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Researchers disagree about when quantifier meanings are acquired. Some maintain that preschoolers don’t know the meaning of “most” (Sullivan, Bale, & Barner, 2018), while others argue that children successfully acquire this word shortly after age three (Halberda, Taing, & Lidz, 2008). Likewise for when children arrive at an adult-like understanding of “each” (for review Feiman & Barner, 2017). These disagreements stem in part from the complexities of tasks used – failures can be attributed to performance limitations (e.g., limited cognitive control) and successes can be attributed to response biases (e.g., always picking the biggest set).
Using a novel, implicit probe of children's quantifier meanings, we show that children's performance is best explained by meaning, not task demands. In two experiments, participants (n=300, ages=3;2-8;3) saw collections of shapes on an iPad (Fig.1&2) and evaluated simple quantificational statements (examples 1-4). After answering (≈3sec), a blank screen appeared and children were asked to touch where groups of shapes had been. Only the sentence differed across conditions; the images were identical. The logic was that, if participants were sensitive to subtle properties of the quantifiers’ meanings, they should encode the same scene differently depending on the quantifier used. Specifically, if they attended to a particular set during the initial display, they should provide a better estimate of its center (Whitney & Leib, 2018), despite center-of-mass being unnecessary for the evaluation task.
Experiment 1 tested children’s understanding of “more” and “most” using statements like (1)-(2) and displays of blue and yellow dots (Fig.1a).
(1) The blue team painted more of the dots
(2) The blue team painted most of the dots
Given that “more” has a comparative meaning and “most” has a proportional meaning, “more” should invite a strategy of directly comparing blue to yellow, whereas “most” should favor comparing blue to the total. If children share this understanding, they should know the center of the mentioned color (blue) equally well following either statement but should know the center of the non-mentioned color (yellow) better after evaluating the “more”-statement. This prediction was borne out (n=224, ages=3;10-8;3): we observe an interaction between quantifier and set (F1,213=6.01, p<.05). Participants were more accurate at remembering the center of the non-mentioned color following “more”-statements than following “most”-statements (Fig.1b). No age effects were found.
Experiment 2 tested children’s understanding of “each” and “every” using statements like (3)-(4) and displays of different colored shapes (Fig.2a).
(3) Each circle is blue
(4) Every circle is blue
“Each” highlights individuals whereas “every” is compatible with groups. This difference leads adults to attend to individuals following “each”-statements and groups following “every”-statements (Knowlton et al., 2018). If children are also sensitive to this distinction, they should represent the circles as a group when evaluating (4), and thus should be able to offer better estimates of its center of mass compared to after evaluating (3). As seen in Fig.2b, our participants (n=76, ages=3;2-7;11) demonstrated this pattern (t63.7=2.33, p<.05). Performance did not change with age.
These results suggest that children have adult-like semantic representations for quantifiers across development.