A Reading Using the Lens of the Anthropological Teaching Theory about a Lesson on Numerical Expressions

Abstract This research is immersed in a research of greater magnitude, in which the Anthropological Theory of Didactics - TAD and its organizational structure constitute the core of the study. In this text, we present a clipping, with emphasis on the transcription of a descriptive protocol of the filming of a 6th grade class of Elementary School II, which dealt with numerical expressions. We undertake some interpretations through a reading using the theoretical lens of said theory in which aspects related to mathematical and didactic organizations were evidenced. In this perspective, our analysis will be based on the descriptive protocol of the class and demonstrate how the TAD can contribute to design an organizational structure of a mathematical object, as well as to reveal gaps linked to the absence of the raison d’être of this content institutionally present in the curricular matrix of this educational level. The documentary analysis, in a qualitative approach was used in this study that followed a configuration and transit through some records of the class transcription and allowed us to weave interconnections with what the TAD postulates. The scope of the article presents, in a first moment, the exposition of the institutional sustentation of the numerical expressions and sums up to the evolutionary path of the TAD exposing in its genesis the study of the conditions and restrictions undergone by the mathematical objects. We culminate revealing the first structure and some elements that will support the class characterization and the mathematical problem that concomitantly turns into a didactic problem.