International Journal on Studies in Education Volume 1, Issue 1, 2019 39 An Attempt to Bring Calculation Closer to Student Reality through Active Methodologies: 4E's Altieres Bomfim Ribeiro University of São Paulo, Brazil Roberta Veloso Garcia University of São Paulo, Brazil, robertagarcia@usp.br Estaner Claro Romão University of São Paulo, Brazil Abstract: The Calculus I course has high failure rates in universities in Brazil and around the world, as well as at the School Engineering of Lorena (EEL). This article seeks to contribute to minimize this issue, adopting as a strategy the use of active learning methodologies. Active methodologies already established in the literature were searched, which served as the basis for the construction this work. A questionnaire was also applied to EEL students to map their most common difficulties and specially to know the students perspective on the current situation of the discipline. From the results of the questionnaire we sought to interpret what were the main factors that contributed to the high failure rates of the discipline in the EEL. From this analysis a procedure was elaborated that united the concepts of the previously researched methodologies, which were more adequate to face the problems highlighted by the questionnaire, aiming to contribute appropriately to the improvement of the discipline learning. Keywords: Calculus, Engineering, Peer instruction, Problem based learning Introduction It is no secret that the Differential and Integral Calculus discipline has high failure rates, since this is not a current problem. Wrobel (2013) shows us that between 1996 and 2000 the failure rate of important Brazilian university, as such as, Fluminense Federal University varied between 45% and 95%, as well as at the Federal University of Rio de Janeiro where this same rate was 42% in the first half and 48% in the second half of 2005. The School Engineering of Lorena (Escola de Engenharia de Lorena - EEL), as well as many other universities in the country, are not exempt from this reality. The discipline of Calculus I is of great importance in courses of exact areas, where it often occupies a prerequisite position for many other disciplines, thus having a great weight for the continuity of the students course (Paula et. al, 2016). The importance of passing Calculus I for the continuity of the course, coupled with the high failure rates (which are well known by students), builds in students a peculiar view of the discipline, where the major challenge is obtaining approval and learning becomes only a necessary part of accomplishing this goal. This atmosphere around the dreaded Calculus I makes the learning needed in this discipline a background, which does not mean that the current method of teaching does not work. However, in the current scenario the situation is common in which the student takes Calculus I for the purpose of passing and not necessarily learning. Rezende (2003) makes us think over on what we want from the calculus course. Do we want a course in which technique prevails? Or do we want a course in which the meanings are well established? The author explains that a consensus among teachers is that students entering undergraduation do not generally have a well- established mathematical basis, which is characterized by mathematical techniques: polynomial factorization, algebraic calculations, trigonometric relations, etc. This problem exists, however it is not unique to Calculus I, as this discrepancy also exists for other higher education subjects, but even so, not all of them have alarming results as in Calculus. In contrast to the techniques of basic mathematics "The semantic field of the basic notions of calculus has much more to do with the notions of "infinity "," infinitesimal "," variables "[...] (REZENDE, 2003, p.18). Meanwhile, Berry and Nyman (2003) propose to relate the understanding of concepts of derivative through graphs or in other words "graphical links between the derivative of a function and the function itself"