Verbal Counting Moderates Perceptual Biases Found in Children's Cardinality Judgments

Abstract

A crucial component of numerical understanding is one's ability to abstract numerical properties regardless of varying perceptual attributes. Evidence from numerical match-to-sample tasks suggests that children find it difficult to match sets based on number in the face of varying perceptual attributes, yet it is unclear whether these findings are indicative of incomplete numerical abstraction abilities early in development or instead are driven by specific demands of the matching task. In this study, we explored whether perceptual biases would be found in data from a numerical task invoking verbal representations of number and whether these biases are moderated by verbal counting behavior. Three- to 6-year-old children classified as proficient counters (cardinal principle knowers) participated in a number cardinality task in which they were asked to identify which of 2 arrays—either perceptually homogeneous or heterogeneous in appearance—contained a specific number of animals (e.g., “12 animals”). Results revealed an overall performance bias for homogeneous trials in this cardinality task, such that children were better able to exactly identify the target cardinality when items within the sets were perceptually identical. Further analyses revealed that these biases were found only for those children who did not explicitly verbally count during the task. In contrast, performance was unaffected by the perceptual attributes of the array when the child spontaneously counted. Together, results reveal that cardinality judgments are negatively impacted by perceptual variation, but this relationship is muted in those children who engage in verbal counting.

ACKNOWLEDGMENTS

We would like to thank the members of the Boston College Infant and Child Cognition Lab, especially Alison Goldstein, Brynn Huguenel, Erica Tavares, Cara Picano, and Allyse Fazio, who assisted in data collection, as well as Michelle Hurst and Ursula Anderson, who provided statistical help. We would also like to thank the Boston Children's Museum and the Living Laboratory at the Museum of Science in Boston, as well as all of the families who participated in our study.

Notes

¹A very similar account has recently been proposed in the preverbal infant literature to account for numerical discrimination failures in the small number range (“signal clarity hypothesis”; Cantrell, Boyer, Cordes, & Smith, 2015; Cantrell & Smith, 2013).

²Exact number comparisons (as required in the matching task) are generally more difficult than approximate number discriminations (as required in the ordinal task; Cantlon et al., 2007; Halberda & Feigenson, 2008). Although accuracy was comparable across their two tasks, the authors indicated (in a footnote, Cantlon et al., 2007, p. 435) that they made participants select the smaller number in the ordinal task because pilot data indicated “considerably higher accuracy” when participants were asked to select the larger number. Thus, it is possible that performance on their ordinal task was more reliant on inhibitory control processes (inhibiting an initial preference to select the larger value) than on numerical abilities, thus muting any potential perceptual biases that may have been found.

³Although our Give-N task was modeled after Le Corre and Carey (2007), it should be noted that Sarnecka and Lee (2009) have argued that knower levels may be overestimated when set sizes are presented in ascending order (as opposed to random order). Thus, it is possible (though unlikely) that a few children included in our task may not have met Sarnecka and Lee's criterion for being classified as a CP knower and instead would have been classified as a subset knower. Conversely, however, these authors also argue that CP knowers may not consistently produce a set of six in the Give-N task, suggesting that our criterion for being classified as a CP knower may have in fact been more stringent and required a higher level of counting proficiency than Sarnecka and Lee would expect of children classified as CP knowers.

⁴Only one study has investigated whether a similar pattern is observed in young children who have recently mastered the count list (Schaeffer, Eggleston, & Scott, 1974). Although data from that study were in line with a heterogeneity bias for counting, it should be noted that their heterogeneous arrays were constructed such that they contained contiguous subgroups of items (e.g., three tigers, two buttons, and three cars), and importantly, children used these subgroups to guide their counting behavior, such that 95% of children counted items within subgroups in sequence (counting all tigers, followed by all buttons, etc.)—a strategy that does not apply to counting arrays in which all individual items are distinct. Moreover, recent evidence suggests that adults enumerate sets that can be parsed into subsets in a distinctly different fashion than standard heterogeneous sets (Cordes, Goldstein, & Heller, 2013; Redden & Hoch, 2009), thus leaving open the question of how young children's counting would be affected by perceptual variability.