You can use vacaroo in class by reporting to a teacher your project. If you are leaving your homework at your house, you could record your work on the internet and show it to the teacher. You would have to explain your work and that could get pretty difficult.
That is where voice thread would come in handy. You could take a picture of your paper and you explain how you got your answer. You can show how you got that answer with the pen it gives you. You can explain how you got the answer by recording your voice.
I think that voice thread is better than vacaroo because it gives you the opportunity to use video also. I have examples on my blog.