Research reported deals with identifying stages in attaining a concept of function by students, eleven through fourteen years of age, of above average ability, taking the experimental mathematics program of the Secondary School Mathematics Curriculum Improvement Study. In order to obtain a hierarchy of the learning stages, both a written test and an individual interview were used. All 201 subjects received the written test and 20 subjects were selected for individual testing on a set of sixteen function tasks. From the written test, five stages were identified: (1) ability to find images of a function, (2) ability to consistently identify instances of mappings in several different representations, (3) operational ability in finding images and domain is exhibited, (4) ability to consistently identify non-instances of mappings in several different representations, (5) ability to find images under the composition of two functions and solve related problems using functions in several different representations. The individual interview test results altered the previous findings to yield the final analysis of stages. These were: (1) concept identification (ability to discriminate instances and non-instances of function), (2) process (ability to work with various representations and names of function in finding images, preimages, domain, range, and sets of images), (3) operations (ability to carry out operations on functions with an indication that the result of the operation is understood again to be a function. (JG)