Abstract:
Demonstration is an important element in the history of mathematics, it is responsible for validating
an argument, explaining, communicating constructed mathematics and even stimulating new ones.
However, we noticed that the approach to validation processes occupies little space in school mathematics,
in the guiding documents and even in academic research. Considering the practice of teachers
who want to address these processes in the classroom, we undertook an educational development
research project with a qualitative approach that aims to develop tasks of an investigative nature in
dynamic geometry environments in order to contribute to the construction of mathematical proof
in problems relating to triangle inequalities. Such tasks were organized into a didactic sequence
that was applied to 5 students participating in the Mais Estudo project in the state education school
system of Bahia. The results were interpreted in the light of our theoretical framework, which is
aligned with Balacheff’s (2000) conceptions of proof and demonstration, as well as his typology of
proofs in terms of the arguments used by students to validate their conjectures. We verified that
the didactic sequence produced made it possible to stimulate the formation of conjectures and the
production of proofs typified as naive empiricism in all the participants and crucial exemple.
