Debate the relative contributions of genetic factors and experience to intelligence. Offer two arguments supporting heredity and two arguments supporting the environmental factors.
While genetic differences can have an effect on innate intelligence -- that is, it can make it impossible to learn things as others do -- I don't believe that it directly affects potential intelligence. Even "normal" people learn differently from each other, and so I think that while obvious genetic defects can limit a person's ability to learn, I don't think that makes a person stupider. To answer the OP, I honestly think a person's ability to learn is mixed between genetics and environments; look at how many people grow up in the worst environments possible and still go on to major success.
I agree with some of the earlier posts in that genetic combinations within the same family unit can still make for variable intelligences. While experience is central to learning (and is not necessarily the same thing as environment) it has a lesser effect on intelligence than genetics and nutrition, for example.
This is a massive debate, but I would want to start it by asking how do you define intelligence. This is another contentious topic, as people have questioned the ability of the IQ test to actually assess intelligence in its fullest form. However, I think clearly research has shown that intelligence can be greatly impaired or aided by nurture, or how a child is cared for and loved, in its first few years. Studies have shown that children who are neglected in their first five years of life suffer a lower intelligence as a result. I personally believe that nurture is a bigger force than nature, although both are clearly important.
Regarding the debate on nature vs. nurture many studies have been conducted with twins who were adopted, or with twins who were separated shortly after their births. In one case of two identical female twins, the children were placed in an orphanage. When the one child was adopted before her first year, a study of the twins development was conducted. As the children grew, their IQs were tested. Even with the added opportunities and extra mental stimuli of a loving home, the adopted girl did not score more than 2 or 3 points on the IQ tests. Thus, a tremendous argument exists regarding the role of heredity. Similar studies were conducted with other sets of twins.
As a teacher, I know that every day I help students reach a level of knowledge and intelligence they may not have been able to attain on their own. Perhaps the true gifted geniuses can just "do it," but most of even my best students need some guided experience and feedback in order to achieve their full potential. Could they understand the essential plot of Hamlet on their own? Probably. Could they note the subtly of language and detail without a little hint? Probably not. Could they be confident in their understanding? Probably not. But once they receive a little instruction, they make great strides on their own.
More evidence of the role heredity can play in the development of intelligence or other abilities can be found by looking at the genius or expert in any field. Mozart began composing and performing at the age of five years; artist Pablo Picasso's first words were a shortened version of the Spanish word for "pencil"; Wilbur and Orville Wright began building things before they were twelve years old. The attainments of any of these individuals were built upon intelligences that were part of their genetic heredity, separate from any training and experience they later acquired.
Like the third post, without the proper environment a person will never reach their full potential. The whole nature vs. nurture argument is a false dichotomy, because both are important. To what degree they are important cannot be known and I would say that it differs from person to person. For example, two children could have similar experiences and one will do much better. In this case, the nature seems to be more important. On the flip side, a child could be slow intellectually at first, but through constant effort and encouragement might succeed to great heights. In this case, the nurture is more important.
The best argument in favor of experience influencing intelligence is the fact that without experience, one cannot learn. One learns by both succeeding and failing. Without these types of experiences, failure and success, one cannot learn (intelligence) about the world and ideologies around them.
The best argument in favor of heredity is the fact that people in the same family can have different levels of (or at least different kinds of) intelligence. Within one family, you can have children who are good with their hands, children who are good at music, and children who are good with language (and that's just me and my brothers). Not every member of the family has the same sorts of abilities. This seems to indicate that intelligence is like skin color or body shape -- it's genetic and therefore you can get large variations within a family.