Educational theory has held that creativity cannot be taught; that any attempts to educate an artist tend, instead, to stifle that creativity.
In my experience as an art student and also as a teacher of art, I've seen many reasons to dispute this. I have seen that raw, natural creativity only takes a student through stages that use knowledge he already has.
For instance, when a child makes something out of sticks and mud, he is able to exercise the fullest creativity he has at that stage because he has already learned something about sticks and mud. When he decides he would rather his creation not be swept away in a rainstorm, he will need to learn how to use something more substantial -- concrete, for instance -- and for that he will need to learn about concrete.
A visual artist often starts out with an idea of what he would like to do, and it's usually grounded in something he's seen before. If he's seen abstract painting he likes, chances are he'll try that. If he has enjoyed realistic paintings or photos, he may try to paint something recognizable.
This artist could go through years or decades experimenting and basically re-inventing the wheel if someone is not willing to mentor him or teach him about some of the basic principles of painting: color temperature, for instance.
Here is an example of two paintings which were done by a young student in one of my classes. She started out as a beginner, using acrylics, and painting from life. A beginning painter will tend to try to draw an object and then paint it in. He or she will try to "stay in the lines" and therefore will wind up with a white edge around the shapes in the painting. Another thing a beginner will try to do is make a smooth layer of color, fighting the paint's natural tendency toward texture.
My student was frustrated by her struggles and she asked for my advice. After only five lessons, she understood how to layer color, how to make decisions about transparent rather than opaque color, how to use brushwork to express her subject, and many other concepts. Right now she is learning processes and techniques. When it comes time for her to express her ideas outside of the class, she will have the tools to make it possible.
I'm really so proud of her! She has come a long way. Here are the before and after: