Learning and Assessment in Mathematics and Science, Gagatsis, A.; Constantinou, C.P. & Kyriakides, L. (Eds.) (2000), Department of Education, University of Cyprus, Nicosia, 157-170 Learning, problem solving and use of representative registers in Italian High School GIORGIO T. BAGNI Summary. Several previous studies showed that the role of semiotic representations is very important in the learning of Mathematics: in this paper we analyse the behaviour of High School pupils (aged 17-19 years) with reference to some exercises in Trigonometry and in Analytic Geometry; an experimental research considered 196 pupils. In particular, as regard strategies and educational implications, we conclude that many pupils try to solve a problem only in the sector explicitly considered: and sometimes this is a remarkable obstacle to reach good performances and it is ineffective for the development of the ability to co-ordinate different registers of representation. INTRODUCTION Two sentences by pupils of Italian Secondary School will help me to introduce the subject of this work. The visual proof of the Theorem of Pythagoras from Chou Pei Suan Ching ________ Some results given in this paper were presented to UMI-Meeting of Salsomaggiore, 2000.