One sector desperately overdue for innovation courtesy of technology is K-12 education, which leads us directly to San Mateo-based Edmodo, the free platform that enables teachers to create closed networks with their students in a Facebook-like UI that virtually reproduces and extends the classroom environment in many ways.

Teachers can assign homework, interact with their students as a group or individually, embed videos and other types of content, manage the grading process, and extend their teaching activity beyond the classroom across any conceivable digital device, from the web on computers to mobile phones and tablets, whether iOS or Android.

Last week, Edmodo announced that it is opening up its API to developers, with an initial partner list of about 40 that includes local organizations from The Buck Institute to StudySync, which we’ve profiled here at 7x7.com.

Since launching three and a half years ago, Edmodo has grown virally to the point where it has 6 million users in 7 languages and 51 countries around the world.

“We try to replicate the experience of a classroom,” says COO Crystal Hutter. “Teachers can communicate to the whole class and also to each student individually. Students can send notes to the entire class or just to the teacher, but not to each other privately.”

Teachers and students create and maintain their own profile pages, which include a “library” of all the content that gets assigned in class. One time-saving feature of Edmodo’s service is that documents, photos, videos and other educational content does not have to be downloaded outside of the UI, but are available and playable right there.

By opening the API to developers, Edmodo is welcoming an ecosystem to form around itself that should unleash a massive new flow of apps, including some that will be premium products that generate a revenue share for both the startup and the developers.

“One of the exciting things for developers, especially in the Bay Area, is being able to make an impact in education,” says Hutter. “Until now there hasn’t been a way to develop apps that teachers say are needed in the classroom in real time. We think an important part of that for developers is to hear directly from teachers.”

For that reason, over the next few weeks Edmodo is also unveiling a way for teachers and developers to communicate directly. Teachers will post ideas for apps, and the community of engaged users on the service will vote ideas up and down – a sort of instant “wisdom of the crowd” referendum.

The company is also preparing features around “topics,” which will help teachers share ideas about classes they are teaching right now, and “insights,” which will help teachers gauge the mood of their students, via a real-time feedback loop.

Hutter says that Edmodo is seeing the trend among its users as they’ve migrated to mobile platforms the past few years. “In the fall of 2010, we saw the emergence of hand-held mobile devices. This school year has been all about tablets.”

The company, which currently has 36 employees, most of whom are coders, is seeking more engineers “who are interested in having a real impact on education,” she adds.