Chromebooks are becoming a popular choice for schools around the US. Some teachers, though have expressed concern over what seems to be limited functionality. After all, if you can only produce content online, how are teachers supposed to do things like video creation?
WeVideo is the best tool I've found to give kids the tools to create, store and share video projects. This is primarily because it's free and it publishes videos directly to Google Drive. Note the use of the word "publish" instead of "save". Here is how it works: You create videos on their servers and are then given the option to publicly publish your video to the internet. In the free version, all videos are public by default. Once you publish the video to your Google Drive account however, making it private is simple. Just adjust the Sharing settings as you would with any other file. Keep in mind that if you have any privacy concerns, you'll have to be careful to adjust the sharing settings to every video you produce.
This option to save to Google Drive is important. First, it gives you immediate control over who may see your students' videos. For example, share the videos with parents, but prevent anyone else for seeing them. You'll also have a simple way of managing all those video files that come in. Put them into folders and organize them in a way that makes sense for you. The Google Drive app provides even more power. With it, those videos can be streamed (without being saved) to mobile devices. If you have the app yourself, you'll be able to take video with a smartphone and simply upload them to your Drive account. From there, you'll be able to edit them with WeVideo.
There are other video editors out there that are both free and produce a decent final video. Thus far, all of them have fatal flaws. Consider Youtube editor. The final result is in Youtube's proprietary format which means you have to use a third party application to download the video. Possibly more problematic is that Youtube is blocked in many school districts, so this wouldn't even be an option. Other video editors store your finished product on their own servers which may be fine. However, they just might reserve the right to use your video as part of their promotional material. "Free" accounts often come with some strings attached. So give this a try and let me know what you think.