Devlin's Angle

December 2007

Predicting Mathematical Ability

Is there any way to predict whether a 3- or 4-year-old pre-schooler will do reasonably well in mathematics when he or she goes to school? Recent research by the psychologist Daniela O'Neill of the University of Waterloo in Canada suggests that there is. What many people will find surprising is that early ability in arithmetic is not a predictor - or at least not as good a predictor as the one O'Neill found: narrative skill. That's right, the ability to tell a story. The more sophisticated the pre-schooler's story-telling ability is, the most likely that child is to do well at mathematics two years later.

O'Neill's result was reported in Science News Online on November 10, 2007 ( 20071110/mathtrek.asp).

A particularly satisfying aspect of this result from a very personal perspective is that it confirms a prediction I made several years ago. In my book The Math Gene, I provided a natural selection mechanism whereby human beings developed the ability to do mathematics, and the hypothesis O'Neill has confirmed came from that thesis.

The argument I present in The Math Gene for the evolution of mathematical ability is fairly lengthy, which is why it required an entire book to present. Part of the reason for the argument's complexity is that mathematics is a very recent phenomenon in evolutionary terms. Numbers are a mere 10,000 years old, and recognizable symbolic mathematics goes back only 3,000 years or so. Thus, doing mathematics must comprise making use of mental capacities that pre-date mathematics by tens or hundreds of thousands of years, capacities that found their ways into the human gene pool because they provided our early ancestors with survival advantages - being good at math not being one of them back then! In my book, I spelled out those abilities and explained how and why they got into the gene pool.

Today, we have so much concrete evidence for many of the individual evolutionary advances that led to Homo sapiens and on to modern Man, that the account I gave has considerable support and is fairly tightly constrained. Still, like many evolutionary accounts, perforce it remains a hypothesis. In such a situation, confirmation must be sought by testing any predictions that follow from the hypothesis.

One of the key cognitive abilities that, according to my account, is utilized in doing mathematics is the ability to follow and tell a story. (In the book, I tried to express this in a memorable way by commenting that "a mathematician is someone who approaches mathematics as a soap opera.")

Actually, I didn't express it exactly in terms of narrative skill (story understanding/telling) as a single ability, but when O'Neill read my book and subsequently talked with me about her proposed research, she took that formulation as the basis for her research. According to my account, the cognitive abilities that are required for narrative are pivotal in being able to think mathematically, so the stronger those abilities are, the better equipped an individual will be to do math.

This is essentially what O'Neill has now shown to be the case.

Here is how she did it. She showed 3- and 4-year-old children a picture book and asked them to tell a story about what they saw. She then measured the stories in terms of sophistication. Two years later, she followed up by giving the children various tests of academic achievement.

Factors such as vocabulary or sentence length in the story-telling test had little correlation to the later test performances, but sophistication of the story-telling itself did. Moreover, the correlation was with subsequent mathematical performance, and not with later performance in reading, spelling, or general knowledge.

The most significant narrative feature O'Neill identified was the child's ability to switch perspectives in the story - an important component of narrative ability.

Interestingly, the narrative factor my thesis suggests will be most significant (or at least, no less significant than any other), namely sequencing, was not found to be correlated with later mathematical ability in O'Neill's study. But this may well reflect that fact that the picture book the pre-schoolers were presented with did not allow for sequencing built upon chains of causal relationships, which is what my thesis suggests will be a major factor. (O'Neill agrees with me on this supposition. She is already engaged in a second, more penetrating study, which also looks at different kinds of later mathematical ability.)

O'Neill's paper makes for fascinating reading, and I highly recommend it. It is available online in preprint form at Storytelling and math.pdf

Sadly, the study I would really like to see may well be too costly to carry out. The strongest form of my prediction, based on the thesis I presented in The Math Gene, is that early narrative skills will be an excellent predictor of how well a child performs in calculus - some fifteen or more years later.

Devlin's Angle is updated at the beginning of each month.
Mathematician Keith Devlin (email: is the Executive Director of the Center for the Study of Language and Information at Stanford University and The Math Guy on NPR's Weekend Edition. Devlin's most recent book, Solving Crimes with Mathematics: THE NUMBERS BEHIND NUMB3RS, is the companion book to the hit television crime series NUMB3RS, and is co-written with Professor Gary Lorden of Caltech, the lead mathematics adviser on the series. It was published in September by Plume.