Do children estimate area using an "Additive-Area Heuristic"?

A large and growing body of work has documented robust illusions of area perception in adults. To date, however, there has been surprisingly little in-depth investigation into children's area perception, despite the importance of this topic to the study of quantity perception more broadly (and to the many studies that have been devoted to studying children's number perception). Here, in order to understand the interactions of number and area on quantity perception, we study both dimensions in tandem. This work is inspired by recent studies showing that human adults estimate area via an "Additive Area Heuristic," whereby the horizontal and vertical dimensions are summed rather than multiplied. First, we test whether children may rely on this same kind of heuristic. Indeed, "additive area" explains children's area judgments better than true, mathematical area. Second, we show that children's use of "additive area" biases number judgments. Finally, to isolate "additive area" from number, we test children's area perception in a task where number is held constant across all trials. We find something surprising: even when there is no overall effect of "additive area" or "mathematical area," individual children adopt and stick to specific strategies throughout the task. In other words, some children appear to rely on "additive area," while others appear to rely on true, mathematical area - a pattern of results that may be best explained by a misunderstanding about the concept of cumulative area. We discuss how these findings raise both theoretical and practical challenges of studying quantity perception in young children.