The Importance of Variational Thinking in the Training of Engineers Case TecNM

In the teaching of the various branches of mathematics, emphasis is placed on algorithms, to such an extent that it is common to characterize someone who is “good at doing math” as being good at math. A look is taken at the applications based on routine procedures and the conceptualization and, most importantly, the training as the final objective of the Construction of Mathematical Knowledge are left aside. Some branches of mathematics encourage the construction of a characteristic thought that, in the case of Calculus, is Variational Thinking. These thoughts imply a change in the way of understanding oneself and one’s environment, which leads to the construction of a certain neuronal arrangement that determines the difficulty of the particular branch. This work highlights the importance of Variational Thinking in the training of engineers in the Technological Education System embodied in the National Technological Institute of Mexico (TecNM). Variational Thinking allows to successfully attack the problems of change, which are characteristic of engineering, focusing its resolution not on “what formula to use” (static thinking) but on what mathematical model enables its resolution (variational thinking). It is identified as an epistemological problem, the activities to be developed to achieve the objective are described and the change of strategy is shown through the resolution of problems in which Variational Thinking is decisive. A paradigm shift occurs when trying to solve a new problem.