A scaffolding toolkit to foster argumentation and proofs in mathematics: some case studies

This paper focus on how language can be seen as an object to be manipulated and how manipulation can act as scaffolding for fostering argumentative competency. To this aim, we have defined a digital toolkit, consisting in virtual “language tiles”, made available to the students. The learners can freely articulate their thinking, drag the appropriate tiles in order build sentences for communicating her findings and arguments. The toolkit can also allow automatic assessment of the sentences. We analyse from a theoretical point of view the didactical potential of the toolkit for supporting cognitive process, activating mathematical knowledge and favouring the passage from reasoning, as production of arguments, to expression of arguments, towards construction of formal proof.