Supporting Students to Work Collaboratively
Working Collaboratively is part of our Developing Mathematical Mindsets Primary and Secondary collections.
This page for teachers accompanies the Primary and Secondary Being Collaborative resources.
You may wish to watch the recording of the webinar, which draws on the resources below to discuss how teachers can support students to work collaboratively.
"The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more." Bill Thurston
If we want to create an environment in our classrooms in which our students feel like they belong to a community of mathematicians, we will need to offer them opportunities to collaborate. We want our students to experience the benefits of collaboration - becoming more resilient and less dependent on the teacher, and becoming confident that they can often achieve more by working together.
If students are to work and learn together; share ideas and support each other, then we may need to think about the following:
Values and ethos
- We can all learn from each other
- All our contributions are valued
- We all have a chance to speak, but also have a responsibility to listen
Students can feel anxious about making mistakes or admitting that they are struggling, so it is important that our classrooms provide an environment in which students trust each other, and feel safe to contribute.
Structural considerations
- Alan Wigley's 'Challenging Model' offers a useful framework for structuring lessons, in which students are presented with a task at the start of a lesson and are then given opportunities to collaborate and share ideas.
- Using Low Threshold High Ceiling (LTHC) tasks make it possible for everyone to start on the same shared challenge, and then have meaningful and constructive conversations about it as the lesson progresses.
- Giving students time to think on their own, and an opportunity to discuss their thinking with one or two other people, as well as sharing their ideas with the whole class, can all contribute to effective collaboration. 'Think-pair-share' and 'Convince yourself, convince a friend, convince a sceptic' offer useful structures in which to do this.
- To ensure all voices are heard, a 'no hands up policy' can sometimes be very effective (see Dylan Wiliam reference below). Many teachers have a system for selecting students randomly.
- In his 14 Practices for Building Thinking Classrooms in Mathematics, Peter Liljedahl makes suggestions about group sizes, ways to arrange the furniture and ways of establishing purposeful interactions in order to facilitate productive collaborative work.
- In her work on Complex Instruction, Jo Boaler draws attention to the merits of group-worthy tasks and suggests that there is value in assigning students different roles when working in groups. This may be particularly useful for students who have little experience of group work.
Facilitating productive interactions
- "How...?" and "Why...?" questions take precedence over "What is...?" questions
For example, asking "How could you work out 17 x 8?", as opposed to "What is 17 x 8?", will generate many more responses and offer opportunities for making connections, and evaluating the merits of different strategies. - Volleyball rather than ping-pong
Many classroom interactions follow the pattern 'teacher-student-teacher-student...' in which students look to the teacher for leadership. Instead, encouraging 'teacher-student-student-student...teacher-student...' interactions makes it possible for students to share ideas and work more collaboratively independently of the teacher. - Encouraging dialogue rather than monologues
When students share ideas, there is a risk that they just talk about their own thinking, and fail to engage with the thinking of others. Sometimes, teachers may need to insist that students respond to what has just been said, so that the conversations build on what has been offered so far. ("Slowing down and opening up" Alf Coles) - Working walls rather than display boards
Offering wall space for students to post ideas and conjectures gives them an opportunity to share insights and questions. This makes it possible for students to collaborate while work is still in progress. - Being stuck and making mistakes offer opportunities for learning
An open and honest attitude to struggle ("I can't do this YET" and "I'm in the pit, can someone help me?") offers opportunities for students to help each other and work together ('Three before me'). - Feedback about quality of group interaction
If we value collaborative work, then some teacher feedback needs to draw attention to how students interact with their peers.
You can find problems that are ideal for students to work on collaboratively in our Primary and Secondary Being Collaborative collections. The teachers' resources highlight how students might collaborate as they work on all these tasks.
Follow-up resources
You may be interested in this collection of follow-up resources:
Peter Liljedahl's book Building Thinking Classrooms in Mathematics, in particular Practice 2 (How we form collaborative groups in a thinking classroom), Practice 3 (Where students work in a thinking classroom) and Practice 4 (How we arrange the furniture in a thinking classroom)
Podcast and transcript of Dylan Wiliam discussing effective questioning in the classroom - the conversation includes reference to a 'no hands up' approach and creating a community of learners
In their article Models for Teaching Mathematics Revisited, published in Mathematics Teaching in 2019, Andrew Blair and Helen Hindle offer a fresh perspective on Alan Wigley's original 'Challenging model' article, originally published in 1992
Collaborative learning in mathematics : a challenge to our beliefs and practices by Malcolm Swan
This article, written by Jennifer Piggott, describes attributes of effective team work and links to 'Team Building' problems that can be used to develop learners' team working skills
This selection of group-worthy tasks have Teachers' Resources which outline how teachers can put into practice a Complex Instruction approach in their classrooms
The NESTA-funded report Solved! Making the case for collaborative problem-solving