The height?+?width rule in children's judgments of quantity

SUMMARY Judgments of area of rectangles by S-year-old children obeyed an adding rule: height + width. This was surprising because simple perception of area ought to follow the physical height X width rule that was in fact obtained with older children. For the younger children, however, the height + width rule was reliable across a variety of experimental manipulations in eight experiments. This height + width rule was interpreted in terms of a general-purpose integration rule and a general metric sense. Young children lack a clear, adult conception of specific quantities such as area. They utilize whatever quantitative cues seem relevant and integrate them by a general-purpose adding rule to arrive at their quantitative judgment. A single general metric sense, which is present at least by age 3, mediates the overt expression of quantitative judgments of many different concepts, both physical and social. In collateral work, 5-year-olds judged amount of liquid in a glass by a heightonly rule. This result was expected from Piagetian theory of centration, which says that young children do not integrate information, but instead base their judgment on a single salient aspect of the stimulus. But this centration interpretation did not hold for the rectangles mentioned above. It was suggested, therefore, that the height-only rule represented transfer from daily drinking experience, not true centration. This hypothesis was supported by experiments showing that judgments of amount of wax in translucent cylinders obeyed the height-only rule when the cylinders were inside of glasses, but obeyed the height + width rule when they stood alone. These results, together with related studies of information integration in children, show that centration is not a pervasive characteristic of the young child's thinking. On the contrary, ydling children can exhibit quite sophisticated integration strategies. It is suggested that the concept of centration has resulted largely from inadequate methodology and that the methods of information integration theory provide a more analytical and correct picture of cognitive development. These results also lead to a new interpretation of conservation. It is suggested that conservation is derivative from object invariance and variegated specific experiential factors. The Piagetian concept of compensation is not causal in the development of conservation, but instead compensation arises from an attempt to articulate a verbal justification for a prior concept of conservation. In this view, conservation develops gradually as an expectancy of object invariance. The methods of integration theory and functional measurement can be used to trace out the course of the development of conservation.