For a New Approach of the Quantitative Equivalence

The contribution is based on the results of research conducted in an IRES group in Montpellier (September 2019–June 2021). This collaborative research was conducted to design and experiment with a system for teaching arithmetic in elementary first year for 7 to 8 years old attending school in France. It made it npossible, among other things, to show how the proposed tasks based on actual manipulations and followed by calculation sessions lead students to establish an equivalence relationship between two numerical expressions. Thus, in response to a “classic” question about the teaching of arithmetic, appears a question on the articulation between arithmetic and algebra.