How to connect school mathematics with students' out-of-school knowledge

In this paper we present an explorative study for which special cultural artifacts have been used, i.e. supermarket receipts, to try to construct with 9-year old pupils (fourth class of primary school) a new mathematical knowledge, i.e. the algorithm for multiplication of decimal numbers. Furthermore also estimation and approximation processes have been introduced, procedures that are not commonly used in ordinary teaching activity. In our study the receipts, through some modifications, have become more explicitly tools of mediation and integration between in and out-of school knowledge, so they can be utilized to create new mathematical goals, thus becoming real mathematizing tools and constituting a didactic interface between in and out-of-school mathematics. In agreement with ethnomathematical perspective we deem that it is a task for the teacher to know, in order to be able to profitably take account of the teaching, the life experienced by the pupil. Future mathematics teachers should be prepared a) to see mathematics incorporated into real world, b) to investigate mathematical ideas and practices of their pupils, and c) to look for ways to incorporate into the curriculum elements belonging to the sociocultural environment of the pupils, as a starting point for mathematical activities in the classroom. In this way the motivation, interest and curiosity of the pupils will be increased and the attitude towards mathematics of both pupils and teachers will be changed.