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The research reported addresses the question whether infants perceive numerosity as an invariant property across continuous changes in the spatial arrangement of a small set of objects (2, 3, and 4). Infants were presented with displays of small numerosities that produced changes in the optic structure such that magnitude was not tied to certain static or dynamic configurational properties of the display, but remained constant across patterns of optic motion. The displays consisted of configurations of figures that moved at a constant speed, and whose movements were translations. An infant-controlled habituation of visual looking-time task was used. First, infants were tested at 5 months for the numerosities 2, 3 and 4 in three randomly ordered sessions. The general results provided no clear evidence for numerosity perception. Inspection of the data suggested that the moving patterns may have consisted of synchronies that distracted the infant's attention from the numerical properties of the display. Using improved displays the results of a second study with 8-month-old infants indicated that infants can perceive numerosity invariance for small quantities of objects.