Teaching exponential functions through robotics gears

Abstract

The central theme of this work is the exponential function and the exponential type through interactions between gears of the LEGO® Mindstorms NXT Kit. For this, we used the construction of a cart with parts from the kit, composed of a 4-speed gearbox, which works under an exponential rate of change. The motivation of this work was to discover if it would be possible or not to abstract this function, from interactions between gears that, in the great majority, are only associated with the proportionality issues and, consequently, with linear functions. But, with analyzes and studies made on materials already obtained, both on interactions between gears and on gear changes made of LEGO® pieces, we could carry out the construction of the proposed gear. We use gears reductions, which, in sequence, form a geometric progression, which, in turn, was associated with the exponential type function. Thus, this exchange is used as an object of study of a didactic sequence and content, both with regard to its construction and its functioning. And as a result of this work, first it is possible to glimpse the great mathematical collection existing in the interactions between gears, which, when associated with Educational Robotics, allows us to fully work on the integral development of students, and second, a didactic sequence for teaching exponential function, which starts from the concrete construction of something, for mathematical abstraction.