Children’s Proportional Interpretation of Most is Facilitated in Continuous Area-Based Contexts

• In Event: New Developments in the Science of Numerical Thinking

Abstract

Children’s understanding of quantifiers – terms that denote amounts of quantities, such as most, some, and all – has been of deep interest to linguists and numerical cognition researchers for decades. The quantifier "most" is particularly challenging because "most" cannot be expressed using first-order logic and requires comparing relative magnitude (Barwise & Cooper, 1981). As such, children struggle with interpreting "most" proportionally (Sullivan et al., 2018). However, much of this work focuses on discrete quantitative contexts, which interfere with children’s proportional reasoning in a range of contexts, such as juice-mixing (Boyer et al., 2008), probability (Hurst & Cordes, 2018; Jeong et al., 2007), and sharing (Hurst et al., 2020). Thus, in the current study, we investigate the hypothesis that children’s difficulty with interpreting "most" proportionally may be due, at least in part, to the saliency of absolute number in discrete numerical contexts in particular.
Four-to 6-year-old children (N = 120) judged which of two displays showed "most", both when the stimuli were continuous area-based quantities (where proportional reasoning should be facilitated) and discrete number-based quantities (where proportional reasoning should be hindered). On each trial, stimuli were introduced using either number words in the discrete block (see Figure 1, left) or using the word some in the continuous block (see Figure 1, right). Children were then asked "who did X to most of their stuff", for example: “who broke most of their drums?” or “who sold most of their lemonade?”. One person always did proportionally most (i.e., more than half), but absolutely less than the other (numerically less in the discrete block or less visual area in the continuous block) and the other person always did absolutely more than the other person, but not most of their own (i.e., less than half).
As predicted, children responded more proportionally on the Continuous trials, M=0.54, than on the Discrete trials, M=0.33, p < 0.001, partial eta-squared = 0.22. Exploratory analyses across the age group reveal that this pattern was stronger in the 5- and 6-year-olds, relative to the 4-year-olds, who performed around chance on both trial types (see Figure 2).
Thus, we replicated prior work suggesting that children interpret "most" as meaning absolutely more when the stimuli are discrete, but our findings also reveal that children were more proportional when the stimuli were continuous. In an on-going follow-up study, we are comparing children’s judgements in these comparison contexts to their verification judgements of whether or not a single stimulus displays "most". We hypothesize that the numerical interference of discrete displays will only be evident in contexts that require between-set comparisons (thereby allowing for interference from a competing option) and be much weaker in single-quantity verification contexts.
In summary, this work highlights both methodological and theoretical considerations for our understanding of children’s interpretation of the quantifier "most" in young children. Most notably, these findings reveal that 6-year-old children’s interpretation of "most" may be more proportional than previously found but is also highly precarious and easily disrupted when numerical cues highlight absolute information.

Authors

• Michelle A Hurst, University of Chicago
  Presenting Author

• Susan Cohen Levine, University of Chicago
  Non-Presenting Author