A construção do conceito de logaritmos

Abstract

Logarithms occupy a prominent place in the history of mathematics as a calculation algorithm and as a function, they are currently applied in different areas of science. Therefore, they are of fundamental importance in the training of students. Teaching logarithms, however, has been a great challenge, due to learning difficulties. The implementation of mechanical teaching activities, without exploring the students' reasoning, prioritize only solving equations with an excessive amount of manipulations, to the detriment of conceptualization, as well as applications. In this sense, the problem of this research was to investigate how students elaborate the meanings of the concept and properties of logarithm and what are the learning obstacles present in this process. A sequence of activities was developed and applied in online mode in a class of the first year of high school. The content of the written manifestations, in the form of digital files and the oral ones recorded in the logbook, were analyzed qualitatively, through a category chart elaborated based on the Theory of Meaningful Learning and the Theory of Obstacles to Learning by David Ausubel and Jean- Pierre Astolfi, respectively. Psychological obstacles were identified, such as problems of attention, perception, concentration and epistemological problems, associated with the understanding of the meaning of subsunitors necessary to the concept of logarithm, such as potentiation, elementary school algebra, equations, exponential function and the consequent difficulty in interpreting stated. The overcoming of these obstacles occurred with the mediation of the teacher, in actions of reflection on the written and spoken records, recovering the meanings through previous organizers and with that, qualifying the subsunitors, which, enabled the construction of the concept and the properties of the logarithms.