Construindo competências e habilidades relacionadas ao conteúdo de vistas ortogonais em geometria: uma experiência com material concreto em uma turma de 9º ano de uma escola pública da cidade do Rio de Janeiro

Abstract

This paper presents pedagogical experiences to teach the contents of the thematic unity Geometry. The knowledge in this subject is fundamental for the formation of High School students and will be intensified through High School, representing around 24% of the mathematics questions applied between 2009 and 2018 in ENEM exams. As defined by Conselho Nacional de Educação (CNE) in the last years, the basic education curriculum for the last year of High School must be updated to include activities related to “orthogonal views”, according to BNCC (Brazilian Common Core Curriculum). However, strategies still need to be developed and considered to support educator and students in the teaching-learning process of these contents in the public school in the district of Rio de Janeiro which do not include guidelines for the development of the skill to “Recognize orthogonal views of spatial figures and apply this knowledge for drawing objects in perspective”. (BNCC; EF09MA17). This paper is justified by the need to investigate, propose, test and evaluate teaching methodologies and activities for the development of the skill related to the subject as way a to fill this gap in the mathematics teaching at municipal school system. Lectures and workshops were performed with two regular classes of the ninth grade of high school in the city of Rio de Janeiro in 2019, aiming to analyze the existing activities and propose new pedagogical practices to promote the discovery of perspective and parallel projections. At first, the research evaluates two groups of students. Afterwards a didactic sequence will be structured and implemented with the group with the largest gap, in order to instrument it and also to improve the result measured in the test on the subject. A sequence of activities was elaborated and applied using tangible material and perspective drawings, furthermore light and shadow in different experiments in the classroom. After each step, the learning was verified and carried out over test made by the teacher. The results of pre-test between the control group (CG) and experimental (EG), that in every ten question, the average of corrects corrected answers was 2,7 (CG) and 1,2 (EG), which highlighted the conceptual gap that exists in the curricular guidelines from in the city of Rio de Janeiro. After the conclusion of didactic sequence, the EG solved the final test with high school level questions taken from ENEM exams and the average of corrects corrected answers was 7,3 in every ten question, meanwhile the CG the average was 4,5. Such results endorse that the punctual work with “orthogonal views” content presented effective results when dealing with issues that mobilize different abilities and competences. It was verified that EG students demonstrated increase motivation and dedication, as well as elevated self-esteem which led them to report great pleasure in mathematics class. It was also proved that students were able to analyze and produce transformations and enlargements/reductions of solid geometric figures. In conclusion the set of changes of BNCC demands a reinterpretation of the School’s role. New studies are recommended to enhance the didactic sequence in order to help with diagnostics of the issues and in the necessary acceleration for the achievement of this knowledges knowledge in the school term predicted by normative national documents.