The Pythagorean theorem in mathematics laboratory

This paper refers to the Pythagorean theorem and the use of physical artifacts (called mathematical machines), which are related to one of the proofs of the theorem. It aims to discuss the didactical use of these kinds of artifact, paying attention to students’ work with them and the role of the teacher. It presents a laboratory approach to this theorem developed within the Theory of Semiotic Mediation in mathematics education for 13-year-old students in Italy. The analysis shows that manipulation of the machine only does not imply the emergence of the mathematical meanings embedded in the machine. It also pays attention to the different graphical representations of the artifact and their role in the learning process.