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

Abstract

T his 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 signi cantly more dif cult 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 dif cult 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 signi cantly easier to make in 1D than in 2D and in 2D than 3D. Deductions were also signi cantly 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. C ette étude porte sur les effets de l'ordre formel et du contenu spatial sur le raisonnement en trois dimensions dans la perspective de la théorie des Règles Formelles et celle des Modèles Mentaux. Vingt-six adultes ont résolu 144 problèmes variant suivant l'ordre formel des entités (ordre référentiel, continuité référentielle) et le contenu spatial (dimensions, orientations, et directions). Les variables dépendantes étaient les bonnes réponses et les temps de réponses. Le nombre de modèles mentaux et les dérivations formelles sous-jacentes aux déductions ont permis de comparer les prédictions opposées faites par la théorie des Règles Formelles et celles des Modèles Mentaux.Les résultats con rment d'emblée les prédictions de la théorie des Modèles Mentaux. Les effets de l'ordre référentiel montrent que les problèmes à deux modèles mentaux étaient signi cativement plus dif ciles que les problèmes à un modèle mental malgré le fait que les premiers impliquaient des dérivations formelles plus courtes que l...