Actually, this semester I was surprised to discover how easy it is to use Teach-Okay for critical thinking. The teacher makes a statement like, "tell your neighbor the difference between metaphysics and epistemology" or asks a question, "what are the main characteristics of Socrates in the Crito?" ... then you say "Teach!" and the students turn to each other and give their answers. Several keys have to be observed. Students keep talking until you say "Class!" ... and, very important, they make gestures as they talk ... that way you can "read" the gestures and see who is on task and who is not. In traditional Teach-Okay, you give information and the students teach it to each other. In critical thinking Teach-Okay, you pose a topic or question and students explore it with each other.
Now, this can be juiced up in lots of ways. Here are three: you can say, "I want to see you using lots of examples. When you use an example, please 'pull it out of the top of your head' like this ..." then demonstrate an example making gesture ... Or, you can say, "I want you to compare and contrast x and y and when you do, use this gesture ..." Then interlace the fingers on both hands together for "compare" and bump the fists of both hands together for "contrast." Or, you can say, "I want you to use your 'anything thing,' your pen, which can stand for anything ... a person, an idea, a principle, as you explain your answer to your neighbor."
Especially effective after midyear, when you know the students' strengths, is divide the class into groups of three ... the strongest student sits in the middle with a weaker student on either side. Then, you can have the stronger teach the two weaker or the stronger monitor the work of the two weaker. You can be quite blunt about the division, saying, "I've looked at everyone's grades and I've picked class leaders from the top 1/3 of the class." Then give each person in the group a number, the 1, the 2, and the 3. The 2 is the leader. You can then say, "2s teach your neighbors." Or "2's encourage the other two team members to use gestures and teach each other."