I think this is Piaget raising his influential head again. There was a thread on here about his developmental theory, so I did some reading on it.
He claimed there are four stages of thinking,
Sensori-motor
(Birth-2 yrs)
Pre-operational
(2-7 years)
Concrete operational
(7-11 years) Recent research suggests that children in Western cultures tend to achieve conservation of number by age 7, conservation of mass and length by age 7 or 8, and conservation of area by age 8 or 9.
Formal operational
(11 years and up) Can think logically about abstract propositions and test hypotheses systemtically
And the last stage, formal operational is where they're supposed to be able to do entirely abstract things like calculus.
I found a couple of articles talking about precocious math children, and it seems that they might be as much as two years early with entering the concrete operational stage, they can get everything through to conservation of area within months (which puts them 3 or 4 years ahead). Then they spend years at that stage before the next switch to formal operational.
I haven't read up on that yet, but I think it's where the teacher's coming from, and I'm interested to hear if it's true or not. Is this the time to delve into other interesting math?
