Aspects of Lakatos’ Philosophy for Mathematics: rational reconstruction of the history of the normal curve

Abstract

In this article we resume the work of Imre Lakatos, deepening the study in some aspects that have been little explored in Mathematics Education so far. We bring to the discussion the Lakatosian concept of Rational Reconstruction of History and a contribution to Mathematics Education. Rational reconstruction is an internalist approach to the History of Mathematics, but it has heuristic value, as it allows the observation of new mathematical contents in a rational process. In the case of Mathematics, such a process is the Method of Proofs and Refutations described in Lakatos (1978). We present the results of a post-doctoral research concluded in 2022, in which we developed a didactic material in the form of a textbook on the Normal Curve, based on studies of original works by Abraham de Moivre. In the Rational Reconstruction undertaken, the Lakatosian heuristic rational process was observed. The study in Lakatosian philosophy contributes to Mathematics Education insofar as it provides new perspectives and opens new possibilities for understanding and producing Mathematics from a historical perspective.