There is almost no trait that is entirely genetic or entirely environmental (to geneticists 'environmental' simply means not genetic). Even the classical genetic disorders are often amenable to treatment by altering some aspect of the environment (diet or drug therapy). On the other hand all of our cognition takes place in our brain - a biological organ built of membranes and enzymes. The structure of those enzymes is coded in genes, along with much of the information as to the circumstances under which those enzymes are produced or the cells connect one way or another.
The key phrase is 'under what circumstances'. Even the structure of the brain is partly influenced by its responses to external stimuli (the environment). This is what is meant by phrases like 'the brain changes itself', and is the same basic principle as our muscles changing in response to exercise, or our plants getting larger when we water them - responding to environment cues and stimuli is part of the development of all living things.
So the argument is over how much our differing abilities and preferences is attributable to our different genetic backgrounds or our different environments. Do parents and offspring have similar levels of success because the offspring inherit genes or because they inherit environmental advantages? Is education and social environment just fiddling around the edges of a genetically determined core, or do we all start out essentially the same, and diverge as our experiences shape us? I believe the latter is much closer to the truth, but this is getting lengthy, and I've finally learned to use jump breaks (see, and environmental effect!) so I'll continue after the jump.
Twin studies claim to show a strong genetic effect, but have a serious flaw. Twin studies assume that since the genes of twins are the same, the more that twins who have been raised apart are similar cognitively, the greater must be the effects of the genes. But to be valid the twins have to be not just reared apart, but to be raised in completely random environments (imagine picking two households at random from across the entire US and plopping one twin into each). Of course this isn't what was done. So the studies might show that twin males raised in the 1950's in rural Arkansas differ in some consistent way from twin girls who grew up in 1980's San Francisco. This is hardly strong evidence for genetic control of our minds. I'm quoting the older Minnesota Twin Study - recent studies are somewhat better, but none can eliminate the common uterine environment of twins.
Environmental influences do not mean a trait is infinitely maleable. An old, if minor, hand injury means that I would have to work a lot harder to be a great concert pianist than if the injury hadn't happened. And I could probably never be 'the best' starting from a disadvantage. This strikes me as particularly relevant to early childhood development (in which I have no expertise) where early differences in some aspect of the child's environment could become amplified in their scholastic achievement later on.
By the same reasoning, some improvement is almost always possible. Neither genetic, nor earlier environmental influences on scholastic achievement are locked in and impervious to improvement. My hand injury doesn't mean I won't getter at piano if I practice. Your houseplant may never grow into a oak, but it will still get bigger if you water it, and wither if you don't. That sounds cheesey, but one hears the argument made sometimes that 'that's just the way they are', and the argument is false.
Alleged racial differences are seriously confounded, because whatever genetic difference might exist is correlated with different environments. So if there is a tendency for one group to score higher or lower, this cannot be automatically attributed to 'innate' genetic differences. (The same goes, mutatis mutandis for gender.) It is virtually impossible to put different ethnic groups into the same 'environment' for a fair comparison, because of the vastly different experience of being white or black or hispanic or asian in our society, even when attending the same school or having the same 'socio-economic status'. What is clear is that when (some of) these factors are taken into account (the statistical technique, ANCOVA, is well established) the differences between races shrink close to zero. (A rough analogy might be to say that of all the variation among the performance of different computers, only a small fraction can be predicted by the hardware difference between Mac's and PC's - the rest being different software, roughly analogous to the educational environment of a person. I can't help noticing that the Mac vs PC partisans can be almost comically tribal as well).
The trouble with any 'predictor' of future scholastic performance is that they are statistical, and probabilistic. They can only predict (often very small) differences in the likelihood of a particular outcome. This only manifests itself as trends over large groups, which is inevitably unfair to particular individuals. I suspect this is as true of reference letters as it is of SAT scores, but I couldn't prove it.
Sorry for the longwinded post. I hope it is helpful. I found a useful quote from Dennett that might sum it up.
Once the caricatures have been set aside, what remains are honest differences of opinion about how much intervention would be required to counteract one genetic tendency* or another and more important, whether such intervention would be justified. These are important moral and political issues, but the often become next to impossible to discuss in a calm and reasonable way.
*I would just add that the same goes for dealing with tendencies induced by past environmental experiences.