Acquisition of the counting principles during the subset-knower stages: Insights from children’s errors

Studies on children’s understanding of counting examine when and how children acquire the cardinal principle: the idea that the last word in a counted set reflects the cardinal value of the set. Using Wynn’s (1990) Give-N Task, researchers classify children who can count to generate large sets as having acquired the cardinal principle (cardinal-principle-knowers) and those who cannot as lacking knowledge of it (subset-knowers). However, recent studies have provided a more nuanced view of number word acquisition. Here, we explore this view by examining the developmental progression of the counting principles with an aim to elucidate the gradual elements that lead to children successfully generating sets and being classified as CP-knowers on the Give-N Task. Specifically, we test the claim that subset-knowers lack cardinal principle knowledge by separating children’s understanding of the cardinal principle from their ability to apply and implement counting procedures. We also ask when knowledge of Gelman & Gallistel’s (1978) other how-to-count principles emerge in development. We analyzed how often children violated the three how-to-count principles in a secondary analysis of Give-N data (N = 86). We found that children already have knowledge of the cardinal principle prior to becoming CP-knowers, and that understanding of the stable-order and word-object correspondence principles likely emerged earlier. These results suggest that gradual development may best characterize children’s acquisition of the counting principles, and that learning to coordinate all three principles represents an additional step beyond learning them individually.

Intrasaccadic motion streaks jump-start gaze correction

Rapid eye movements (saccades) incessantly shift objects across the retina. To establish object correspondence, the visual system is thought to match surface features of objects across saccades. Here, we show that an object’s intrasaccadic retinal trace—a signal previously considered unavailable to visual processing—facilitates this match making. Human observers made saccades to a cued target in a circular stimulus array. Using high-speed visual projection, we swiftly rotated this array during the eyes’ flight, displaying continuous intrasaccadic target motion. Observers’ saccades landed between the target and a distractor, prompting secondary saccades. Independently of the availability of object features, which we controlled tightly, target motion increased the rate and reduced the latency of gaze-correcting saccades to the initial presaccadic target, in particular when the target’s stimulus features incidentally gave rise to efficient motion streaks. These results suggest that intrasaccadic visual information informs the establishment of object correspondence and jump-starts gaze correction.

Intra-saccadic motion streaks jump-start gaze correction

Rapid eye movements (saccades) incessantly shift objects across the retina. To establish object correspondence, the visual system is thought to match surface features of objects across saccades. Here we show that an object’s intra-saccadic retinal trace – a signal previously considered unavailable to visual processing – facilitates this match-making. Human observers made saccades to a cued target in a circular stimulus array. Using high-speed visual projection, we swiftly rotated this array during the eyes’ flight, displaying continuous intra-saccadic target motion. Observers’ saccades landed between the target and a distractor, prompting secondary saccades. Independently of the availability of object features, which we controlled tightly, target motion increased the rate and reduced the latency of gaze-correcting saccades to the initial pre-saccadic target, in particular when the target’s stimulus features incidentally gave rise to efficient motion streaks. These results suggest that intra-saccadic visual information informs the establishment of object correspondence and jump-starts gaze correction.

Effects of Transient and Nontransient Changes of Surface Feature on Object Correspondence

Object correspondence is a fundamental problem in perception. Classic theories hold that the computation of correspondence is solely based on spatiotemporal information. Recent research showed that surface features also play an important role. However, the surface features of objects in many studies did not change throughout a trial. This study investigated the effect of feature change on object correspondence using the object-reviewing paradigm. Two moving objects underwent transient feature changes on color dimension (Experiment 1A) or a combination of three dimensions (Experiment 2A). Moreover, the objects moved behind four occluders to make the feature change nontransient (Experiments 1B and 2B). Object-specific preview benefits were reduced or eliminated when feature changes were transient, but the benefits were not affected when feature changes were nontransient. The effects of transient versus nontransient changes of surface feature in object correspondence are discussed.