At the beginning of the current century many educational researchers believed that the problems of teaching and learning mathematics within technological environments had not been deeply addressed. After 17 years of research in this area, some of these problems have been solved while others still persist. Taking the perspective on this problematic as a complex system, in this document, we analyze different variables that come into play in the learning process in the training of mathematics teachers in the province of Quebec (Canada), with particular attention to the use of the interactive whiteboard (IWB). The use of IWB was introduced in primary school (6-11 years old) and secondary school (12-17 years old) in 2007 in Quebec, taking mathematics teachers and textbook authors by surprise. Adding to this disequilibrium, shortly before that time the Ministry of Education of Quebec had conducted an education reform centered on mathematical competencies. In this document, we introduce the notions of global theoretical model and local theoretical model, as tools that enable us to conduct an analysis of the complex system that is the problem of mathematics teacher training around the use of technology.

technology, interactive whiteboard, complex system, teacher training, local theory of representations.