PHYSICS WITHOUT CALCULUS?

The purpose of this paper is to investigate the interplay between physics and mathematics in educational context. Although mathematics has always been closely related to physics, they 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. Our attempt focuses on the rising tide of the mathematizing of physical problems with the aim to comprehend better the troubles it generates for students and to propose some solutions to be introduced in the theory of didactics. 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 elliptical 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 study progression of mathematical concepts involved in the learning of physics, and to explore a possible didactic itinerary for a better integrated course 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 would be coherent and smooth.