Developmental and evolutionary foundations of mathematical cognition
Anyone who has raised a child knows that babies can't do long division or multiplication. And we don't see monkeys in the wild working away at math problems! Even if they could, how would we know? We can't ask babies or animals about their thoughts. Can any concrete thought take place without language?
Astonishingly, recent research tells us that yes, babies and animals can think abstractly and they can even think about concepts as seemingly complex as number. Studying numerical cognition provides a test bed for the challenge of understanding cognition without language. As adults we measure, order, label, and categorize almost every aspect of the world with numbers. Without numbers much of modern civilization would be impossible. The ability to use number is one of the most complex cognitive abilities that humans possess and is often held up as a defining feature of the human mind. A crucial reason for interest in nonverbal number representations is that number is an abstract property of a set of stimuli. While two pork BBQ sandwiches and two petunias do not look, feel, taste, or smell alike they are equally good examples of two-ness. As adult humans we recognize the numerical equivalence between sets as diverse as four ballet dancers and four pirouettes, three musicians and three saxophone notes, or two presidential candidates and two political philosophies. Such examples illustrate that we form numerical representations when viewing simultaneously occurring visual sets (e.g., ballet dancers), successively occurring visual events (e.g., four pirouettes), successively occurring auditory events (e.g., three musical notes), or when thinking about sets as abstract as ideas. These examples also illustrate that number representations are abstract in that they require us to equate sets that differ in many physical dimensions (e.g., size, shape, color) and instead classify based on an emergent property of the set . Can a baby or a monkey hold such an abstract concept?
Are there developmental and evolutionary building blocks that serve as a foundation for adult mathematical cognition? Without a doubt no monkey nor human baby can come close to achieving the mathematical ability of a college student. However, while educated adults possess a complex symbol system for representing and manipulating numbers, we share with nonhuman animals and preverbal human infants a more primitive system for representing number as mental magnitudes that can be manipulated in arithmetic operations. As we delve into the neural bases of these nonverbal numerical abilities we are finding that homologous regions of parietal cortex are being used in adult humans, young children, and rhesus monkeys. This essay reviews the ground-breaking behavioral and neurobiological work that has led to our current understanding of the building blocks of adult mathematical cognition and identifies some of the many challenges that remain.
1. Gallistel, C.R. and R. Gelman, Preverbal and Verbal Counting and Computation. Cognition, 1992. 44(1-2): p. 43-74.