Its great that the election is over and the new president has been installed. We can get back to normal with our daily lives. Now is the time to look at the idea that their are different levels of convincing. I'd never thought of that until I read something by Robert Kaplinsky on the subject.
There are three levels of convincing according to his article. Each level has a different level of convincing needed. It makes sense.
1. The first and easiest level is convincing yourself of something. If this were a trial, you would be the defendant because you begin by convincing yourself you are innocent. If you believe it, you are more likely to have the ability to convince others.
2. The next level is to convince your friends of that same thing. In the trial, you would be convincing your defense lawyer of your innocence so he will take your case and work to convince others.
3. The third level is when your friends work on convincing others who might doubt you like the jury. The jury is undecided and are their to listen to your lawyer convince them you are innocent. While the hardest person to convince is the doubter who is not ready to be convinced. Someone who needs a lot of convincing to change their opinion much like the prosecuting attorney.
So what would this look like in the math classroom? Well the first level is when a student successfully finds the answer and convinces their partner their answer is correct. The other student listens to the explanation and agrees with it. The solution is shared with the rest of the class who have yet to solve the problem and take time to listen. They are like the jury, ready to be convinced. The hardest people to share this with are those who already have a solution and know their answer is correct so they are harder to convince.
In reality, convincing in the math classroom means students have to construct an argument which supports their answer such as using a pizza to determine which is bigger, 1/6 or 1/8 rather than saying our teacher last year told us it was so.
In addition, the levels do appear in the classroom because a student has to believe in their argument before they can share it. The level it takes to convince ones self is different than trying to convince someone who already holds a belief. Furthermore, it helps develop mathematical thinking.
Remember "Convince me" promotes inquiry and discourse without being judgemental.
If you use it in your classroom, let me know.