Includes bibliographical references (p. 319-333).

Research perspectives on conceptions of functions: summary and overview. Glossary. Theoretical perspectives for development of the function concept : On understanding the notion of function -- Operational origins of mathematical objects and the quandary of reification-The case of function -- The nature of the process conception of function. Theory-based teaching experiments : Functions from an algebraic and graphic point of view: cognitive difficulties and teaching practices -- Horizontal and vertical growth of the student's conception of function. Conceptions held by students and teachers : On the development of a sense for functions -- Students' understanding of a function given by a physical model -- The function concept as a prototype for problems in mathematics learning -- Teachers' mathematical knowledge of the concept of function. The use of pedagogical software : Dynamic representation and the development of a process understanding of fuction -- Getting students to function in and with algebra -- Patterns in students' formalization of quantitative patterns .