Covariate reasoning in calculus: development from the use of tasks - Gonçalves, William José; Trevisan, André Luis; Silva, Daniel Daré Luziano da; Ribeiro, Alessandro Jacques (Universidade Estadual de Campinas, 2020)
The design of coordinated analysis as variables of two interdependencies (covariational reasoning - CR) is a central aspect of Calculus learning, the most discussed skills are mobilized amid the mathematical routines triggered by work with tasks. Realization of a qualitative research, interpretive, from records of written production and excerpts from dialogues of a group of students without work with a task in conjunction with a bottle that fills. The task made possible the exploration of the skills including: quantity and reasoning about its measurement process; imagine minute varying continuously; coordinate pressure pairs that can vary together (time, height, volume and radius).  In addition, students were able to establish a relationship between height and volume, building a representation in which the inversion in the concavity of the graph showed an understanding of the existence of a change in the rate of change in this situation.