Some Didactical Issues About the Teaching of Vectors and Translations in Mathematics and Physics Based on a Historical Approach

In mathematics, students learn about vectors and translation, in physics they model forces, speed, acceleration, etc. with vectors and study movements of translation. Do they make the connection between these concepts introduced in different disciplines or do they put things in separate boxes? In this paper we will start with some partial considerations on the history of vectors and we will give some references. Then we will show some examples of naïve illustrations of vectors from physics in mathematics textbooks. We will then present a non-conventional example and the difficulties it created for both mathematics and physics teachers. Finally, we will develop an example of a possible collaboration between teachers of both disciplines in relation to movement of translation