Employing genetic ‘moments’ in the history of mathematics in classroom activities

Abstract

The integration of history into educational practice can lead to the development of activities through the use of genetic ‘moments’ in the history of mathematics. In the present paper, we utilize Oresme’s genetic ideas – developed during the fourteenth century, including ideas on the velocity–time graphical representation as well as geometric transformations and reconfigurations – to develop mathematical models that can be employed for the solution of problems relating to linear motion. The representation of distance covered as the area of the figure between the graph of velocity and the time axis employed in these activities, leads on naturally to the study of problems on motion by means of functions, as well as allowing for the use of tools (concepts and propositions) from Euclidean geometry of relevance to such problems. By employing simple geometric transformations, equivalent real life problems are obtained which lead, in turn, to a simple classification of all linear motion-related problems. When applied to a wider range of motion problems, this approach prepares the way for the introduction of basic Calculus concepts (such as integral, derivative and their interrelation); in fact, we would argue that it could be beneficial to teach the basic concepts and results of Calculus from an early grade by employing natural extensions of the teaching methods considered in this paper.