Il pensiero algebrico:questioni di natura epistemologica e didattica

The subject of this thesis is the study of the birth of algebraic thinking, as a generalization process, in 10 to 14 years old pupils. We analyse the relationships between the ways of describing a general algorithm, the strategies applied in solving arithmetical-algebraic problems and verbal and symbolic languages. As a result of the study, we can confirm that the causes of some difficulties in learning elementary algebra are due to a didactic obstacle rather than to an ontogenic obstacle. Furthermore, we have found some features of didactical activity in classroom that can further or prevent generalization processes