Representações semióticas em um ambiente de aprendizagem interativo no estudo de progressões e funções

Abstract

This qualitative research, conducted through an action-research approach, aimed to analyze how students transitioned between different registers of semiotic representation and how problem solving and the use of virtual learning objects (OVA) can support this process, en- hancing the learning of progressions and functions. The proposal was developed over twenty classes organized into investigative workshops, with a group of eleven students from the 1st year of the Technical High School in Informatics at a full-time public school located in the municipality of Concórdia – SC. Data were produced through the GeoGebra Task platform, written records, images, and a logbook, and analyzed using content analysis techniques. Ped- agogical practices mediated by digital technologies (TD), combined with contextualized prob- lem solving, proved promising for knowledge construction, in line with the principles of the Theory of Registers of Semiotic Representation (TRRS). This approach mobilized different systems of meaning, requiring from both students and the teacher not only technical conver- sions but also understanding of the functioning of each register. The OVA, built with GeoGebra software, contributed to the identification of patterns and behaviors, allowing stu- dents to manipulate parameters such as ratio, initial term, and number of elements of arithme- tic progression (PA) and geometric progression (PG), as well as to study relationships with linear and exponential functions in a fast, practical, and dynamic way. This interaction fa- vored direct observation of effects in algebraic and graphical representations, distinction be- tween discrete and continuous models, interpretation of linear and exponential function graphs, and the application of formulas such as the infinite sum, associating it with the con- cepts of convergence and divergence. The proposed problems deepened this understanding by embedding the content in real and challenging situations, requiring interpretation, argumenta- tion, and decision-making from the students. The integration between OVA and problem solv- ing fostered the construction of meanings, mastery of mathematical signs, and the develop- ment of an investigative and reflective attitude. Most students were able to perform conver- sions between at least two distinct registers, algebraic, graphical, geometric, numerical, and written, indicating understanding of the concepts addressed and indicating that the research objectives were achieved.