The effects of rigidity on school geometry learning

This study attempts to explain certain difficulties which ninth grade students face in tackling geometrical "problems to prove", by relating them to general and to specific rigidity and cognitive style variables. The specific Geometrical Rigidity (GR) construct was conceived as comprising a perceptual component named Geometrical Functional Fixedness (GFF) and a conceptual component named Geometrical Method Embeddedness (GME). The general rigidity constructs were SDI and BRT that were derived within the Field Theory of K. Lewin and the Gestalt Theory respectively. The cognitive style construct was articulated-global style (measured by EFT). The results show that (a) GFF and GME are mutually independent (b) GR and its components have small negative correlations with SDI (c) GR and its components have insignificant correlations with BRT (d) GR and its components have strong negative correlations with articulated-global style (e) school geometry achievement has strong negative correlations with GR and its components, positive correlations with SDI and EFT, and insignificant correlations with BRT (f) GR is a potent and efficient predictor of future failure in school geometry learning. These results confirm the conceptual analysis of GR and indicate that GR has an independent existence as a cognitive style construct rather than a personality trait.