From Galileo to ... the Mathematics Classroom

Abstract

The close relationship between Mathematics and Physics during their historical development is generally considered to offer motivational power to the educational praxis. In this paper, we discuss a teaching approach inspired by history in which the integration of genetic ‘moments’ in the history can lead to the designing of a specific activity. We exploited historical elements from the mathematical study of motions in the later Middle Ages (14th century) and Galileo (17th century) in order to introduce first-year undergraduates in the Department of Mathematics to the Fundamental Theorem of Calculus. The activity was based on a problem of motion and its representation in Cartesian axes of velocity/time. We used an original text from Galileo’s book “Dialogues Concerning Two New Sciences” concerning the free fall of bodies. In this paper, we present: (1) elements of the History of Mathematics and Physics which we used in designing the activity, (2) the didactic aims of the activity, (3) worksheets and excerpts from the students’ interviews, and (4) observations from analysis of the collected data.