A mathematician considers the early signs of mathematical ability.

Have you ever wondered whether there is any reliable way to predict whether a three- or four-year-old child will be good at mathematics when he or she goes to school? Many people find it surprising that an early aptitude for arithmetic is not a terribly good indicator.

A 2004 paper by the psychologist Daniela O'Neill and her colleagues at the University of Waterloo in Ontario, Canada, suggested something better. O'Neill and her team showed three- and four-year-old children a picture book and asked them to tell a story about what they saw. The researchers then measured many parameters of the children's story-telling, including the diversity of vocabulary used and the length of the sentences constructed. Two years later, the team set the same children various tests of academic achievement (D. K. O'Neill et al. First Lang. 24, 149–183; 2004).

O'Neill and her co-workers found that vocabulary and sentence length in the initial study bore little relation to the test performances a couple of years later. However, the sophistication with which the children told their stories was important. The most significant feature of this sophistication was children's ability to switch perspectives as they related the stories. Crucially, the correlation that the researchers found pertained not to later performance in reading, spelling or general knowledge, but to future mathematical ability.

I have long thought that the human capacity for mathematical thinking must predate symbolic arithmetic, because numbers are a relatively recent invention. This study backs up this idea, because it suggests that the ability to solve mathematical problems has co-opted other innate capacities that have been important for much longer in our evolution.

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