What bothers me about this question is the word "innovation." It is too big. From a learning standpoint, there is no need for innovation. Research is pretty clear about the methods by which learning takes place. We have decades of materials and studies and experience. Of course there is always new research that might put a fine point on some of these methods, but the basics are well-known.
From a teaching standpoint, there has some been innovation in the last 15-20 years. This comes primarily from technology in the form of brain scans and neuroscience. Even still, good teachers have been using methods that take advantage of this knowledge. But we used it before we knew how it actually worked. Good teaching hasn't changed as a result, but we are able to show (and convince) new teachers why you should use a given methodology.
From a technology standpoint (since this is HN I assume that is the direction you want to go), don't waste your time. Computers in classrooms are just another tool, like a TV or pencil or book. Technology is just another body of knowledge students are expected to know before they graduate. We have had enough studies now that show putting computers in classrooms make no difference in outcomes. It is only helpful if a teacher is trained to use that tool, in the same way that a teacher is trained to use books and notes. Effectiveness is dependent on its use and not merely its presence.
The current classroom innovations in education, and the ones making the most impact in our schools, and many others, are human relationships. (I will address innovation outside the classroom in the next paragraph). Students who connect to teachers learn more in that class. Period. They show up to school, they listen, they are more likely to do the work, they are more interested in the material. This has been the saddest revelation to me in my teaching career. These kids in inner city schools have no dad, many times no mother and are usually one of several children by different fathers. All of them know of someone personally or an immediate family member in prison, or dead from violence or addictions. They are transient with no permanent home. In short, they are desperate for an adult to care about them. They live day to day and never learn skills like organizing, planning, or time management. They have no role model, and it is very difficult to be one as a teacher when you have 35 kids in your classroom for 40 minutes a day. Until a student knows you care, they don't care what you know or what you have to show them. It helps if they have a parent who values education, but those are rare. Many students tell me their parents dropped out of high school and they still have a house and food and car and cell phone. They do, but it is provided by the government.
The biggest innovation to be made is in the structure. Everything is broken. Everything. Steve Jobs summed it up nicely. I'll add that as long as education remains a political issue, politicians with assume control with regulations and laws that benefit the most powerful voters - the voters most likely to re-elect them. For a long time that was unions. It is currently shifting to parents. In some places, business wields the most influence. Let parents decide where to send their students. Give their money back and let it follow the kids. Free teachers to achieve a set of standards using the methods and tools most appropriate for their communities. The standards don't need to change, but the freedom to teach in the way that is best for your current group of kids has been taken away.
That's enough - nothing is going to change.