Mathematics is a complex cognitive skill, requiring years of formal study. But of course some math is much simpler than others. Counting is fairly basic; calculus is not. To what degree does ability at the simpler tasks predict ability at the more complex? None at all, it was assumed, but research with adolescents has found an association between math ability and simple number sense (or as it’s called more formally, the "Approximate Number System" or ANS).
A new study extends the finding to preschool children. The study involved 200 3- to 5-year-old children, who were tested on their number sense, mathematical ability and verbal ability. The number sense task required children to estimate which group had more dots, when seeing briefly presented groups of blue and yellow dots on a computer screen. The standardized test of early mathematics ability required them to verbally count items on a page, to tell which of two spoken number words was greater or lesser, to read Arabic numbers, as well as demonstrate their knowledge of number facts (such as addition or multiplication), calculation skills (solving written addition and subtraction problems) and number concepts (such as answering how many sets of 10 are in 100). The verbal assessment was carried out by parents and caregivers of the children.
The study found that those who could successfully tell when the difference between the groups was only one dot, also knew the most about Arabic numerals and arithmetic. In other words, the findings confirm that number sense is linked to math ability.
Because these preschoolers have not yet had formal math instruction, the conclusion being drawn is that this number sense is inborn. I have to say that seems to me rather a leap. Certainly number sense is seen in human infants and some non-human animals, and in that sense the ANS is assuredly innate. However what we’re talking about here is the differences in number sense — the degree to which it has been developed. I’d remind you of my recent report that preschoolers whose parents engage in the right number-talk develop an understanding of number earlier, and that such understanding affects later math achievement. So I think it’s decidedly premature to assume that some infants are born with a better number sense, as opposed to having the benefit of informal instruction that develops their number sense.
I think, rather, that the finding adds to the evidence that preschoolers’ experiences and environment have long-lasting effects on academic achievement.
 . Preschool acuity of the approximate number system correlates with school math ability. Developmental Science [Internet]. Submitted . Available from: http://onlinelibrary.wiley.com/doi/10.1111/j.1467-7687.2011.01080.x/abstract