Here's an example: how I use Talking Points both before and *for* mathematical conversation

OK, here's an example of how I used Talking Points first to get students primed for listening and considering other viewpoints, and then to get them to listen to and consider other viewpoints that can cause them to change their minds.

As our first activity following our first test of the semester, we did these Talking Points to start class.

These talking points were not especially successful, but they opened the door for the similar triangles discussion that followed.

We debriefed a bit, then I handed out this lovely, subtle activity from Park Math (Book 3, #20), and I asked them to change (a) to become a Talking Point, as in, "Triangle PRQ is similar to triangle STU." They were, as always, charged with doing three rounds and justifying their opinions.

Ten minutes of conversation ensued.

Next, I wrote three headings on the whiteboard (Agree, Disagree, Unsure) and asked each table in turn to tell me which conclusion they had come to and why. One by one, I wrote the table numbers under the categories where they located themselves (Agree, Disagree, Unsure).

And I held my tongue as table after table disregarded the order of vertices to tell me that, Duh, of course, they are similar triangles. I held my tongue because I trusted the process and had a felt sense that in a room full of 37 people, surely SOMEBODY would express a different, correct opinion.

And lo, it came to pass.

Table 6 bravely offered their belief that the triangles named were not similar because the order of vertices in each was not corresponding.

And one by one, the little lightbulb moments popped around the room.

I kept the discussion going until we were through with all 9 tables. Then, and only then, did I give tables another round in which they could change their opinion about what was actually going on in the diagram. 

Afterwards, we discussed what had happened. What did happen, I asked them. And they responded that something they heard made them realize they wanted to change their minds.

So that was my perfectly imperfect day of Talking Points. On the one hand, kids understood (some for the first time) that listening to somebody else could have value for them. On the other hand, many spent most of the exercise not listening to each other and simply waiting for their own turn to talk.

This doesn't mean that it was a failure. It just means it was a first step. 

I believe that if you want students to take ownership of their own learning (and listening... and opinions), then you have to allow space for them to do it in their own perfectly imperfect way. I have found that when I trust the process, I get the best results.

I am posting this to help you understand that every round of Talking Points I do is not a cornucopia of unicorns and rainbows.