“Multiply by adding”: Development of logarithmic-exponential covariational reasoning in high school students

• We report the development of logarithmic-exponential covariational reasoning.
• The teaching experiment contributed to the students perception of the changes.
• The students infer the juxtaposition of the operations: “multiplying by adding”.
• The sketch of a graph demonstrate the development covariational reasoning.

This paper reports the development of logarithmic-exponential reasoning in high school students in a teaching experiment as a contribution to the growing body of research addressing covariational reasoning. The design of the teaching experiment articulates the static perspective of exponential covariation and a reformulation for the discrete case of the dynamic perspective of the covariation. The static perspective considers that amounts of one quantity varying in arithmetic progression are associated or juxtaposed with amounts of another quantity varying in geometric progression. On the other hand, the dynamic perspective coordinates two varying quantities while attending the ways in which they change in relation to each other. The conceptual framework also takes into account the results of previous epistemological-historical studies about the development of the concepts of exponential and logarithmic functions. The data analysis aims to define the logarithmic-exponential covariational reasoning of the participants through the identification of the mental actions and levels of reasoning achieved during the teaching experiment. The results show that the teaching experiment contributed to the students’ perception of the changes in the involved variables and to infer the juxtaposition of the operations: “multiplying by adding” and “divide by subtracting”. Therefore, we consider that the sketch of a graph and algebraic expressions demonstrate the development of logarithmic-exponential covariational reasoning in students.