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This paper aims to identify what relationships we can establish between the mathematical organization existing in the textbook and those existing in the teacher's practice about the teaching of fractional division operation. This theme has caused a lot of concern on the part of teachers and researchers about their teaching and learning conditions. The theoretical and methodological framework in which this study is supported is the Anthropological Theory of Didactics, developed by Chevallard and collaborators. This theoretical framework has proven to be a powerful tool for analyzing and describing teaching practices and textbooks. This is a qualitative investigation with descriptive and interpretative cut of the case study type. We chose as subject of the research a Mathematics teacher who works in a 7th grade elementary school class of a public school. Regarding the results, both in the textbook and in the analyzed class, it was possible to find three types of tasks related to the teaching of the division division operation: T1, T2 and T3. The techniques used in both cases to solve the types of tasks were based on the idea of inverse operation. The formation of the technological-theoretical environment was almost always based on geometric representations. However, a certain distance can be affirmed between the technological-theoretical discourse presented in the book and the one presented in the teacher's class. In addition, it was possible to realize that the tasks used in the classroom by the teacher to illustrate the types of tasks were not problematic compared to those presented in the textbook.

A TRANSPOSIÇÃO DIDÁTICA ACERCA DO ENSINO DA OPERAÇÃO DE DIVISÃO COM FRAÇÃO: UM ESTUDO SOB A ÓTICA DA TEORIA ANTROPOLÓGICA DO DIDÁTICO