Numerical Cognition - Developmental Studies

Developmental Studies

Developmental psychology studies have shown that human infants, like non-human animals, have an approximate sense of number. For example, in one study, infants were repeatedly presented with arrays of (in one block) 16 dots. Careful controls were in place to eliminate information from "non-numerical" parameters such as total surface area, luminance, circumference, and so on. After the infants had been presented with many displays containing 16 items, they habituated, or stopped looking as long at the display. Infants were then presented with a display containing 8 items, and they looked longer at the novel display.

Because of the numerous controls that were in place to rule out non-numerical factors, the experimenters infer that six month-old infants are sensitive to differences between 8 and 16. Subsequent experiments, using similar methodologies showed that 6 month old infants can discriminate numbers differing by a 2:1 ratio (8 vs. 16 or 16 vs. 32) but not by a 3:2 ratio (8 vs. 12 or 16 vs. 24). However, 10-month-old infants succeed both at the 2:1 and the 3:2 ratio, suggesting an increased sensitivity to numerosity differences with age (for a review of this literature see Feigenson, Dehaene & Spelke 2004).

In another series of studies, Karen Wynn showed that infants as young as five months are able to do very simple additions (e.g., 1 + 1 = 2) and subtractions (3 - 1 = 2). To demonstrate this, Wynn used a "violation of expectation" paradigm, in which infants were shown (for example) one Mickey Mouse doll going behind a screen, followed by another. If, when the screen was lowered, infants were presented with only one Mickey (the "impossible event") they looked longer than if they were shown two Mickeys (the "possible" event). Further studies by Karen Wynn and Koleen McCrink found that although infants' ability to compute exact outcomes only holds over small numbers, infants can compute approximate outcomes of larger addition and subtraction events (e.g., "5+5" and "10=5" events).

There is debate about how much these infant systems actually contain in terms of number concepts, harkening to the classic nature versus nurture debate. Gelman & Gallistel 1978 suggested that a child innately has the concept of natural number, and only has to map this onto the words used in her language. Carey 2004, Carey 2009 disagreed, saying that these systems can only encoded large numbers in an approximate way, where language-based natural numbers can be exact. One promising approach is to see if cultures that lack number words can deal with natural numbers. The results so far are mixed (e.g., Pica et al. 2004); Butterworth & Reeve 2008, Butterworth, Reeve & Lloyd 2008.