Recognition of practices, objects, and processes in solving mathematical tasks: a mathematics teacher's competence

The analysis of mathematical tasks and its different ways of solving them are necessary to understand the potential and actual students' learning difficulties. The design and implementation of a training intervention in a master course for prospective Secondary school teachers are presented in this paper. The goal is to develop competences of onto-semiotic analysis, that is identifying and discriminating the types of practices, objects, and processes put into play in the mathematical problems solving, which involve using visualizations. The design is based on the use of some theoretical and methodological tools of the onto-semiotic approach. The data analysis is focused on identifying significant didactical facts regarding the design and implementation of the training intervention. The results reveal the complexity of achieving this type of competence and its importance for teachers' professional development.