Seminars

Much research suggests that some number-relevant representations, including those for quantifying small sets like one, two, and possibly three, are present in the innate human mind. Nevertheless, the canonical view of number development holds that children’s learning of meanings for the words “one,” “two,” and “three” is slow and protracted, taking over a year in typical cases. This lag occurs even though the words are present in the input and produced by children in their spontaneous speech, leaving a mystery as to why these words are hard to learn. Despite young children’s miraculous speed at acquiring words in general, these particular words seem to pose a special challenge. This talk will take a detailed look at children’s acquisition of the word “two” to argue that the canonical view is wrong: Contrary to most prior claims about children’s slow learning of the small number words, children do initially map the word “two” to the innate concept TWO. In other words, their initial acquisition of the word meaning is neither protracted nor incorrect -- just as would be expected if the learning task was to map a word to an innate, readily available concept. Evidence for this claim comes from children’s spontaneous speech and from a violation-of-expectation task in toddlers. However, the period of ‘correct’ mapping is brief and fleeting, lasting about a month or two, which explains why it has been overlooked and often missed in research studies. After this initial correct phase, children reanalyze the meaning of the word “two” several times, ultimately building an enriched meaning that is embedded in a number system (the system of positive integers) and likely facilitating the acquisition of the rest of the system. Evidence for the reanalysis claim comes from behavioral studies with 3-year-old children in which they demonstrate knowledge not just of the meaning of “two,” but also piecemeal understanding of the integer system. This revised tale resolves the mystery about why children don’t map the word “two” to their innate concept TWO (they do), and sketches how these initial learning steps might provide entry into the process of learning further number words. Time permitting, I will share some newer evidence that the ongoing process of understanding the integer system is also substantially more gradual than previously claimed, differentiating the arduous process of building new concepts from the quick task of mapping words to already-existing ones.

Four decades of research has established rich innate, abstract representations in non-human animals and prelinguistic infants—so called systems of “core knowledge” in domains of number, intuitive physics, agency (intentional, causal, communicative), geometry, abstract relations (such as sameness/ difference), and logic. I begin with a puzzle: Given evidence for innate abstract representations in these domains, why are external symbols for the same content (words, formal notations) so hard to construct, requiring tens of thousands years of cultural construction (or more) and many years in individual child development to master? I will provide two answers: first, the content in non-linguistic thought is partial; the non-linguistic representations capture some of the target concepts’ meanings but not all. Second, the representational systems in core knowledge are different in kind from those in adult cognition. I will focus on differences in format, and will argue that core knowledge systems are systems of perception, not cognition. I will illustrate with two case studies of the representations in non-linguistic thought and those in language: number and the abstract relations same/different.

When we communicate using language, we must choose what to say and how to say it, and these decisions about framing can influence how people think, feel, and act. Consider the statement “Girls are just as good as boys at math.” Although it appears to express an equivalence between groups, this construction leads more people to endorse stereotypes about boys’ natural math ability compared to a statement with the positions of the groups reversed. While traditional accounts view framing effects as irrational byproducts of biased processing, I present an alternative explanation grounded in pragmatic reasoning: Readers rationally infer that specific words and syntactic constructions communicate relevant information and incorporate this into their evaluations. Drawing on recent studies from my lab, I defend this more rational account while explaining why framing effects tend to be modest in size: when a message frame contradicts strongly held beliefs, people often resist its implications.