Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function

Abstract

This study investigates the praxeologies teachers use about the inverse function in the teaching process when the curriculum is changed. A case study, one of the qualitative research methods, was used in the study. The participants of the study were three experienced mathematics teachers. The data were collected by recording the teaching process of the teachers with a video camera and a voice recorder. The praxeological analysis method of the Anthropological Theory of Didactics (ATD) was used in the data analysis. The findings of the study show that teachers use two different praxeologies in the inverse function. The first one is praxeology based on informal mapping with the effect of the dominant definition of the concept of function in the curriculum, and this praxeology was used to introduce the concept of inverse function. The other praxeology, which shows the monoid structure more clearly, emerged due to both a necessity and the necessity to exhibit an approach appropriate to the curriculum in more complex tasks and was shaped as a mixed praxeology. It was determined that teachers did not structure both praxeologies well and made sudden transitions from one praxeology to another.