A PRELIMINARY GENETIC DECOMPOSITION FOR THE CONCEPT OF LOGARITHM AS A REAL NUMBER

Abstract

This article addresses the difficulties in understanding logarithms as real numbers, a key concept in mathematics, and proposes a preliminary genetic decomposition based on the APOS theory (Actions, Processes, Objects, and Schemas). Through a qualitative approach grounded in theoretical and historical analysis of John Napier’s work, the study identifies the mental structures and mechanisms involved in its construction. The results highlight three phases: manipulation of geometric progressions, development of a discrete model, and its extension to a continuous model. This proposal not only facilitates the understanding of logarithms but also provides pedagogical tools that integrate epistemology and history, contributing to a more effective teaching of the concept. By exploring the al and epistemological development of this fundamental concept, the study aims to deepen the understanding of its mathematical essence and the cognitive complexities inherent in its conception.