Communication and Collaboration in the Mathematics classroom can sometimes be an afterthought. As teachers, we are prone to focusing on problems instead of the discussion. Discussions are also harder and require structure for our students to be successful. But, having discussion based activities in Mathematics class allows you the flexibility to navigate the classroom and hear how well students are understanding the concept, so they're worth it!
To create structure, I like to lean on the Standards for Mathematical Practice and leverage practices that support conversation. The first cluster, reasoning and explaining, cannot be done well without encouraging communication and collaboration.
Here are 5 ways to encourage Communication and Collaboration in Math Class to tackle the Reasoning and Explaining cluster:
When stations are done well, you are working on SMP 2: Reason Abstractly and Qualitatively. You could also leverage stations to tackle SMP 4, 7, or 8. This all depends on how you would like to structure the activity. Are you using stations for practice or are you using stations to introduce applications or new concepts? You can do either of these and anything in between.
To do stations well you need student groups of 3-4 students and you need problems placed around the room. Every 5-7 minutes you would have these groups rotate and try the next problem. In a typical stations activity in my class, students will get exposure to about 5 practice problems; don't reinvent the wheel, I always cut these up off of an old worksheet or grab some problems from the book.
I often hear from teachers that stations are difficult because one student always does the work. Here are two things you can do to combat this:
Hold Students Accountable
Collect just one sheet of work per group at random, holding each group member accountable for recording information.
Use a Template
Using a template for student work will help kids keep track of their solutions to each problem and allow for you to give credit for the activity.
Use the "Marker Rule"
The student with the marker is not allowed to write unless they are writing what other group members are communicating to them. When I observed this activity, the marker holder couldn't speak and would hand off the marker when they wanted to contribute. The teacher checked that this was happening by asking group members without the marker to explain the group's work.
2. Gallery/Museum Walk
I've seen this done in elementary classrooms, but I've also observed gallery walks done to showcase end of class products. At the elementary level, gallery walks were used to support student thinking. When done well, a gallery walk can help support SMP 3: Construct viable arguments and critique the reasoning of others.
If I were to leverage a gallery walk to support student thinking, I would give students a few minutes to work either independently or in a small group on a real world problem or inquiry problem. After a few minutes, I would have students get up and walk around the room to observe the work of other groups. I would then have students sit back down with their problem and make adjustments to their work. After a few more minutes I would have students share out on the following questions:
How did your group start your work on the problem?
What did you notice about one other group's work?
How did you adjust your work based on what you saw?
These questions are not tough, but they're open-ended enough to encourage some whole-class discussions. I would take this a step further and create the rule that you cannot repeat another student's comments to ensure that the discussion continues and each group contributes unique thoughts.
3. Think, Pair, Share
I know I'm not being inventive here, but the "Think, Pair, Share" structure does support SMP 3 and is a worthwhile routine. I think it's important to recognize that there are three components here; we have to include the share piece and give students an opportunity to completely engage in the discussion. Here's how to structure it:
The thinking portion of the activity should be done individually and silently. This gives students the opportunity to process what the question is asking and develop their own ideas. If you choose the right problem, you're covering SMP 2 here.
Be sure to structure this well. Don't just have students turn to their neighbor and say their answer, make them talk to each other by requiring a bit more structure through questioning:
What concepts did you identify were relevant to your problem?
How did you solve your problem?
How does your strategy compare to your partner's strategy?
Sharing out as a whole group can become repetitive. Structure the conversation to avoid this. Have each partner group share out what they talked about and rotate through each one of the questions asked so that it does not get boring. When you've gone through each of the questions, start having groups either cycle back or display their work at the front of the room.
4. Socratic Seminar
When I first heard of Socratic Seminar it was of course in an ELA class. I love to steal from ELA and make it "mathy." If we leverage this discussion technique, we are tackling SMP 4 and placing an emphasis on critiquing the reasoning of others. Here's how I would do it:
Layout: One table in the center of the room with four seats. The remainder of the room is in a U or O shape around the center table.
Grouping: Have student groups pre-assigned, but do not give them the problem ahead of time.
Call groups at random to sit in the center and assign them a problem.
The center group is charged with talking out loud about their solution strategy and working through the problem with the members of their team.
The outer circle is charged with answering the following questions:
What concepts is the group identifying as being relevant to the problem?
What is their solution strategy and what are their steps?
Do you agree with their answer?
When the center group is done, students in the outer circle have an opportunity to contribute to the discussion by answering the outer circle questions.
The center group is given an opportunity to respond to the larger discussion.
A new group is chosen for the center, and the process continues.
If done well, this can be a great way to practice proofs or real-world application problems. It can also be used for more difficult concepts, but I do recommend that the problems chosen have multiple steps. This may not be identical to a Socratic Seminar, but it's a math spin that forces critiquing the reasoning of others.
You can set up a write-around in the same way that you set up stations. Have 5 or 6 different problems around the room and have each student group start at one. The goal here is to have students contribute to the work of other groups and make corrections along the way. A perfect example is solving a system in 3 variables. Here's how I would structure it:
Round 1: Simplify to a system in 2 variables.
Round 2: Solve for the first variable.
Round 3: Solve for the second variable.
Round 4: Solve for the third variable.
Round 5: Check your work and put together your answer in the form of an intersection point.
Each time students rotate, they are checking the work from the previous step, making corrections, and then contributing their work. By the time they have rotated through, they have contributed to five different problems and have reviewed the work of their classmate's in each round. Make sure students share out their group problems to the class and also be sure to ask them to discuss how seeing and correcting each other's work helped them continue to the next step.
I believe that kids cannot truly without being able to effectively communicate in the language of Mathematics. To do that, we must look for opportunities to facilitate discussions and be mindful of creating the structure to support communication and collaboration in Math class. These are just 5 ideas that can be modified as you see fit or even just added to your repository of classroom discussion techniques to be used.