Humans and other animals posess an innate ability to distinguish quantities, especially 1, 2 and 3. After that, approximations get fuzzy. A squirrel knows that 10 nuts is more than three, but it couldn't discriminate between a pile that had 10 nuts and one that had 9. The French cognitive neuroscientist Stanislas Dehaene calls this ability our "number sense" in his book, aptly titled, The Number Sense: How the Mind Creates Mathematics.
When we teach children mathematics, we may be building on this natural born ability. (Reading, on the other hand, is a wholly human cultural invention that is achieved by rewiring existing brain circuits for a new purpose, a process Dehaene has called neuronal recycling in his more recent book Reading in the Brain: the New Science of How We Read.)
If the number sense is a foundation for mathematics learning, can educators predict which learners will have problems based on cracks in that foundation?
Sara D. Sparks of Education Week's Inside School Research blog has an informative post this week on a new study that says this:
While barely out of toddler years, a child's ability to intuitively estimate and compare the number of objects in a group can predict how well she will perform under formal math instruction, according to a new study by researchers at the Kennedy Krieger Institute in Baltimore.
If it's the former hypothesis, then differences in the precision of this natural ability could predict future problems. Educators could screen for it and get kids the extra help they'll need earlier. Such a marker could also identify children who are more gifted and adjust their studies accordingly. However, if the natural ability simply changes with formal instruction, then "fine tuning" number sense early might not make a difference.
The authors found a strong correlation between the precision of the innate number sense before formal schooling, referred to as the ANS (Approximate Number System), and future mathematical proficiency.
Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.
Meanwhile, across Lake Erie, Daniel Ansari at the University of Western Ontario in London, Canada, has been working on understanding the neural basis for dsycalculia, a learning disability involving mathematics which is unfortunately not as well known or studied as its correlate in reading, dyslexia. Here's what Ansari had to say last month about his work in this profile in the journal Science:
About 5% of children have a learning disability known as developmental dyscalculia, which interferes with the processing of numerical information. That's about the same prevalence as dyslexia, and yet dyscalculia has received a fraction of the research attention. "There's a terrifying statistic that shows that the ratio of papers on dyslexia to those on dyscalculia is 14 to 1," says cognitive neuroscientist Daniel Ansari of the University of Western Ontario in London, Canada. That disparity is troubling, he says, because "individuals and society at large pay a large price for low numerical and mathematical skills." Low numeracy is not only a strong predictor of school success but also associated with worse health care, greater likelihood of criminal behavior and incarceration, and higher risk for depression and other illnesses.
Figuring out the brain basis of numerical and mathematical abilities, what causes dyscalculia, and how to remedy the disorder are the central aims of Ansari's work. Using a combination of behavioral and neuroimaging methods, he and his colleagues examine how children develop foundational number-processing abilities, such as the ability to judge which of two numbers is larger or to estimate numbers' position on a number line; why these basic cognitive processes sometimes go awry; and how to help children with serious deficits in numerical processing.