De la concepción global a la concepción local. El caso de la recta tangente en el marco de la convención matemática

this document shows the results of research aiming to facilitate the transition from the global conception (euclidean) of the tangent line to the local conception (leibnizian) through mathematical convention. for this purpose, we designed a series of activities that led higher education students (1819 years old) to look for consensus, which would allow them to overcome the cognitive conflict resulting from the contradictory nature of the conception of tangent that touches a point on the curve with the conception that admits that it can be cut. the results indicate that most of the students were able to overcome the cognitive conflict by establishing a mathematical convention that redefines the euclidean tangent and replaces it with the leibnizian tangent.