A dramatic illustration of the incomplete association between chronological age and spatial performance comes from research using a “shadow projection task,” originally developed by Piaget and Inhelder (1956) as one method to study children’s developing projective spatial concepts. In this task, children were asked to predict (through drawings or via selections among response alternatives) the shadows that would be cast on a screen if a light source were directed at an object. Of particular interest were children’s predictions about shadows as the object was systematically rotated. Illustrative is a pencil that was initially positioned so that the side of the pencil was in the path of the light (thus casting a rectangular, horizontal line-like shadow) and then gradually rotated toward the light source so that the shadow line became shorter, and eventually became a small circle (once the light source directly faced the pencil point or pencil eraser end). Protocols from children under 9 or 10 years of age were used to demonstrate that young children have difficulty in using projective geometry to represent spatial transformations. For example, “knowing” that pencils are long and thin made it difficult for young children ever to give up the idea that the shadow would be line like.
Although the original reports suggested that children gradually and universally mastered projective spatial concepts and hence performed well on the shadow projection task, later research with an adult college population (Merriwether and Liben, 1997) demonstrates that many adults (more women than men) have the same kinds of difficulties on the shadow projection task that Piaget and Inhelder (1956) had reported for children some 40 years earlier. For example, adults were asked to draw the cast shadow of 10-mm-thick plastic shapes—circular, triangular, and hexagonal—when the shape was rotated 30, 60, and 90 degrees towards and away from the screen. Adults of both sexes averaged only about one correct answer for the 30 and 60 degree rotations, and although most males were generally correct ( in about five of the six trials) on the 90 degree rotation (which casts a simple thick line [rectangular] shadow), females fared far worse (averaging only about three of six correct). Furthermore, the errors were not trivial. Figure C.1, from Downs and Liben (1991), shows three participants’ responses. These data provide a striking illustration of the point that just as some young children succeed especially well on spatial tasks (as in the classroom location and direction task), some adults appear to have difficulty in visualizing or representing events that draw on spatial concepts.