A abstração da função exponencial de interações entre engrenagens lego®

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Universidade Federal de Goiás


In this paper, the central theme is the abstraction of the exponential function and the exponential type of interactions between gears in the LEGO® Mindstorms NXT Kit. Through the construction of a cart using parts of this kit, was found that it is composed of a 4-speed gearbox, which works with an exponential rate of change. The motivation of this paper was to discover whether it would be possible or not to abstract this function, based on interactions between gears, that in the great majority, are associated only with the proportionality issues and, consequently, with linear functions. With analyzes and studies made based on materials already produced, both on interactions between gears, and on gear shifts made of LEGO® parts, we were able to do the construction of the proposed gearbox. For this, we use gears reductions of spins, which in sequence was able to create a geometric progression, which was associated with the exponential type of function. Thus, this gear is used as an study object of a didactic sequence and of contents, both with regard to its construction (detailed in the didactic sequence) and as to its functioning (explored in the form of exercises). The sequence, as an objective of assisting the teacher in teaching the exponential function is based on the Zabala’s (1995) theory, which is based on Piaget's constructivist conceptions (1978) on the cognitive process construction of knowledge. Based on the choice of using gears and educational digital technologies, through educational robotics, we bring the guidance of Saymon Papert (1985), author of the constructionist theory. And with the positive result of this work, it was possible to see the great mathematical arsenal existing in the interactions between gears, which, when associated with Educational Robotics, allows to fully work on the integral development of the students, by relating in the execution of their activities, in a simultaneously way, such as concepts, procedures and attitudes.



Função exponencial, Engrenagens, Sequência didática, Robótica educacional, LEGO®, Exponential function, Gears, Following teaching didactics, Educational robotics


COSTA, C. P. A abstração da função exponencial de interações entre engrenagens lego®. 2020. 196 f. Dissertação ( Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2020.