A trajectory for developing conceptual understanding of logarithmic relationships

Abstract

While there has been a recent expansion of research related to the development of conceptual understanding of exponential relationships in individual students, the teaching and learning of logarithms continues to be understudied. In this report, I documented the mathematical progress of a classroom community as they developed an exponential number line to explore logarithmic relationships. In particular, the students in the community grappled with the ideas of coordinating arithmetic and geometric growth, made sense of fractional exponents, and interpreted logarithms statements (i.e. equations with logarithms in them) in terms of story problem and then related those interpretations to an exponential number line. The focus on logarithms was fruitful as this analysis resulted in new perspectives on how to address the conceptual difficulties students face when exploring exponential and logarithmic relationships.