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The Representation of Number: Origins and Development

Number systems are present in most human languages and cultures, and a world without access to numbers seems unimaginable and foreign to adults in many linguistic and cultural communities. From nursery rhymes to baking recipes, from calendars to engineering plans, from sports rules to financial transactions, numbers are present in every aspect of human activity. Number is deeply embedded in human culture in ways that have transformed societies through the ages. Number is also, fundamentally, a product of the human mind and a powerful domain for discovering the mechanisms that govern how the human mind works. Many things about number come easily to us. It is generally agreed that a rudimentary ability to perceive and represent number is present in human infants (and many kinds of animals). Furthermore, young children across different cultures and languages seem capable of gaining access to the system of natural numbers before they are exposed to formal schooling, simply by interacting with people in their environment. Nevertheless, other aspects of number knowledge come less easily to humans and seem to require considerable cultural support. Even though children learn number word meanings before they begin formal education, they initially lack full appreciation of their logic. Furthermore, the ability to engage in exact mathematical operations (“Ambition, Distraction, Uglification, and Derision,” in Lewis Carroll’s famously mocking words) can seem daunting to many older children and even adults. For cultures without number words (or other equivalent symbolic tools), precise numerical calculations appear severely limited or downright impossible. From the perspective of modern cognitive science, the complex nature of number knowledge touches on several foundational issues in the study of human cognition: How do people represent number and quantity? How much of this representational machinery is unique to humans? How does the ability to reason about number develop from infancy to early childhood, to adulthood and throughout the lifespan? How does number make contact with the language system? Are there universal aspects of the representation of number? Can our brain architecture explain what makes numbers sometimes so easy and sometimes so hard? Attempts to answer these questions have generated some of the most elegant, influential and broad-ranging work in cognitive science. Beyond its intellectual appeal, the effort to understand how number is coded in the human mind has immediate relevance for a host of societal and policy issues, including how we approach mathematics education, or treat math-specific learning disabilities. These considerations led the present author and the leadership of the Society for Language Development to organize a symposium on the topic of number representation on November 6, 2014, at Boston University. The invited speakers were Elizabeth S. Spelke, Elizabeth M. Brannon and Jessica F. Cantlon. The goal of the symposium was to bring some of the broad findings, theorizing and debates in the number domain to the attention of the language acquisition community, and to foster discussion of the origins and development of number representations and their relation to language. The current special issue of Language Learning and Development contains papers that the three invited speakers and their collaborators later wrote on the same theme. In her article, Elizabeth S. Spelke addresses the origins of natural numbers. She reviews the proposal (first made by Randy Gallistel and Rochel Gelman) that natural numbers are a product of cognitive evolution and the more recent alternative proposal (put forth by Susan Carey) according to which