Hmm, interesting, but colour me unconvinced that anything terribly informative is necessarily going on here. (Disclaimer: I have not read the full paper.)
This "number sense" which seems to be basically subitising is very highly trainable including in babies. I've failed to google up evidence of what I remember, but I'm sure I have seen experiments in which experimenters easily and quickly teach small babies (6 months?) to subitise (i.e. tell exactly how many objects are present without counting) way above the range in which adults can do it, over 50 objects IIRR. They used flash cards and I think I recall that they did check that it wasn't only that the child learned those particular cards, i.e., could still do the task when the arrangement and type of object was novel.
Therefore, the idea that measuring how well a 4yo does this tells you something about how that child was born is dubious: the child's experiences so far may easily have had a strong effect on how the child performs.
For example, children who for whatever reason are interested in, or have been deliberately exposed to, mathematics might well have developed their subitising abilities beyond the average.
So given that what they've found is a correlation between number sense aged 4 and maths skills aged 4, the headline might just as well have been Kids who excel in math have �number sense� which might not have attracted so much attention!
I suppose I see this as basically a negative finding. It would have been much more interesting if they had found that number sense age 4 did not predict mathematical skill age 4, but did predict mathematical skill age 14, for example.
If anyone has read the full paper, I'd be interested to know whether that sheds more light...
