Last week we looked at the first critical component of making sure collaboration is productive: students have to know each other to feel comfortable sharing their ideas.

Now we’ll look at our next challenge: how do we get all students talking and participating?

### Tip #1: Consider what it is you’re asking students to do in groups. Is it “group-worthy?”

It probably goes without saying that not all tasks or activities are equally well suited for group work. Giving students a set of practice problems and saying “work on this in your groups” will likely not garner a lot of discussion besides the occasional “what did you get for number 3?” So what makes a group-worthy task?

An idea worth exploring: There has to be some kind of interesting prompt that students want to discuss. It could be a real-world application but it doesn’t need to be. Any question that sparks curiosity or is posed as a puzzle will work.

Multiple entry points: Low-floor activities ensure that every student has access to the content and that there are multiple solution paths or strategies that will work to find an answer. Even if not all these strategies end up being equally efficient, all students should be able to apply some piece of prior knowledge to get started. Even a trial-and-error approach can give students insights about the kinds of answers that work and don’t work. If we ask students to do something and the only possible answer is our preferred, formal, streamlined method, then the student that already knows that method will plow through the activity and leave others in the dust. Remember, formalizing comes later. Rough-draft thinking, stops and starts, ideas that might not lead to an answer, are what we want now.

Individual and group accountability: Students need to be held accountable for their participation in the group and their contribution to the group’s final product. Assigning roles is one way to ensure that each group member is committed to the success of the group. While there are a variety of roles you can assign, we generally use “facilitator/timekeeper”, “reader”, “question asker”, and “reporter/recorder”. Make sure these roles switch up so students take turns at each of them. Another helpful strategy is to use an activity where each group member works on something slightly different and the combined results are needed to help the group move forward. For example, each group member calculates the derivative at a different point and plots that slope so that the group/class notices a pattern in the slopes graph. This is not the same as a “divide-and-conquer” approach. The individual responses have to be combined in some meaningful way that contributes to group understanding. Sum ‘Em Up review activities also foster this kind of individual and group accountability.

The good news is that you can increase the likelihood of rich discussion and equal participation not just by picking an interesting task, but by adding small routines or protocols that make explicit how students are to participate. This brings us to our next tip.

### Tip #2: Be explicit about what you expect group work to look like and sound like.

Early on in my teaching career I just assumed that students in Precalc and AP Calculus would know how to work productively in groups. After all, they’re juniors and seniors and have been through many previous math courses (And I know their previous teachers! They were doing group work!) But this assumption always got me in trouble because it just wasn’t true. Whether we attribute it to the summer slump or some other reason, most of our students do not know the skills, dispositions, and attitudes needed to make group work successful (after a year of remote learning, this is even more the case!). So we need to plan on teaching them.

Just like anything we teach, we need to be intentional with how we want students to access that new knowledge and how we plan for students to practice that new understanding. Here are a few ideas.

Helpful/unhelpful list: Early on in the year (or new semester) give students an interesting problem to work on in groups with little instruction. Set aside time for a debrief where you list the behaviors that were helpful for group work, and those that were unhelpful for group work. Press students for specificity. Listening and respect are important, but often too vague to help students actually work together effectively.

Model desired and undesired behaviors: We use the read-discuss-write protocol to help students internalize a pattern of approaching a question together, taking time to listen to ideas, and then writing down some conclusions that incorporate those shared ideas. This protocol also helps students stay on pace with each other. Don’t assume that students know this is important to you. I always say things like “I should NOT be seeing Angela on question 7, while Bradley is on question 3. The goal is to have good discussions in your group, not just to finish as fast as possible.”

Communicate beliefs about what it means to do and learn math: Many of our students are only used to math classes where the goal is always to finish a bunch of problems as quickly as possible. Old habits die hard. I tend to do a lot of framing around why I care so much that they’re working in groups by sharing my beliefs about learning math.

Every student is responsible for developing understanding and contributing to and supporting the understanding of others.

Math is not about speed, memorizing procedures, or “getting done”; it is about ideas, creativity, and sense-making.

We focus on learning, not performing.

Collaboration moves our thinking forward.

### Tip #3: Be realistic.

Here’s the truth: students are not going to be excellent at group work on day 1 or even day 21. It requires a lot of practice (180 days worth, maybe?). Set small goals for yourself about what you would like to see. For example, by Christmas break, I want students to naturally do read-discuss-write without being told. Or, by Spring break, I want to hear at least one student in each group ask a question about another group member’s thinking.

Although the heavy lifting of this work is done at the beginning of a new year or semester, it needs to be sustained throughout the year. Kids need reminders. When you set groups off to work on an activity give them just one thing to focus on in terms of their group work. “Today I’m going to be paying close attention to how your groups are sticking together. This means you’re checking in with each other to make sure everyone understands.”

Every year that I teach, my students get better at group work because I get better at teaching group work. Productive group work is possible for any group of students at any level of math; we just have to be clear and realistic about our expectations.