The transition from algebra to analysis: the use of metaphors in a graphic calculator environment

This paper focuses on the introduction of the concept of limit at secondary school level. Drawing on research on the role of metaphors, movement and perception in the construction of mathematical concepts, we developed an approach to the concept of limit which considers perceptive elements as a starting point. The students are required to construct and manipulate representations of functions in a graphic calculator environment (namely, the TI89). The transition from the register of graphical representations to the symbolic one takes place in two ways: through the re-elaboration of the language used by the students to describe their graphic manipulation of the functions and through the introduction of symbols which will support the algebraic manipulation to be done later on.