Logarithmic-exponential covariational in future mathematics teachers. A case study

Abstract

The present study contributes to the body of research about the development of covariational reasoning in future mathematics teachers. We report the mental actions and levels of logarithmic-exponential covariational reasoning perceived in sixth semester undergraduate students in mathematics during a teaching experiment developed by a future mathematics teacher who is immersed in a research project. The tasks of the teaching experiment begin with a geometric construction of points of a curve using GeoGebra for students to explore the variations and describe the curve that adjusts the points. The students determine a general expression for the construction of any point by recognizing the two progressions: arithmetic and geometric. However, they show the complexity of developing a continuous covariation reasoning from a task that encourages discrete covariation reasoning.