Mathematics in its relation to other disciplines. Some examples related to economics and physics

Resumen

Mathematics is often seen as a very specific subject, either by students, parents, media or even mathematicians themselves. In many contexts, mathematics is feared and seen as a subject for selection, disconnected from interesting applications to real life. Moreover, the structure of teaching institutions, in many cases, makes the collaboration between teachers from different disciplines very difficult. At the same time, mathematics is more and more invisible in everyday life, since high technology tends to hide the mathematics necessary for its creation in sophisticated black boxes. As a result, it is quite a challenge to give an adequate answer to those who, legitimately, wonder what mathematics is useful for.

Our purpose in this paper is to see how mathematics in different curricula is actually connected to other disciplines and to give propositions to make this connection more effi- cient for the benefit of both mathematics and other subjects.

The results presented here emerged from different research works that we lead in relation to physics and economics.

After a short introduction presenting the situation in France.we will give two kinds of examples:

- In the context of French upper secondary scientific education: the use of vectors in physics and the connection between the notions of translatory and rotating movements in physics and the notions of translation and rotation in mathematics.

- In the context of French upper secondary and university education specialised in economics: the use of matrices for linear models of production and the use of functions, and especially of the concept of derivative and its relation to the notion of marginality in eco- nomics.

Our study reveals that, most often, teachers know very little about other subjects, even in relation to their oyen subject. Mathematics teachers do not want to get involved in too specialised applications while physics or economics teachers send their students back to their mathematics teacher for explanations on the use of mathematics in their field. As a result, students are used to seeing mathematics and other subjects as disconnected. This is reinforced by cultural differences, especially visible in the use of vocabulaiy or recipes that create artificial gaps between different disciplines.