally mathematical praxeologies'life, within the institutions, institutions being considered as key components of human societies. Different dynamics are considered from emergence to transposition and use in various professional as well as teaching contexts. Supporting on examples associated with these different dynamics, chapter 3 presents an evolution of the ATD praxeological model with a double-faced purpose: 1.explicitly taking into account the range of knowledge produced in the various institutions in which mathematical techniques live; 2. representing in the model the institutions and the processes which produce and recognize the considered praxeology. This model is finally briefly related to several fields of research dealing with professional topics, from the UK works on mathematics in the workshop to some French vigotskian ones on cognitive ergonomy and professional activity.
