Illusory tilt and Euclidean schemes as factors in performance on the water-level task.

The water-level task was designed by Piaget and Inhelder (1948/1956) as part of their investigation of children's development of spatial concepts. Children were typically shown a partially filled upright bottle and were then asked to predict the orientation of the liquid edge when the bottle was tilted. Even after observing a partially filled, rotating bottle, young children performed poorly on this task, often responding that the liquid edge would be in some nonhorizontal position. According to Piagetian theory, children were not able to predict the invariant horizontal position of the liquid because they had not yet developed a conceptual system of integrated horizontal and vertical coordinates with which to observe and represent the physical world. As it turns out, a large number of adults also have difficulty on paper-and-pencil versions of the water-level task (for reviews see Kalichman, 1988; Liben, 1991a; Pascual-Leone & Morra, 1991). Moreover, these adults, like the children observed by Piaget and Inhelder, appeared to be resistant to learning the water-level principle from visual observations of either dynamic (e.g., Liben, 1978) or static water-level displays (Thomas, Jamison, & Hummel, 1973). These findings are problematic for Piagetian theory because all normal adults should have a Euclidean conception of space.