Processos del pensament matemàtic avançat

The research involved in this project is concerned with three aspects: 1) Mathematic processess implicated in the learning and teaching of mathematics as: abstracting, analysing, categorizating, conjeturating, defining, demostrating, formalizing, generalizating, mmodelling, synthetisizing, representating, conceptualizing, inducting and visualizing, which have a progressive importance in the curricula of the higher degrees. 2) topics of cognitive developement wich come from the distinction between mathematic concepts formally defined, and cognitive processess of the advanced mathematical thinking. 3) topicl linked to mathematic behavior as problem solving wich is concerned with pupil's believes when they are solving problems, heuristic processes involved in solving open problems and mathematic strategic games, and analysiss of metacognition in experts. Moreover, this research is concerned with teaching phenomena, when the individuals studied are teachers, and learning phenomena, when the individuals studied are students. The metodolology of research is qualitative (data and analysis).