# Teaching functions/mappings early

Functions and mappings are usually introduced late in the curriculum, and functions of arity two or more are considered "advanced" (many don't even see them before college).

On the other hand, the concept of a mapping ("the dogie gets a bone, the kitten gets a fish, the bear gets an apple") is intuitive and many of my non-math friends told me when asked, that mapping from pairs or triplets isn't really a hard thing, just that they never thought about it from this perspective.

Hence, the questions: why it is not feasible to teach multiple-argument functions earlier, perhaps even before the addition is introduced in a more systematic way (the moment where one learns that it is one of many possible operators, and that multiplication is one too, and that there is some order to apply those operators, etc.)?

• What's wrong with talking about binary functions (resp. $n$-ary) as taking pairs (resp. $n$-tuples) as an input? BTW I think there is too much attachment to graphs and it causes problems when higher-order functions appear. I had to draw a lot of silly examples for them to repeat the foundations and only then continue to the actual topic. Commented Mar 18, 2014 at 15:48