Perceptual and memorial constructs in children's judgments of quantity: a law of across-representation invariance.

Children at three different ages made judgments of physically presented (perceptual estimation) or symbolically represented (memorial estimation) rectangles. Height and width were integrated according to different, age-dependent algebraic rules. Memorial data obeyed the same integration rules that operated in the original perceptual judgments even when younger children and older children used completely different combination models. Valuation operations were the same in perception and memory for the youngest group (6-year-olds) but became discriminably different at older ages (for the 8- and 10-year olds). Three additional experiments on judgments of volume, liquid quantity, and visual length yielded strong cross-validation support for the general invariance claim (with respect to integration rule theory) but less strong support for the specific invariance claim (with respect to valuation function for the 6-year-old subjects). Results are interpreted as demonstrating lawful and long-enduring ecological constraints on internal representation.