Since its 17th-century origin, logarithms have significantly advanced fields like astronomy, engineering, and medicine. Their power lies in connecting arithmetic and geometric patterns, transforming products into sums and quotients into differences. They are non-trivial mathematical objects, represented by a notation (logab) which does not reveal any intrinsic properties, i.e. what happens within the function to the input b. They often pose challenges for students, as reflected in errors and misconceptions.
The logarithm can be defined and introduced in various ways: as a function, an inverse, an area, a tool to simplify expressions, an exponent, to name a few. Mathematically, all these definitions lead to the same theorems and applications. However, when teaching about the logarithm, the instructor usually picks one representation to begin with, that is, one answer to “What is the logarithm?”, whereafter others may be added and explained. The question is, which way of presenting the logarithm do teachers choose? Are there motivations for and reflections of this choice? How does the chosen representation influence the narrative taught, and does it impact learning?
In my dissertation, I will explore how logarithms are taught, focusing on the definitions given and how the narrative evolves, including connections to other mathematical topics.