Metáforas e toques em tela: potencializando aprendizagens discentes no estudo de retas paralelas e transversais

Abstract

Touch screen mobile devices (TSMD), such as the smartphone, are physical extensions of the human body that reconfigure and enable the enrichment of interactions, including in the imagery metaphorical field and in conceptual elaboration. Admitting this specificity of the device and assuming that the construction of concepts goes through experimentation and occurs as a continuous process that involves the theories (explanations) that the subjects have about ideas, categories, entities, mathematical relationships, etc., this research aims to analyze the construction and development of concepts by students with a teaching methodology that values the production of metaphors through writing for the construction of meanings, interactions, analysis and reflection in exploratory and investigative tasks through manipulations in smartphone screens when using the GeoGebra application. The question that guides the study is the following: “what contributions and challenges can a GeoGebra class environment offer for conceptual development in the study of mathematical relationships between parallel lines cut by a transversal through tasks that value the production of metaphors and the touchscreen manipulations of 8th grade elementary school students?”. Development research is the methodological approach that guides this thesis, which is based on the following actions: 1. Elaborating, implementing and analyzing tasks that allow reflection from writing and interaction through construction and analysis through the GeoGebra application for smartphones. 2. Elucidating conceptual metaphors produced by students. 3. Investigating how construction and conceptual development occurs from the adopted teaching methodology. 4. Mapping contributions and challenges of an Dynamic Geometry Environment (DGE) to TSMD in addressing the relationship between lines and angles. The investigation was carried out with students from two classes of a School Unit of the Rio de Janeiro’s State Education Department, at Resende city, through the discipline of Mathematical Problem Solving. The following procedures were performed for data collection: (a) audio and video recording, (b) screen capture of the touchscreen manipulations of the smartphones used by the students, (c) written responses from the activity sheets and (d) notes from the researcher. The research highlighted that, to a certain extent, visualization and conceptualization are related, as the development of the ability to visualize, enhanced by on-screen manipulations, can compose the construction and conceptual development. It exposed the rupture in the Euclidean hierarchy in the approach of geometric concepts in an DGE, the synchronicity of touches in the construction and analysis of geometric objects, the development of touches that follows the triad environment-constructive domain relational domain, and that the constructions in an DGE for TSMD follow the same direction of looking at a digital interface (left → right, in Western culture). The results showed that it is possible to teach a good part of the geometric contents foreseen for the final years of Elementary School from the approach of parallel lines cut by a transversal one, when it values the interaction and the different forms of language and assumes the TSMD as a physical extension of our body. The research revealed organizational challenges in carrying out activities with the GeoGebra application, effective and technically related to manipulations on screens