Integrating Arithmetic and Algebra in a Collaborative Learning and Computational Environment Using ACODESA

In the transition from arithmetic to algebra and in light of the disjunction between the natural and symbolic approach to algebra and the choice of a natural way of learning, this paper discusses the development of a cognitive control structure in pupils when they are faced with a mathematical task. Researchers sought to develop, in novice pupils in both Quebec (12–13 years old) and Mexico (14–15 years old), an arithmetic-algebraic thinking structure that would promote mathematics competencies in a method based on collaborative learning, scientific debate and self-reflection (ACODESA, acronym which comes from the French abbreviation of Apprentissage collaboratif, Debat scientifique, Autoreflexion), and immersed in an activity theory approach. This paper promotes the equal use of both paper and pencil and technology in order to solve a mathematical task in a sociocultural and technological environment.