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We present some fragments of a teaching experiment realized in a first gradeclassroom, to sow the seeds for a mathematical definition of rectangles thatincludes squares. Within the paradigm of semiotic mediation, we studied theemergence of pivot signs, which were exploited by the teacher to pave the waytowards an inclusive definition of rectangles and squares. This was done tofavor overcoming children's spontaneous distinction of these figures intodistinct categories, reinforced by everyday language. The experiment is anexample of an approach towards the theoretical dimension of mathematics inearly childhood.

Using pivot signs to reach an inclusive definition of squares and rectangles