On the Order of TeachingMapping and Function

The important status of mapping in mathematics is discussed and the feasibility of putting the teaching of mapping before the teaching of function is examined. The method of teaching the definition of function by abstracting function from mapping has two advantages: One is to expose students to the process of mathematization from mapping to function, in- cluding abstracting process and symbolization process; The other is to help students find the nature of function, namely, func-
tion is mapping of one non-empty number set mapped onto another non-empty number set. Moreover, students will be much easier to understand the relation between mapping and function. Two examples of abstracting function from mapping are intro- duced:one is from evaluation of mapping to function;the other from the mapping of shooting to function.