The effects of formal order and spatial content on reasoning in three dimensions

Abstract

This study investigates the effects of formal order and spatial content on reasoning in three dimensions in view of the Formal Rules theory and the Mental Models theory of spatial reasoning. Twenty‐six subjects solved 144 spatial deductive problems that varied by the formal order of the entities (referential order, referential continuity) and the spatial content (dimension, orientation, and direction). There were two dependant variables: the correct responses and their response times. The number of mental models and the formal derivations underlying the deductions allowed comparison of opposite predictions made by the Formal Rules theory and the Mental Models theory of spatial reasoning.The results overwhelmingly supported the Mental Models theory's predictions. The effects of referential order showed that problems yielding two possible mental models were significantly more difficult than problems based on one mental model, although the former problems involved a shorter formal derivation than the latter. The effects of referential continuity also generalized the Mental Models theory's prediction to reasoning in all three dimensions. The effects of referential continuity showed that problems that required independent layouts in memory were reliably more difficult than problems that allowed the continuous integration of the entities in a mental model. We obtained these results despite the fact that the former condition required a shorter formal derivation than the latter. The effects of spatial content were also reliable despite the fact that the formal derivations were the same across spatial content. Thus, spatial deductions were significantly easier to make in 1D than in 2D and in 2D than 3D. Deductions were also significantly easier to make from left to right along the horizontal axis of a mental model, and from top to bottom along the vertical axis rather than from the respective opposite directions. The effects of spatial content suggest that mental models reproduce spatial relations relative to reference frames.