Developing learners’ collaboration skills in the classroom and at home

It’s not a new notion that collaboration is an important tool to develop ideas. Research from influential theorists like Lev Vygotsky and George Pólya highlights the importance of a collaborative approach to learning and describes the many benefits of this peer-to-peer learning approach.

While a collaborative approach can be applied in a range of teaching situations — one area that can benefit greatly from it is the writing, sharing, and completion of problems written by the children in your class.

Plan and evaluate problem-solving strategies in your classroom

Looking to build peer learning and collaboration skills in your maths classroom? First, you need to do a bit of planning.

1. Start by understanding the problem

This may seem obvious, but we need to make sure that our maths learners understand the problem they’re about to write. The context of the problem is important. Does it make sense and are we likely to come across it in the future? Do the numbers used in the problem match the context of the problem?

Say we use a problem like:

Lulu runs 189 km before lunch and 275 km after lunch. What is the total distance Lulu has run?

The likelihood of coming across a similar problem in the textbooks, exams and tests is very low. Lulu may be a great runner but the context of this problem does not match the numbers or vice versa.

2. Make a plan

Your learners need to know how the context of a maths problem connects with the numbers and also how the mathematical strategies and approaches relate to that context and the numbers.

Children need a clear idea of what will be involved in solving the problem before they get started. They also need to think about the appropriate representations that can be used to solve their problems.

3. Carry out the plan

Once the maths problem is written, your learners have to carry out the plan. This may involve calculating using the representation they think is correct and deciding on a final answer.

4. Evaluate the problem

This final step is important. At this point you want learners to revisit each of the steps above and decide whether changes need to be made in order to make the problem better.

Was the representation they decided on right for the problem?
If they were to support their friends with this problem, do they think that they can guide them through the steps of the problem to end in success?

This collaborative and supportive way of thinking is heavily influenced by George Pólya (1887–1985), a highly respected mathematician at Stanford University. His work can help create a sound approach to maths problem-solving, problem writing, and collaboration using the problems that have been created.

Pólya made an excellent point in his widely used book, How To Solve It,

“The mathematical experience of a student is incomplete if they never had an opportunity to solve a problem invented by themselves.”

At this stage, something magical can happen. The problem is ready to be shared.

Ask learners to share the problem

This is such a valuable stage of the process. Sharing maths problems not only helps your learners feel proud of their work, but it also offers them the opportunity to provide support to their friends and to evaluate the problem for a second time.

There are a number of ways to share maths problems in the classroom. Here are a few of our favourites.

1. Shared journals

Once a problem has been written, learners can take turns completing the problems in their maths journals. Taking someone else’s work away in a learner’s own journal can raise lots of points for discussion.

Why have they completed the problem this way?
If they were to change one part of the problem, which would it be and why?

In order to get better at writing their own problems, children need to see well-written problems or get the opportunity to critique a problem and discuss what could make it better.

Learners willing to share their own journals with others in their class can allow this to happen.

2. Class-to-class story books

Take the idea of a shared problem one step further by asking learners to write maths stories for the year below. These stories can have a central theme, but should rely on maths problems to work through the book. This continuation of a maths idea (in this case, looking at the previous year’s objectives) shows children that maths isn’t a series of isolated lessons. There is continuity and connections within mathematical ideas.

Children also love being read to by their peers. It can prompt questions from those being read to and the authors of the stories sometimes provide valuable support. Particularly since the reader may have recently been in the same position as the learner, they’re well placed to recognise the misconceptions they overcame when looking at the same idea initially.

3. Shared problem space

In the same way we use community boards to post notices for parents and the wider school community, we can set up shared problem boards within the school.

One way of doing this is to place these boards in Key Stage areas. You can post the problem on the board but also print it out to make it available for learners to take home. This gives students the opportunity to complete the problem and return it to the author or authors. These solutions can be posted alongside the original problem demonstrating the many different approaches learners take.

4. Mum and Dad’s maths

Making a point of celebrating differences in approaches to maths and bringing family members into the experience can be valuable and rewarding. A great homework task is to set a question in a standard representation. For example:

43 x 28 or 12 x ¹⁄₂

Asking family members to complete the same problem as the learner can create a great deal of discussion when the representations are different.

It may also be the case that a family member is unsure of how to complete the problem. This would give your learner an opportunity to show their understanding to their family members and also show the strength of a collaborative approach.

Working collaboratively allows us to understand the feeling of support and it can give us a sense of pride when our work is celebrated. It is a treat and we should use every opportunity to think of it that way.