The students in a *Math Trailblazers* classroom work both collaboratively and independently. Working with a partner or in small groups enhances students’ opportunities to communicate about mathematics. Students learn from and help each other as they struggle to find solution paths, explain solutions, critique the work of others, and settle differences—mirroring the work of real mathematicians.

There are many ways to group students to ensure success. Grouping needs to be flexible, meaning that the number of students in the group changes based on the task. Regardless of the group size, the importance of cooperation, respect, and individual accountability is stressed, and the classroom must be arranged to make cooperation possible.

The following are appropriate ways to group students for instruction:

- Small groups of 2, 3, or 4 students
- Pair sharing
- Names picked randomly
- Partners chosen by students
- Groups based on how students work best
- Groups assigned by ability
- Whole class as one group

While whole-class instruction and working individually are not often considered grouping strategies, both are appropriate and essential in learning mathematics. Whole class instruction is especially useful when explaining the day’s problem, introducing a new manipulative or tool, correcting a common mistake, or summarizing a lesson. Whole-group instruction is most effective when it is brief, focused, and the information applies to all students. Clarity is enhanced when teachers provide a few minutes for student pairs to discuss new ideas.

Working alone is powerful and effective as well. Giving students time to reflect and record their strategies before joining the group increases participation and helps students assess their own needs.

A *Math Trailblazers* classroom might use the following different student groupings for effective instruction:

- Students work independently, giving each child a chance to think through a question and come up with a way to problem solve.
- Students turn to a partner to rehearse their answers or to make their answers more complete.
- Students work in groups to complete a task. They share ideas, responsibilities, and materials. These tasks would be difficult to complete independently.
- Students work as a whole class evaluating peer problem-solving strategies or receiving direction from the teacher.