Convince Yourself, Convince a Friend, Convince a Skeptic

I have recently learned a new strategy for students to use as they work in groups called "Convince yourself, convince a friend, convince an enemy" described in Jo Boaler and Cathy Humphreys' book Connecting Mathematical Ideas. However, in order to keep this strategy from developing a negative connotation, Humphreys changed the last portion to "convince a skeptic" instead of using "enemy."

This strategy focuses on encouraging students to reason through problems and justify their arguments. As students work through a particular problem and eventually find a solution they think solves the problem, students must follow three steps. First, the student must convince herself that the solution she obtained is indeed correct. Next, the student must convince her partner (or "friend") of her answer by explaining her reasoning and showing evidence that the answer is correct. Finally, once her partner is convinced, the student must justify her reasoning to a "skeptic." This skeptic is one of her group mates that begins by being skeptical of the answer (whether this student actually is or not). The skeptic's job is to look at the evidence presented for the solution and determine whether this evidence is sufficient in supporting the solution.

By using this in the classroom, less emphasis is on whether the solution is correct, and students can focus on determining whether an explanation of the solution is convincing. I want to test out this strategy one day in my own classroom in order to get students thinking about the reasonableness of an answer and practice delivering and analyzing arguments.