There is free software.
Here's what I recommend.
download a copy of Windows media encoder 7 -
it's free to the pc you are going to stream from (the newer versions don't do a good of a job encoding live but will work). It's a pain to roll back, but it's doable.
Get a host that allows windows streaming (you may want to archive these for later use and windows streaming server will archive it automatically). You don't need it but if there are many people watching you will.
Set you capture rate lower (15 fps) to allow 56K modems and cut down on bandwidth used (particularly the sound - mono 12 - 8 is better play with it.)
I've set it up for government agencies to broadcast live council meetings, training etc.
as far as seeing the students also you have to do a different option -
flash communication server
the next option is
webinar (it costs)
but the cheapest option is install windows streaming and a chat so students can ask questions, and they can see her and she can respond -
http://msdn2.microsoft.com/en-us/library/ms867202.aspx