  We present some fragments of a teaching experiment realized in a first grade
classroom, to sow the seeds for a mathematical definition of rectangles that
includes squares. Within the paradigm of semiotic mediation, we studied the
emergence of pivot signs, which were exploited by the teacher to pave the way
towards an inclusive definition of rectangles and squares. This was done to
favor overcoming children's spontaneous distinction of these figures into
distinct categories, reinforced by everyday language. The experiment is an
example of an approach towards the theoretical dimension of mathematics in
early childhood.
