Geometric form perception has been extensively studied in human children, but it has not been systematically characterized from the perspective of formal geometry. Here, we present the findings of three experiments that use a deviant detection task to test children's and adults' sensitivity to geometric invariants in a variety of visual displays. Children as young as 4 years of age analyzed shapes by detecting relationships of distance and angle but not by detecting the relationships that distinguish an object from its mirror image (hereafter, sense). Patterns of visual form analysis showed high invariance over development: the properties that were least detectable by children also posed the greatest difficulty for adults. In general, sensitivity to all tested properties improved with age, with an asymptote at about 12 years, before the onset of instruction in formal geometry. When presented with a carefully controlled set of forms that varied exclusively in length, angle or sense, children were found to develop sensitivity to these properties at different rates, responding first to length, then to angle, and last to sense. Between 8 and 10 years of age, moreover, children began to confer a privileged status to the relation of perpendicularity. Geometric competence therefore appears to emerge as an interplay between developmentally invariant, core intuitions and later acquired distinctions.
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