Mathematical modeling for the study of affine function: a possibility of learning from the water bill

Abstract

The present work aims to present the results of a research carried out with 1st year high school students from a public school in the city of Ituiutaba – MG, which sought to investigate the potential and limitations of a teaching intervention based on the account analysis of water from these students, following the assumptions of Mathematical Modeling and Theory of Semiotic Representation Records. The qualitative and quantitative study included the participation of 30 students who, during sixteen meetings, carried out activities that made it possible to model water consumption in homes in the municipality of Ituiutaba. The proposed tasks were based on the possibility of using cognitive activities of conversion and treatment, related to Raymond Duval's theory. Given the records presented, it was evident that in activities with treatment of numerical records, students performed better than using the conversion of records. It was also diagnosed that the transition from the algebraic register to the graphic register of the mathematical object (affine function), presents a difficulty for students. In another perspective, students began to have a critical attitude based on the results found, to the point of discovering that different rates are charged in the municipality depending on the neighborhood, and that, for the first range of consumption, the individual who obtained a lower real consumption , pays the same amount as the one who consumed more.