“Looking for tricks”: a natural strategy, early forerunner of algebraic thinking.

Starting from the assumption that very young children exhibit some naïve forms of algebraic skills, in this work we present and discuss an episode occurred within a grade 2 classroom experimental work. This work is centred on an exploratory activity (namely, looking for regularities) in the domain of natural numbers. We observe that this kind of activity, if suitably managed, can activate the search for tricks to help mental calculation, inducing in children a first shift from an arithmetic behaviour, based on search for results, to an algebraic attitude, based on the search for relationships. Moreover, we notice how a guided use of suitable representations can transform children’s natural bent to look for regularities into ‘awareness of, or attention to, structure’, in the sense of (Mason et al., 2009).