Expanded model for elementary algebraic reasoning levels

The development of algebraic reasoning from the earliest educational levels is an objective that has solid support both from the point of view of research and curricular development. Effectively incorporating algebraic content to enrich mathematical activity in schools requires considering the different degrees of generality of the objects and processes involved in algebraic practices. In this article, we present an expanded version of the model of levels of algebraization proposed within the framework of the onto-semiotic approach, establishing sublevels that provide a more microscopic view of the structures involved and the processes of generalization, representation, and analytical calculation at stake. We exemplify the model with mathematical activities that can be approached from primary education, classified according to the different sublevels of algebraization. The use of this expanded model can facilitate the development of didactic-mathematical knowledge of teachers in training on algebraic reasoning and its teaching.