The question of concept and formalization amongst the community of teachers in physics
Résumé
This study focuses on the links between concepts in physics and the mathematical formalisms that translate them. A physics concept ought to be explored from an epistemological disciplinary perspective, one that shouldn’t be confused with the formalization process that aims at translating it. The notion of divergence of a vector field can be used to highlight the confusions that might exist between concept and formalization. Using an internet survey, an important proportion of French professors of higher education were asked to give the definition of the divergence of a vector field. 80% of the answers defined that term as the sum of the partial derivatives of the components of the field in relation to the corresponding coordinates. The paper shows how Maxwell and Heaviside have clarified this concept and how they have shown that an intrinsic definition based on vector analysis leads to the correct articulation between former concepts and new ones. By defining divergence as the limit of the electric flux per unit volume through a closed surface when the volume tends towards zero, the introduced concept takes root in previous knowledge whose limits were highlighted; it helps in pursuing the initial reflection and hence in making more sense. The poll showed surprisingly that this definition rarely appears. One might wonder about the introspection of teachers concerning the meaning of the elements they teach in physics. Can we really make do with obscure formulae and thus infer that the epistemology of physical sciences thus ought to be reduced to a mere symbolic representation of quantities emptied of their meaning? This article shows that much work on Science teaching remains necessary despite the great amount of results that the discipline has already achieved.
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