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Do you ever struggled to get students to converse productively about mathematics? It sort of reminds me of when I learned about parallel play in my human development classes in high school. Wikipedia defines parallel play as "play in which children play adjacent to each other, but do not try to influence one another's behavior. Children usually play alone during parallel play but are interested in what other children are doing. This usually occurs after the first birthday. It usually involves two or more children in the same room who are interested in the same toy, each seeing the toy as their own. The children do not play together, but alongside each other simply because they are in the same room. Parallel play is usually first observed in children aged 2–3. An observer will notice that the children occasionally see what the others are doing and then modify their play accordingly."
This kind of interaction is often what I see when I put my students into groups. They're sitting next to each other, working on the same problem, and interested in what the other person might be writing down. But they don't know how to actually interact with each other to discuss their mathematical reasoning. When I want my students to engage in less 'parallel play' type of group work and more 'exploratory talk', I design a Talking Points activity for them.
Talking points is a structure created Lynn Dawes and recently adapted and made popular by @cheesemonkeysf, a California math teacher. This introductory post by @cheesemonkeysf is a very helpful. Here is a picture of a talking points that my students did in class recently.
Talking Points does not always have to be about mathematics. In fact, especially at the beginning of the year, I like to have my students use Talking Points to talk about what good group work looks and sounds like. Last year, @cheesemonkeysf led a Morning Session about Talking Points at the TMC14 Conference. You can find a wealth of other information Talking Points, including many examples of Talking Points for various topics and grade levels, on this page of the TMC14 wiki.