ON FUNCTIONS: REPRESENTATIONS AND STUDENTS' CONCEPTIONS

The main research questions of the present study are: a) does the way students conceive a function depend on its representation and b) are the procedures used by the students related to their conceptions about the notion of function? To this purpose a test was administrated to 190 students (17-years old). Functions were represented numerically, algebraically and graphically. Students' answers were analysed according to the procedure used and the way the function involved were conceived. The main results were as follows: a) students' conceptions depend on the function's mode of representation, b) in the case of the graphical representation of a function, conceptions and procedures used are related and c) when a function is represented numerically or algebraically, conceptions and procedures are not related.