The generalization of the solution process in a mathematical problem-solving activity with an Advanced Computing Environment

In a problem-solving activity, generalizing is an important process by which the specifics of a solution are examined. Technologies support this process, making it possible to create interactive explorations that allow to see how the result changes as the initial data vary. In this article we focus on the generalization of the solution process during a mathematical problem-solving activity using an Advanced Computing Environment (ACE). Our research questions are: how can we analyze the skills students develop while generalizing a problem? What are the most frequent difficulties? We analyzed the solution of a problem-solving activity with an ACE submitted by 75 students using a model specially developed by us for studying generalization using interactive components. The model considers three phases: design and choice of interactive components, programming of the system and control stages of generalization of a problem. For each stage we established a set of indicators to understand the competences achieved by each student. The results show that the students generalized the problem using different strategies, with some difficulty in the programming and control phase. The model developed allows to reflect on the skills achieved by students in the various phases of the generalization process.