The degree of heritability of IQ places no constraint on the degree of modifiability that is possible. ... think about two facts: (a) the heritability of height is about .85 to .90 and (b) gains in average height of a standard deviation or more have appeared in a generation or less in several countries in the world. The average height of thirteen-year-old Korean boys increased by more than seven inches between 1965 and 2005, a difference of 2.4 SDs. The forty-year time span is far too brief for genetics to have played a role in the increase. ... the heritability of a characteristic within a given population places no theoretical constraint on the modifiability of that characteristic by environmental forces.
Richard E. Nisbett
Book: Intelligence and How to Get It: Why schools and cultures count. (2009). Norton; p 38