Manifestations of the ideology of certainty in mathematics textbooks

Directions in the field of geometry

Abstract

This text contains an excerpt from the first author’s master’s research, under the guidance of the second. In it, we aim to present and analyze the ways in which the ideology of certainty manifests itself in Brazilian Mathematics textbooks, in particular, in the chapters of Geometry. Despite being an old discussion in the field of Mathematics Education, the ideology of certainty is mainly characterized by the understanding of mathematical discourse as pure, generalizing and rich in applications, which we see as a still current discussion. We chose to analyze the Geometry present in textbooks because it is a topic of interest to our research group, and also because in the literature review used in the master's research, no investigation similar to this one was found. Starting from a documental analysis, we investigated the chapters of Geometry of two collections of textbooks destined to the Brazilian High School, trying to study all its content. In these textbooks, there is both content intended for students, with concepts, examples, exercises, among others, and didactic guidelines for teachers, which cover aspects of using the material, informative texts, answers to exercises, etc. When interpreting the data, we identified that the ideology of certainty manifests itself in the chosen chapters through the structure elaborated by its authors, in which, from the exposition of a geometric concept, examples of application are inserted, being followed by exercises. This ‘concept, example and exercise’ pattern, in our view, also finds support in the construction of geometric knowledge itself. We also identified that from contradictions between what is expected from the student and what is presented to the teacher, the development of the discourse given by the ideology of certainty is even more reinforced. We understand that questioning and weakening the ideology of certainty becomes a challenge that is not limited to what is exposed by textbooks, but must be part of the political, social and cultural agenda of Mathematics Education. Thus, criticisms and reflections on the mathematical knowledge discussed in the classroom need to consider in what ways the ideology of certainty manifests itself and in what ways it can be faced.