Accumulation of Degree-hours and category of modelling. A resignification of the definite integral with mathematics teachers

This research analyzed the resignification of the definite integral by mathematics teachers in a situation of change, argued by accumulation. To this end, an instrumental case study was conducted with four teachers in Chile, who developed a classroom-based learning activity using GeoGebra. Framed within the socioepistemological program Forgotten Subject and Transversality of Knowledge, the data were analyzed using constructs from the category of modelling and document analysis techniques. The results revealed a resignification in which quantities of continuous variation functioned as the instrument, comparisons of states as the procedure, and areas between curves and accumulations of degree-hours as the meanings. The discussions proposed modeling phases from an educational perspective to identify situated resignifications of mathematical knowledge. In conclusion, this study is expected to contribute to the design and implementation of school situations to analyze the students' resignifications through the different phases of this model.