Multiple Measures of Numerical Cognition and Quantifier Interpretation

Abstract

How do numerical knowledge and knowledge of language interact? There has been a great deal of work that tries to explain how language is used in counting and mathematics, but less work has been done trying to explain how numerical ability might relate to language ability. A reasonable place to begin to look are the natural language quantifiers (e.g. some, all, none, each, few, etc.). An example of a plausible math-language connection is found in sentences with quantifiers that represent collective or distributive actions. Children across an array of languages are delayed in learning to interpret such distributive and collective sentences. For example, Each minion pushed a rock. is accepted by children in collective contexts, in which there is one rock pushed by multiple minions together, which adults reject. While much of language is acquired early, this interpretative ability is delayed until children are roughly 11 years old. An as-yet unexplored connection would be between the domain of language that is responsible for these interpretations and children's numerical knowledge. In this project, we use four different tests of child numerical knowledge and independently test children's distributive-collective linguistic interpretations to determine to what degree, if any, these aspects of number and these aspects of language are related. Our four numerical tests include pre-linguistic analog magnitude estimation, symbolic and non-symbolic number line estimation and number set calculation. Our linguistic measure of quantifier interpretations is receptive experiment in which children watch a video depicting collective or distributive actions and are then asked whether a sentence describing the video in either collective or distributive terms is correct. Results showed that children in our dialect categories were not significantly different from one another in their numerical abilities, but that they were different in their quantifier interpretations. Quantifier interpretations and numerical abilities did not correlate. This shows that dialect variation in African American vernacular and mainstream English acts as a language obstacle that is only seen in quantifier interpretations. Consequences of our findings are relevant to the relationship among cognitive abilities deployed in mathematical reasoning and other linguistic expressions of number.