From Arithmetic to Algebra: Triangular Numbers, technology and ACODESA

The aim of this document is to address the articulation between arithmetic and algebra. The literature reports a discussion of arithmetic or algebraic thinking, not mentioning at all the importance of a pre-algebraic thinking related to an arithmeticalgebraic thinking. Through activities designed for this purpose, we propose a visual approach, with the intention of promoting mathematical visualization processes, which in turn constitute cognitive structures on the control exercised by students in solving a mathematical task. Our design is linked to a theoretical framework for action, collaborative learning (ACODESA) and use of technology in the mathematics classroom. In this study, we present our research project between Quebec and Mexico, but restrict ourselves to the results obtained with the Mexican population in relation to polygonal numbers in secondary school.