Yes, Wowza Streaming Engine provides a great back-end server option for the real-time exchange of audio & video streams as part of your classroom web application. Our product's been used by a wide variety of vendors who provide hosted video chat or conferencing services as well as by our partners who sell integrated technology to their own edu or enterprise clients for intranet training apps. Some of our partners have even integrated our product with popular lecture capture technology.
To move forward with your own product, you'll need to develop the front end web application for this use case -- or purchase that type of code from one of our third party partners or a recommended independent consultant.
If you're planning to develop this yourself, I recommend starting by with learning how the example code in these articles works: