Mathematical Connections Associated with the Exponential and Logarithmic Functions Promoted in the Mathematics Curriculum

Abstract

This article aims to identify the general mathematical connections and those related to exponential and logarithmic functions, promoted by the Colombian intended mathematics curriculum. In this research, Content Analysis was used, and the official and institutional Colombian intended mathematics curriculum (of 5 schools) at the middle and high school level were used as a source of information. In Colombian, the official curriculum is made up of three official documents and to select the institutional curriculum, convenience sampling was used. Among the results, we find that, although the Colombian intended curriculum assumes the idea that making mathematical connections contributes to the development of understanding and promotes some of these (feature, meaning, different representations, and modeling), the reversibility connection is not identified — which we consider central — between exponential and logarithmic functions, which shows that the teaching of these is encouraged separately. This can influence what occurs in the classroom and, therefore, is one of the possible causes of the difficulties presented in students when solving tasks related to both functions. In this sense, it is necessary that institutions consider that making mathematical connections contributes to the understanding of students and therefore must be considered when designing the curriculum. It is necessary to promote the mathematical connection of reversibility between the functions that are addressed in this study and between the objects with which it is possible to make inverse relationships.