Yes, test your staff, don’t assume they know how to do things, or that they would never know or understand that new Microsoft product. Setup a small series of tests, not in the traditional sense of a sit down 20 minute exam, just ask a member of staff to undertake a task for you when you are next visiting their classroom. Something simple like open a document, rename it, email a copy to you. etc something that they should know how to do. This will help you to identify any training needs.
If you notice that there is a need for any training, think about how to implement it, different staff have different ways of learning, this may mean that you have to create several resources for the same training, but it is worth the effort when staff come back to you and thank you for the effort, and also reduce the number of support calls that they are putting in for “simple” requests.
Once you have issued the training, keep an eye on them.. If the training has worked you will find that they seem happier to undertake that particular IT task, but if the training was not sucessful, they may avoid you for fear of appearing to not understand.