You can move items within a collection using Ctrl-Up/Ctrl-Dn (Windows) or the context menu (right mouse button).
You can move items between collections or between chapters (i.e. 2 open chapters in 2 different teachit windows) using Ctrl-C/Ctrl-V. You have to select the item you want to copy first. This does not work for videos, because the clipboard does not hold videos, but it works for math items.
Presently you cannot select multiple items at once.
When moving images/math the sizehint info is lost because it is not copied into the clipboard.