There are two schools of thought on this question. Some people say that creativity is a trait that a lucky few are born with, and that it can't be taught. However, there are others that believe that a sense of creativity can be fostered; they believe that a person's background, environment and personality are the most determinant factors in how much creativity they have.
Those that believe creativity is an inborn trait say that environmental factors are just tools which augment natural creativity, and that they would be worthless without that "divine spark". People that showed creativity at a later stage in life did so because they just didn't take the time to develop their natural skill. The issue has been a debatable subject for years, and some say that the root of the debate is the concept that creativity is too vague a concept to be quantified.
The more conservative line of thinking says that when people are born, they are given certain abilities and interests, but those are useless without the acquisition of the skills to use them properly. When a child is born, neither they nor their parents know what their future holds, or what their later-life talents may be. Because of this lack of knowledge, all a parent or a school can teach a child is how to think for themselves. That is really the ideal education- it would allow us to make our own decisions on how our unique abilities and talents will be put to use. Children and adults need to be taught how to innovate and keep pace with ever-shifting environmental, behavioral and technological factors. So, in a sense, yes- creativity can be taught.
Today's public education system is moving toward the greater use of standardized testing in determining a person's creativity. This measure is not only woefully inaccurate, but it is an impediment to real creativity, because no one can measure a person's creative potential. The trait of creativity is one that only comes to the surface when it is nourished, and because these incidences don't come around that often, creativity cannot be measured. Given this conclusion, how can one person be judged to be creative, while the person next to them cannot be?
The debate on the teaching of creativity will likely continue for years on end. Some people have been able to enhance their creativity in an educational setting, while others use teaching as a mere tool. However, it is reassuring to know that the very debate that surrounds the subject is a sign of creativity, and the more the subject is debated, the more that creativity is nurtured.