Aspects of Newton’s cooling law addressed in a high school task

Abstract

This study aimed to explore the Law of Cooling proposed by Newton and carry out an experimentation with easily accessible materials, contemplating an experimental activity for the study, in high school, of the exponential function, as well as some ways to characterize it. Regarding the mathematical development of the law of cooling, we made use of the basic theory of ordinary differential equations. As for the development of the experimentation process, we rely on specific competences and skills contained in the National Common Curricular Base – BNCC - envisioning an interdisciplinary task involving the area of Mathematics and Physics for the study of exponential  function. Keeping traces of the empirical activist conception, in the activity of experimentation carried out, we value the development of the student's activity from the mobilization and coordination of  everal registers of semiotic representations, with different contents and meanings, but with reference to the same mathematical object. This study proved to be quite prominent, as it is easy to reproduce in the classroom and allows for very rich theoretical discussions about the processes of experimentation, argumentation, communication of results, semiotic representations involved in the mathematical writing used, in addition to allowing the integration of digital technologies in the processes of teach and learn mathematics.