The way the concept of velocity is presented in elementary mathematics textbooks builds on text problems and nowadays also on the use of tables. However the genesis of the velocity concept refers to a centuries-old search within the context of motion underlined with philosophical ideas. The concept that stands behind modern school mathematics refers back to Newton who himself relies on the work of Galileo Galilei. The historical development of mathematical education has shown that both mathematics and physics classes have their respective characteristic manner using this term. However, the mathematical potential for teaching this concept is by far not exhausted and asks for a philosophical background knowledge on the part of the teachers.