3 Math Tasks You Already Use That Can Foster Collaboration

Picture a “traditional” math class and then a “21st-century” math class. One of the most obvious differences is probably how students are interacting: No longer silently sitting in rows of desks, students are talking to each other. They are collaborating. 

Collaborative learning promotes higher-level reasoning, self-esteem, and positive relationships at school. To unlock the benefits of collaborative learning for young mathematicians, teachers can plan accessible tasks. When students don’t have to devote as much “brain space” to understanding the directions for a task, they can focus instead on collaborating on the math itself. This supports all students, including multilingual students and students with disabilities.

Start with tasks that are engaging, but not content-heavy, so that you can prioritize laying the groundwork for collaboration. Even a task as simple as taking turns drawing a picture can be productive for discussing expectations around sharing work and communicating. From there, you can use the warm-ups, word problems, and manipulatives that you and your students are already familiar with to generate accessible and meaningful collaborative tasks.

1. Collaborate Using Your Warm-Ups

Routines like warm-ups, number sense routines, or number talks invite students to reason and discuss, typically in a whole group setting. However, these can be done collaboratively as well. 

Selecting warm-ups for collaboration: Look for routines that have many possible “right” answers, so that all group members will be able to contribute meaningfully. This doesn’t have to be multiple numerical answers; it could also be many ways to get to a solution—for example, different ways to see a total in a dot talk. When you do this routine as a whole group, you may find yourself saying to students, “Wow, I hadn’t thought of that!” Those activities lend themselves well to collaboration.

Preparing warm-ups for collaboration: In a whole group discussion, you use your learning objectives to steer the conversation as it happens. For example, if we were discussing “Ways to Make 1/8” as a whole class and students were only talking about shapes, I might ask the class to think about a number line. If this discussion were to happen in collaborative groups, that steering needs to be built into the task. One way to do this is with a checklist. For example, when my third graders did “Ways to Make 1/8” as a collaborative task, each group got this checklist:

• 2 ways to make 1/8 of a square
• 2 ways to make 1/8 of a rectangle
• 1 way to make 1/8 of a circle
• 1 way to make 1/8 on a number line
• 2 ways to make 1/8 of numbers (example: 1/8 of 16 is 2)

The checklist makes it obvious to students how they should be contributing, and even though I might not be part of every conversation, I know that key points are surfacing throughout the room.

2. Collaborate Using Your Word Problems

Whether writing word problems yourself or using the ones in a curriculum, word problems are a feature of every math class.

Selecting word problems for collaboration: Make sure the context of the chosen word problem is accessible, or plan for making the context accessible. You might use images or videos to make sure students understand the vocabulary and can make connections to background knowledge. If the word problems in your curriculum have instructions like “Use an array model to solve,” leave those parts out. Groups should solve in ways that make sense to them, and diversity in strategies both within groups and between groups will lead to important mathematical discussions.

Preparing word problems for collaboration: You can turn one word problem into an extended collaborative task by planning a series of increasingly challenging number sets to fit into the story. For example, “Allison filled up 8 baskets of peaches, with 10 peaches in each basket. How many peaches is that?” followed by 18 baskets of 10, then 18 baskets of 25. If groups are working at vertical surfaces like whiteboards, they can look around the room after finishing one number set to see what number set to work on next, as described by Peter Liljedahl in Building Thinking Classrooms. This promotes knowledge mobility and frees the teacher to discuss with groups as needed. 

3. Collaborate Using Your Manipulatives

Counting collections is a rich collaborative task for students across elementary grades. You might be surprised by how excited students are to count even the most familiar math manipulatives. 

Preparing counting collections: Students will need “right-sized” collections, tools for organizing, and space to record. Don’t be afraid to offer big collections. Collections of, say, 45 for kindergartners or 845 for fourth graders can be meaningful opportunities for developing place value understanding. Tools like cups, plates, paper trays from the cafeteria, and your number lines or hundred charts should be available for students to take up as they need. Finally, think about how you want students to record their collections: on paper, on whiteboards, and/or digitally on a platform like Seesaw.

To grow your collection of collections beyond your classroom manipulatives and supplies, invite students to bring in collections from home, or round up unwanted items around your school. I have many beautiful collections of transparent manipulatives left over from the overhead projector days.

If At First You Don’t Succeed…

Collaboration is tricky. Even with extensive planning and coaching, students and groups will struggle at times. But if collaboration is hard for your class, that means they need to practice it more, not less. More collaboration doesn’t have to mean planning more tasks from scratch; you can and should use the resources you already have and turn those into revisit-able routines. Having familiar routines for collaboration means that students can dive straight into the learning, while continuing to develop their identities as good group-mates who know how to support each other and work together.