In primary school for example, we learn maths by memorising times tables and solving thousands of basic arithmetic problems. This was important in a time before calculators as being able to compute functions is a skill that students might need.
Today though, arithmetic should be taught, not because it might be useful, but because from arithmetic we can discover interesting properties about numbers themselves. I think maths would have been more interesting if you showed students how properties of pure numbers have this nice association with any set of real world objects that can be ordered.