Summary: The introduction of algebraic reasoning in primary education is a subject of interest for research and curricular innovation in mathematics education, which supposes an extended vision of the nature of school algebra. In this paper we propose a way to conceive of algebraic reasoning based on the types of mathematical objects and processes introduced in the onto-semiotic approach to mathematical knowledge. In particular, considering a mathematical practice as algebraic is based on the intervention of generalization and symbolization processes, along with other objects usually considered as algebraic, such as binary relations, operations, functions and structures. This way to conceive of elementary algebra is based on and compared to the characterizations given by other authors. We also propose a typology of algebraic configurations that allows defining degrees of algebraization of mathematical activity.