Improving school geometry learning through rigidity reduction by the instruction of a heuristic problem solving model

Rigidity has shown to exert negative effects on the solution of geometrical problems. A reduction of rigidity was attempted by the instruction of a geometryspecific heuristic problem solving model, the Geometric Proof Finder (GPF). Four groups of highly rigid students (G1, G2, F and N) were formed within each of four ninth grade classes. Groups G1 and G2 were taught to solve proof problems by the GPF model, group F had extra practice with the regular mathematics class model, and group N received no instruction. The instruction of the GPF model reduced the rigidity, and had facilitated subsequent learning of school geometry: (1) immediate geometry achievement improved in group G1 and in the combined groups G1 and G2, but no change was observed in groups F and N; (2) at the end of the year, geometry achievement was higher in groups G1 and G2 than in groups F and N; (3) at the end of the year geometry achievement of groups G1 and G2 equalled that of their non-rigid classmates; (4) the inferior geometry achievement of groups F and N relative to their non-rigid classmates persisted over the year. These results render the GPF model a powerful instructional means to remedy deficient school geometry learning.