Press Release from the University of Nottingham.
Children are able to solve approximate addition or subtraction problems involving large numbers even before they have been taught arithmetic, according to a study conducted by researchers from The University of Nottingham and Harvard University.
The study, published in the journal Nature and undertaken at Harvard University, suggests that children do not need to master either the logic of place value or the addition table in order to perform approximate addition and subtraction.
Children's difficulty with learning school arithmetic may stem from the need to produce an exact number when solving problems.
I remember John Holt talking about this in one of his books (one of the early books I read on unschooling). It was timely, for me, as I remember witnessing this kind of innate skill in my oldest. She was probably around three at the time.
I am still impressed with the way my children trust themselves with numbers while I'm still counting on my fingers to "check" what I think I know.