POTENTIALLY EXPANSIVE MOVEMENTS WITH STUDENT-ISOMETRIES-GEOGEBRA IN THE CONSTRUCTION OF TANGRAM FIGURES

Abstract

This study represents the third article that composes a dissertation in the multipaper format of a master's research, whose objective is to analyze the strategies used by students in overcoming internal contradictions, which may indicate potentially expansive movements in the student-isometries-GeoGebra relationship when building Tangram figures. The study was guided by a qualitative approach, configuring itself as an exploratory type of research. The research data were produced, due to the pandemic moment, exclusively through transcriptions and prints of recordings made in the Google Meet and WhatsApp environments. We based the study on the theoretical-methodological assumptions of activity theory, using the potentially expansive mini-cycles from this theory as an analytical tool. Our revealed significant overcoming of internal contradictions, in which, we believe, evidence of the occurrence of potentially expansive learning. The first of these potentially expansive learnings emerged from the divergence between what is established in GeoGebra's own guidelines and strategies created by students after handling the software, innovating the translation procedure by a vector, making it more practical and accurate. We believe that the second potentially expansive learning process emerged after the generated by the students when they realized disagreement and justified the need to use only three of the four isometries of the GeoGebra plane suggested for the formation of Tangram figures, excluding, without prejudice, one prejudice of the isometries on the plane. The results found in this study showed us how research in Mathematics Education can contribute to the expansion of the researchers' own knowledge.