Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal

Abstract

This paper proposes a novel methodology, based on the semiotic-cognitive theory of learning (González, 2018), to address issues of lagrangian mechanics, a subject of the higher level of physics professors and Physics undergraduates, exemplified in Noether's theorem, which links the symmetry of mechanical configurations, with the corresponding first integrals of motion. Instead of the classical way of presenting the theorem, by means of a statement, demonstration and exemplification, we start with a table of properties (including symmetries and conservation of different specific configurations) which the student is asked to relate hypothetically, and then construct a formal expression based on the Lagrange equations, by means of a recursive procedure from which the proof of the theorem is extracted as a conceptual scheme, which will finally be applied in a generic form, detached from the previous specific configurations. Although it is exemplified with a subject of lagrangian mechanics, the method is applicable in a general way, adapting it to the corresponding subject and topic.