Abstract:

This research is part of a doctoral thesis which aims to evaluate the possibility of monitoring the construction of the notion of definite integral through concept maps. Therefore, considering the assumptions of the theory of Conceptual Fields, was created a didactic sequence in which the concept of convergence was one of the target concepts. Data have been collected in a short course offered to first year students of undergraduate courses, which voluntarily enrolled (in total 13) and were, on occasion, studying Calculus I for the second or third time, or already attending Calculus II. Several researchs study the difficulties of learning the discipline of Differential and Integral Calculus I, for which the concept of convergence is essential. However, it is noticed that many times the student, even developing the necessary calculations to obtain a limit, for example, does not understand the meaning of the notation and the procedures adopted. The use of computational resources has been indicated, in such research, as an important supporting role in the exploration of mathematical concepts. In planning activities designed to the notion of convergence, was tried to provide situations that would enable students to move between different semiotic systems: graphics, numerical and symbolic writing. The analysis of the convergence of numerical sequences supported by graphical representations in R and R^2 were requested to students, as well as the writing of convergence using the same notation limits. The records of the analysis both in natural language and in algebraic language were required. It was noticed that the registry in natural language, of the behavior of a numerical sequence, is not natural, but the collective discussion supported in graphical representations in R and R^2, and simultaneous use of numerical and graphical representations, facilitate the understanding of the concept and consequently how to register it in native language, with subsequent conversion to algebraic registry. Furthermore, it was noted that some terms used in definitions are misunderstood by students, which also complicates the understanding of the concept that is wanted to explore.

Keywords:

Calculus, Convergence, Didactic Sequence.