La didattica della geometria e le rilevazioni nazionali

Italy has been involved in international surveys made by IEA (International Association for the Evaluation of Educational Assessment) for about 20 years and by OECD (Organisation for Economic Co-operation and Development) for about 15 years. From 2007 national assessments are made regurarly by INVALSI (National Institute for the Evaluation of the Educational System) too. International researches have never presented a brilliant picture of the Italian educational situation. This thesis focuses on the teaching of geometry and analyses the concept of geometry that all these surveys suggest. In the first part of this work the principal steps of the evolution of geometry are summarized in order to reflect on the educational importance of this science. In the second part the aims and the characteristics of the international IEA and OECD surveys are described. Then the methodology and the idea of geometry, which are presented in the INVALSI National test for pupils at the end of the lower secondary school, are discussed. Moreover some tests are shown according to the observations done before. In the last two chapters conclusions and purposes of this thesis are shown and geometry tests from competitive examinations held by Italian national commissions to select candidates for the teaching profession are analysed briefly. In conclusion we can say that geometry (euclidean bi- and tri-dimensional), introduced from primary school, should be shown as a training skill for reasoning, as a source for abstract problems whose solutions clarify the meaning of the same knowledges and as a way to interpret real situations and to solve everyday problems. Through the analysis of the National tests prepared by INVALSI and to the observation of Italian geometry course books for students of lower secondary school it is possible to explain the relation between geometrical entity and its representation; sometimes these two concepts can be confused or misunderstood by students.