Does this exist? Projector showing screen as you write

I teach a writing course in which I sometimes use an overhead projector.
I’d like to do an exercise with the class where we write a story or a description or a poem together.
I could, of course, write each line on the whiteboard, but my handwriting is execrable, and also it would be handy to have the story look as it would when the students are typing themselves. Is there any way of showing, on a screen (in this case the same whiteboard) what’s happening on your computer? So that I could open Word (no Scrivener on the school computer, unfortunately) and type each line as the students suggest it.

Something like one of these: http://www.projectorshop24.co.uk/projector/projector.html?gclid=Cj0KEQiAts-kBRCbgrXc1rnXw7MBEiQAnFqTdpZbCJI3M_F4cqB3hmUVQpnHZjuUfHB0siUnhDKoueYaAoEi8P8HAQ ? (There used to be transparent liquid-crystal displays that you could place on an overhead projector and connect to a computer, and that were less expensive and more transportable than a projector itself, but I can’t seem to find an example.)

If you connect the computer to a projector you can mirror the screen via the projector, so anything you do on the computer is seen on the screen. This is the standard behaviour of most computers.

Or do you mean something else?

No, that’s what I mean, thanks. Normally I plug in a USB with a short film on it to the PC and it magically works with the projector.