My first experience with creative problem solving competitions involved a group of rather ambitious second graders. Rather than opting for the easier non-competitive primary challenge they insisted on doing one of the more difficult ones. They spent a lot of time trying to build structures out of fragile materials that actually functioned. Then, they had to come up with a performance to tie everything together. We largely ignored preparing for the spontaneous problem solving challenge.
They built a somewhat sturdy structure that received a higher score than students in grades above them. But, they scored last in the spontaneous problem solving challenge. Afterwards we brainstormed on what went wrong. They had been give a question, “What would you take on a trip to the moon?” Only one answer had been given more than the minimum point, and as they recalled only one answer had been completely “out there.” One girl wanted to bring a shopping mall to the moon.
These seconds graders were not lacking creativity as much as they lacked experience in what others perceived as creative. After they understood what was expected of them, their scores soared on spontaneous problem solving challenges. However, I noticed that two of the students refused to give up practical answers and therefore did not come up with as many possible solutions. Restricting the search to an answer that really would work seemed to be a personal choice.
All of this musing on past experience with children and creativity brings me to a notion currently made popular by Sir Ken Robinson. The idea is that children are born creative and the school systems educate the creativity out of them. After all research shows that 98% of children age three to five are creative but only 2% of adults 25 year-olds are.  Actually only one research project showed this. It was a 1968 study by George Lands described in Breaking Point and Beyond.
Most definitions of creativity include both originality and usefulness. Throwing usefulness out the window in a test of divergent thinking changes the results. My second grade group learned how to increase their spontaneous problem solving scores not by being more creative, but by “conforming” to what the judges were seeking. Children often respond the way that they think you want them to. If you want a large number of answers, they will readily “carpet bomb” without regard to how much sense each answer makes.
Other researchers have not replicated George Lands’ result of drastically reduced creativity in adults. A long term study of students who took the Torrance Test of Creative Thinking in the late fifties and early sixties found a significant correlation between children that scored high on the test and later real world creative achievement as adults (especially for the males).  The creativity scores did show some fluctuation based on grade, but the percentage of creative younger students was not significantly greater than the percentage of older ones. Many of the younger students did not score as highly creative. One reason that this differs from George Lands’ results is that Torrence’s test is not just a one dimensional test of divergent thinking.
So, if you read that research shows that children are born creative and it is educated out of them by society, read further. Creativity means coming up with ideas that are different from the rest of society, but also useful. If most children come up with random unsuitable responses to a questions, they are not being more creative, but rather imitating other children.