Author: MaryAnn Moore
Previous volumes: Volume 1, Volume 2
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.
I created this after my students took a quiz in which they needed to place some rational and irrational numbers on a number line. Almost 90% of my students incorrectly placed the irrational numbers on the number line by placing them directly above the closest rational number. I used the exact same number line from the quiz and hand-wrote in the numbers where the 90% of my students had placed them on the quiz. I then divided my students into groups of 3 or 4 and had them take turns telling whether they agree or disagree or are unsure whether each number was correctly placed, using the Talking Points structure described by @cheesemonkeysf. What was wonderful about this activity was that it provided a structure that caused them to engage in some mathematical debate while still providing a safe environment. And boy did they ever debate! There may have even been some raised voices when it came to determining the correct location for pi plus one. The next day I gave my students a different version of this number line quiz and over 95% of the students placed all of the numbers correctly.
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.