Mathematics in physics problem-solving. A kinematics study in high school

One of the objectives of the high school is to support a domain of thought aimed at expanding the phenomenological field so that the experiences can give a greater basic efficacy to the scientific schemes to be adopted. This requires a conceptual change: teachers must guide students towards the awareness that the schemes of spontaneous knowledge and those of scientific knowledge have different contexts of use and this is not easy, also due to the limitations of linguistic tools. From a constructivist perspective, conceptual change mainly concerns the ability to recognize the proper context of a schema and the specific meaning of the words used in the different schemas. A methodological approach that allows us to go in this direction is that of problem-solving, often neglected in Italian secondary schools for various reasons. This contribution, which is placed in the aforementioned perspective, aims to underline the relationship between mathematical language and science. Specifically, through an example of didactic activity -based on problem-solving -it is shown how the study of kinematics can be abstracted into purely mathematical expressions.