Oggetti matematici, rappresentazioni semiotiche e significato: il problema dei cambi di senso

In this article we develop two themes that have characterized recent research in Mathematics Education. On the one hand we face the issue of meaning of mathematical objects as regards their semiotic representations and furthermore as regards semiotic transformations. On the other hand we discuss the epistemological statute of Mathematics Education as a scientific field, its internal coherence and its role in providing school institutions with effective instructional design. The article is a “dialogue” between a specific didactical problem – the change of meaning of mathematical objects due to semiotic transformations – and the intrinsic need of Mathematics Education to connect different theoretical perspectives (networking theories) to find its internal unity and coherence. On the one hand the understanding and interpretation of the changes of meaning requires the networking of different theories, on the other hand the issue of changes of meaning opens the way to a meta-theoretical reflection on Mathematics Education and the possible connecting strategies.