Sequências e Séries

This article presents the results of the implementation of a teaching sequence through activities on the convergence of Sequences and Series applied to 11 students in an Engineering course. The Theory of Semiotic Representation Registers and Didactic Engineering were considered in the composition and application of the activities. The tasks were presented to the students on printed sheets, with spaces for writing answers, in a computer lab environment to be solved using GeoGebra. The collected material was analyzed to understand the construction of the concept in question through tasks involving natural language, arithmetic, algebraic, and pictorial registers and the necessary conversions and treatments. The analyses showed that the use of multiple records, facilitated by the use of GeoGebra, enabled the construction of links between the mathematical notions of “as close as desired” and “arbitrarily large,” verbal records contained in the definitions of limits and convergence, with individual perceptions of ‘approximation’ and “unlimited growth,” as planned in the a priori analyses. The records written by the students also showed the real symbiosis between student and media during the construction of the concept of convergence.