DIDACTICAL ENGINEERING OF THE SECOND GENERATION - A PROPOSAL OF THE DESIGN AND A TEACHING RESOURCE WITH THE SUPPORT OF THE GEOGEBRA SOFTWARE IN BRAZIL

Oct 15, 2026

Uploaded by Aditya

This article presents an excerpt from an ongoing master’s research on methodological and theoretical aspects of problems drawn from the National High School Exam (ENEM), focusing on the teaching and learning of volumes. A didactic situation is proposed under the Theory of Didactic Situations (TSD) and supported by GeoGebra to construct and solve a cylinder volume problem. The design is developed through Didactic Training Engineering (EDF) to guide math teacher education, using technological resources to enable didactic transposition, reduce geometric conceptual difficulties, and strengthen mediation in ENEM-oriented assessment contexts.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

AccessFree to download

1. Introduction

Didactic Training Engineering (EDF) and the Theory of Didactic Situations (TSD)

ENEM context and didactic situation proposal

GeoGebra and the teaching of cylinder volume

Relevance of spatial geometry software in mathematics classes

DIDACTICAL ENGINEERING OF THE SECOND GENERATION: A PROPOSAL OF THE DESIGN AND A TEACHING RESOURCE WITH THE SUPPORT OF THE GEOGEBRA SOFTWARE IN BRAZIL Francisco Régis Viera ALVES; Rosalide Carvalho de SOUSA; Francisca Cláudia Fernandes FONTENELE Abstract: This article presents a partial excerpt from an ongoing master's research on the methodological theoretical aspects of problems related to the content of volumes, selected from the evaluations of the National High School Exam (ENEM) . The Exam consists of a test proposed by the Brazilian federal government, which aims to assess the performance of students at the end of high school, in addition to being used as a selection criterion to enter higher education. In this way, a didactic situation is proposed in the context of ENEM structured in the Theory of Didactic Situations (TSD) and subsidized by the use of the GeoGebra software as a technological resource for the construction and resolution of the problem situation on the volume of a cylinder. The didactic session was consolidated in Didactic Training Engineering (EDF) and developed to design a didactic resource for teaching and training mathematics teachers. GeoGebra was used to carryout the didactic transposition of the problem, as it benefits the student to break the difficulties inherent in the understanding and appropriation of geometric concepts. This structure facilitates didactic mediation, in addition to giving a new meaning to the study and teaching of volumes in the context of ENEM assessments. Key words: Didactical Engineering of Second Generation, Didactic Situation, Didactic Resource, GeoGebra Software, Teacher training in Brazil. 1. Introduction In the last decades, there has been a marked contribution of methodological and investigative resources from the Didactics of Mathematics, of French origin, related to the training of Mathematics teachers and the design and proposition of didactic and methodological resources that can support the teacher to improve planning and the execution of its didactic sessions for teaching mathematics. In Brazil, for example, it is undeniable the existence of difficulties and obstacles in the study and teaching of mathematics by teachers during their respective academic training and the exercise of the profession, because according to Damaceno (2018, p. 43), the problem “consists in the initial training of teachers, who work in the teaching of mathematics, who for the most part finish their courses without the essential knowledge for the exercise of teaching, with regard to concepts, procedures and mathematical language ”. From a concern with teaching and learning the content of volumes in the Brazilian scenario, the problem that guided our investigation was constituted: How to conceive a didactic resource that allows to improve the teaching of volumes, in order to develop both the student learning regarding the teacher education? In this sense, the notion of Didactic Training Engineering (EDF) or Didactic Engineering of 2nd Generation is embodied as a methodology or design that relates research and teaching in order to develop resources for teaching Mathematics, as well as for the formation of math teachers. In Tempier (2016, p. 263), he describes this methodology as an instance of the basic design of the research with some peculiarities, among them, being “supported by an explicit basic theory, of intermediate level, the Theory of Didactic Situations (TSD) . Such a relationship will allow the construction of a situation through an epistemological study of a mathematical concept, in order to provide a theoretical model that serves as a basis for designing situations for a resource that guarantees the verification of the study and promotes student leadership. In view of this scenario, the article presents a didactic situation proposal for the teaching of Geometry, specifically for the teaching of the mathematical concept of volume of a cylinder, which is ca

FAQs

What problem does the research address regarding the teaching of volumes?

It investigates how to conceive a didactic resource that improves the teaching of volumes while supporting both student learning and teacher education.

How is the ENEM framework used in the proposed didactic situation?

The didactic situation is structured around questions selected from ENEM evaluations, aiming to connect mathematical learning of volumes with assessment-oriented contexts.

What role does GeoGebra play in the learning process described in the article?

GeoGebra supports the construction and resolution of the problem situation about the volume of a cylinder, enabling didactic transposition and helping students visualize and overcome difficulties with geometric concepts.

Oct 15, 2026

Uploaded by Aditya