Strategies for a Certain Type of Geometric Problems Solvable without Calculations

The article concerns pupils’ strategies for a geometric problem effectively solvable without calculations. The problem was solved by 125 pupils (aged 12 – 17) whose work was analysed using techniques of grounded theory. Three types of solving steps were identified: geometric in theoretical space, geometric in spatio-graphic space, calculation. Spatio-graphic steps were used even by older pupils. Calculations were more frequent in the older group (mainly girls who were less successful than older boys and younger girls). The younger pupils used spatio-graphic solutions more often than theoretical. The older pupils were more successful than the younger ones but not significantly.