One of the best shows on television (some years back) was the Brit version of Whose Line is it, Anyway? The off-the-cuff nature of the show reveals an interesting set of creative, critical thinking that could be handy in a classroom. Here's one of my favorites:
What's really noticeable in this episode is "Cliche' Boy". Not only does Brad have to think of a cliche', but he also has to think of one in context. If someone were to ask you to come up with a cliche' off the top of your head, you probably could. But try and come up with one on the spot in the context of, say, fox hunting.
Guess I'm barking up the wrong tree, with that one, so let's try politics. Well, Newt is reaping what he's sown. And so on...
It takes a few minutes, doesn't it? Add on the pressure of doing this in front of group, and you'll probably experience that deer-in-the-headlights feeling, which is exactly what the participants of Whose Line have learned to overcome.
That on-the-spot thinking skill helps you think more quickly and more adaptively and without a doubt, more creatively. In order to improve our students' critical thinking skills, we have to be three steps ahead of wherever they happen to be at that moment in order to lead them to where they need to be! Likewise, we have to move and flow along with their intake and understanding with acute mental agility.
It's easy enough to practice this on your own. Simply find an episode, take the "given" prompt, and see what you come up with. You may find yourself better at certain games than others. For example, I tend to do better at Questions Only than I do at Props. However, the mental agility used is the same. Work on one until you've got it, then see how you can apply that same skill to a new set.
When you head back into the classroom, you won't be "playing" one of these games. However, consider that the game of a lesson does have a structure that can be predicted. You may find that students receive your instruction with a bit more interest. Not because you're funny (don't even try to be funny with high-schoolers), but because you're mentally more aware.
Want agility? Get Improv.