The oldest, and still the most powerful, teaching tactic for fostering critical thinking is Socratic teaching. Jesus often used this method. In Socratic teaching, the focus is on asking students questions, not giving them answers. This forces the student to think critically, something sorely missing in our society today.
In Mark 8:14-21 Jesus uses this method of teaching to teach his disciples a deeper spiritual truth. He asks no fewer than 8 questions to get his disciples to think critically. He was helping them to develop spiritual discernment, something else sorely lacking in churches today.