A Diagram Helping the Mathematical Problem Solving Procedure

The Author verified in the middle school that its setting up a diagram for solving problems in arithmetic or in geometry was considered completely different from that developed in Primary school (grade 7). For this reason, he has decided to verify, since 2017, with pupils and the collaboration of a Primary’s teacher, the possibility of sharing, as possible, the same solution diagram both to make the aforementioned passage as less traumatic as possible, and to better understand the question of the mathematization of reality and the metacognitive processes underlying it. The proposed diagram, analyzed only in middle school, must not give the false certainty of solving the problem correctly, i.e. it must not be seen as a solution algorithm but only an helping for better and ordered writing the resolution procedure for error checking.