Analysis of a textbook of geometry based on depth hermeneutics

Abstract

The paper presents results of the analysis of a Geometry textbook too much used in Math teacher’s edication in
Brazil called Elementos de Geometria Plana, written by João Lucas Barbosa. We were guided by the follow
questions: how are the most common Euclidean geometry books organized / structured in the training of
mathematics teachers? and what kind of tasks are proposed to your readers? For this, we use the Depth
Hermeneutics as research methodology because we understand that the textbook is a "symbolic form" (human
intentional production). The study contemplated an investigation of the context of the production and circulation
period of the first edition of that book and an analysis of its structure, with emphasis on a classification of the
tasks proposed there. We perceive strong ties of the book with ideas characteristic of the Modern Mathematics
Movement, such as the overvaluation of the teaching based on the logical-deductive construction, notably, the
great proposition of exercises directed to proofs of conjectures.