Aprendizagem significativa da geometria espacial: análise de uma sequência didática para o ensino médio

Abstract

The present work, characterized as a teacher's research, aimed to analyze a didactic sequence, aimed at high school students on the subject of spatial geometry, regarding the significant potential of the learning material and its contribution to the conceptual formation and to the development of geometric skills. For this research, a qualitative and descriptive approach was chosen, concerned with presenting the educational phenomena that occur. It was based on David Ausubel's Theory of Meaningful Learning and theoretical models of conceptual training levels and geometric skills by Pierre Van Hiele and Alan Hoffer, respectively. The didactic sequence was applied to 20 students of the third year of high school in two different environments of a state public school in Minas Gerais (a classroom linked to the library and the computer lab), totaling six weekly classes of 50 minutes each and consisting of of three modules: the first module was applied in three classes with concrete materials; the second module was applied in a class with concrete materials and impressions of plans on A4 sheets of paper; and the third module was developed in two classes in the computer lab, containing basic instructions and notions of the GeoGebra software, a tutorial on the construction of geometric solids and construction tasks. The classes were recorded and the tasks were collected after completion. It is concluded that the material had characteristics of a potentially significant material, since the activities were organized according to a logical and hierarchical conceptual hierarchy and made possible, through the exploration of the physical materials, the promotion of dialogues and the use of the GeoGebra software, the meaningful learning mechanism (prior knowledge, meaning x mechanics, reception x discovery, progressive differentiation and integrative reconciliation). Regarding the levels of geometric thinking, it is considered that the sequence has contributed to obtaining Level 2, since the activities allowed the identification of properties of spatial figures and the establishment of some relationships, which characterizes some progress towards Level 3 As for geometric skills, the activities in the didactic sequence may have contributed to the development of verbal skills – notably in encouraging dialogue and performing tasks – and visual and graphic skills – especially in solid planning activities and animations favored by the software GeoGebra. It is considered that the didactic sequence has contributed to the teaching of various contents of spatial geometry in basic education, especially in the post-pandemic situation, and that carrying out this research has had notable relevance for the continuing education of this researcher. It is expected that the educational product produced – containing the sequence, objectives, activities (script and materials), a summary of the main theoretical topics and some reflections arising from the experience of applying the material in the classroom – will contribute to the area of teaching and learning mathematics.