PHYSICS WITHOUT CALCULUS?

The purpose of this paper is to investigate the interplay between physics and mathematics in an educational context. Although mathematics has always been closely related to physics, the two disciplines are different in objects, aims, methods and tools. Nevertheless, mathematics provides physics with the language it needs. However, this language has to be presented through its historical, cultural and epistemological development to be properly understood. On the other side, physical problems are often overshadowed by mathematics. The result is that students are more concerned with the mathematical machinery rather than with a proper understanding of the physical situation. Our aim is to comprehend better the troubles that such an approach generates for students and to propose innovations in teaching and learning. More precisely, the question of the rearrangement of physics from pre-calculus to calculus will be approached through historical and epistemological analyses. Under this approach, learning is conceived as a permanent activity of building and re-structuring, in an helicoid way, the key mathematical concepts and functions needed to analyze physical models. Our research will involve the following three dimensions: 1 Historical and Epistemological Perspective (HEP) 2 Cognitive and Learning Perspective (CLP) 3 Didactic Perspective (DP) The main goal of this type of analysis is to discuss the role and the learning progression of mathematical concepts involved in the study of physics and to explore a possible didactic itinerary for a better integration of mathematics and physics. Specifically, our purpose is to study the transition from primary to secondary school and from this to the university in the mathematics field, with the ambition to re-design a curriculum in which the steps from basic to advanced mathematics are as more coherent and smoother as possible.