Cálculo diferencial e integral I: análise de erros em turmas semipresenciais

Abstract

What is a mistake? Is the error in solving a given problem situation not in the reading and interpretation of the statement? Since g '(c) = 0 = g' '(c), at x = c what is there: maximum, minimum, or inflection? For what reason, when using the part integration technique, ∫udv = uv - ∫vdu, do not consider a constant when integrating dv? These questions were presented in classes of semipresencial Calculus in a Brazilian public university. All students had been disallowed in Calculus discipline, in the face-to-face modality, therefore, in theory, some of the previous questions, among others, should be partially answered by the student body. This paper reports on the experience of inverting Differential and Integral Calculus topics with a variable, presenting them in the blended mode, in order to answer a question: why follow the didactic sequence of adopted books? The trapezoids method for calculating an area above the x axis and between concave parabolas down was a starting point, as well as some applications of integrals, such as work and center of mass, using the said method. Despite some didactic inversions, the reason for certain expressions, such as the fundamental limit of trigonometry, were presented from a contextualization. Although the use of new strategies focusing on a more meaningful learning, it was verified that the same errors in the traditional teaching of limits, derivatives and integrals were observed.