Uses of quantification and category of modeling. A transversality of mathematical knowledge - Gaete-Peralta, Claudio (2024)
[Objective] The teaching of quantification tends to focus on formulas for quantifying the measurement of geometric magnitudes, ignoring their uses in other disciplines. This makes it essential to formulate reference frameworks that allow such teaching to meet the functional justifications demanded by other domains of knowledge. For this reason, and within the framework of socioepistemology, the aim of this research was to formulate an epistemology of the uses of quantification. [Methodology] The methodology was qualitative and consisted of a theoretical-methodological corpus that articulated constructs of a modelling category with empirical data. This formulation was carried out in two phases. In the first one, an epistemology was hypothetically formulated based on an analysis of resignification of the uses of quantification constructed in two specific measurement situations: one specific to an interdisciplinary community, and the other to the mathematical work entitled Intégrale, Longueur, Aire. The second phase analyzed the emergence of a resignification of the uses of quantification by engineering students during the development of a school situation designed on the basis of hypothetical epistemology. [Results] This emergence made it possible to empirically validate this epistemology and to express a transversality of uses of quantification in specific measurement situations, made up of meanings, procedures and instruments that together can be used to derive quantification arguments. [Conclusions] This epistemology of uses makes it possible to capture the measurement situation as an educational reference to establish the use, resignification, and transversality of quantification.