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.

摘要 本研究隶属于一项更大规模的科研课题，其中教学人类学理论（Anthropological Theory of Didactics，简称TAD）及其组织结构为本研究的核心内容。本文节选该课题的部分研究内容，重点转录了第二学段小学六年级一节以数值表达式为主题的课堂教学录像实录。我们依托该理论的分析视角展开解读，梳理并揭示其中涉及数学与教学组织的相关特征。基于本次课堂的转录实录文本，本分析将阐释TAD如何助力构建数学对象的教学组织结构，同时揭露该教学内容虽已被纳入本学段课程体系却缺失存在依据所引发的研究空白。本研究采用质性研究中的文献分析方法，通过梳理课堂转录记录实现与TAD理论核心主张的互证关联。本文的论述脉络如下：首先阐明数值表达式的制度化支撑体系，继而梳理TAD的演进历程，剖析其起源阶段针对数学对象所经受的条件与限制开展的研究；最终阐明支撑课堂特征刻画的初步结构与相关要素，以及同步转化为教学问题的原初数学问题。