Students Explaining Math Problems

Alexander Isakov, a graduate student in physics, has his students explain in class how to do crucial steps of math problems for Math 21a. 

In order to do the activity, students need only to have looked at the homework and know the lecture material. During section, the instructor starts working out a problem, and then feigns ignorance about how to do crucial steps. He makes sure that multiple people have the chance to give him some ideas and explain why they think their idea is better. Then, he proceeds a bit more with the calculations/proof (as the case may be), and calls on other students to fill in details. 

Alexander finds that this activity works best in smaller sections; if you have a larger section, make sure that everyone is involved. Even if someone clearly does not know what to say, give them a small hint or ask them to take a guess. Don't rush it.