How do we encourage and develop creativity and innovation?

I recently was reading an article that referred to the difference between letting computers do stuff to children (feed them curricula) and having children create something by doing stuff to computers (programming). (Have a look at http://www.hackeducation.com/2013/07/30/visiting-seymour/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+HackEducation+%28Hack+Education%29)  This got me thinking about how current educational trends steer us away from content delivery and I was wondering what the impact of that might be on students. The students who, in my experience, actually "do stuff to computers" tend to be the ones who have invited/responded to their pre-defined curricula (in maths and science largely), who have let computers (or humans) "do stuff to them". I am interested in both...I think the emphasis on creation and innovation is great but I think it is even greater with an emphasis alongside it on knowing information and processes (particularly referring to the basic information and processes in maths and science that can easily be transmitted in an interesting way)

The growing resistance we seem to see  to direct teaching (instructional -knower to learner) is a concern to me. There is a strong emphasis in education today on students driving their own learning which I embrace but I am not sure we all mean the same thing. Does this mean that content should not be delivered/transmitted? Here's an example: It is assumed that it would be preferable for a student to "discover" that multiplication is actually repetitive addition by stumbling upon that concept in a carefully constructed exercise/game as opposed to it being taught this directly with a few good explanations/diagrams etc.... Indeed- first prize in education would be for the child to want to know what is similar about multiplication and addition and devise a question that leads them to investigate that concept and make the discovery for themselves. In my experience, however, students who are fed more information, ideas, and concepts at a younger age, who are taught stuff directly about the world and know both facts and processes at a young age, these are the ones who tend to ask questions about the content they have been given and these are the ones who are well-equipped to create. Discovering concepts takes time, sometimes this is truly worth it, sometimes it is a waste of time...sometimes a child can swiftly be taught a number of concepts and processes that give them the "stuff" which which to think and create at a deeper level instead of having creative capacity and curiosity in a vacuum.