When DD8 was first tested for IQ and achievement she was 6.3 years old, and had just completed kindergarten and first grade in 1 year. Her achievement score was higher than her IQ score. She was retested for IQ this past spring and her IQ is now equal to her old achievement score.
So, while I can see where having a good support system for education would help improve achievement scores, DD did not really have good support at school, we pushed for her to be moved to grade 1 and she was still unchallenged with that placement. But, maybe her age and the inexperience of the tester were more influential on her IQ score than her educational support.