RUOLO DEI PROBLEMI E DELLE FUNZIONI PER L'AVVIO ALLA GENERALIZZAZIONE IN MATEMATICA.

We examine issues that may arise with students attempting generalization when solving problems involving linear functions. We focus on the concepts of regularity, function, and generalization in mathematics education, examining how junior high school students produce and represent generalizations in an Early Algebra environment. It is important to nurture a transition from empirical generalizations based on conjectures regarding cases at hand, to theoretical generalizations that follow from operations on explicit statements about mathematical relations. The arithmetical, algebraic and geometrical dimension is explored through the study of a particular case.