Published December 2017
The ability to problem-solve collaboratively is more important than ever. Current developments such as driverless cars and drone deliveries signpost an increasingly automated environment. In a world where we will need to be able to problem-solve even more than before, and with others too, it is essential that we understand how to support young learners to develop collaborative
problem-solving (CPS) skills. Nevertheless, CPS has a complex set of requirements which we need to understand in order to plan effective lessons.
To help embed effective CPS in classrooms, NRICH worked with ten Cambridgeshire schools and the Cambridgeshire Maths Team. We identified five key aspects of CPS (Luckin et al., 2017):
• Choice of task
– it must offer specific roles
• Level of engagement
– tasks must be engaging so that learners want to find the solution(s)
• Individual responsibility
– each learner must know what is expected of them
• Group responsibility
– the group must be aware of their final goal
– learners need opportunities to reflect and identify areas for further development
Let’s see how teachers addressed each of these five key aspects with two of our most popular NRICH activities, beginning with Stringy Quads
Using NRICH resources to promote CPS - lessons from pilot schools
Example 1: Stringy Quads
Choice of Task
It sounds obvious but effective CPS activities require team work. With Stringy Quads
we found that the most successful lessons involved groups of five, rather than four, learners: four learners took turns suggesting possible shapes and holding the string whilst the fifth kept notes for later feedback.
Level of Engagement
Learners need a task with which they can readily engage and Low Threshold High Ceiling (LTHC) tasks are ideal (you can explore a selection of LTHC tasks in this feature
). Stringy Quads is a very engaging LTHC activity but some teachers went even further to ensure that their learners were fully engaged with the challenge. One of the most effective
strategies was revisiting the classroom environment: some teachers rearranged their classrooms before the lesson by clearing away tables and leaving out clipboards for the learners to record their group’s ideas. This approach certainly had an impact on the classes - one learner clearly remembered walking into the lesson and realising that ‘something special was going to happen today.’
One of the most frequently voiced concerns about CPS is ensuring that everyone makes an effective contribution towards solving the challenge. For Stringy Quads, some teachers encouraged groups to listen to everyone’s ideas before making a collective decision about their next steps and most of the teachers set the expectation that any member of a group might be asked to feedback to the
Just like working with individual learners, our teachers found that it helped to be specific about what to expect your groups to achieve in the session. With Stringy Quads, they needed to explore lines of symmetry of different quadrilaterals. It was a clear objective and all of our teachers reported that it was successfully achieved with their classes.
One of the most effective ways of developing CPS is allowing time to reflect on the task and consider next steps, and sufficient time needs to be set aside for this. Several learners admitted that they found it frustrating to know an answer when someone else was struggling. However, some admitted that they felt very satisfied when they kept their counsel and allowed others time to reach the
answer. In the focus groups, we also asked learners to rate their CPS skills out of a maximum of five and provide a reason for their scores. Several teachers reported that they would model a similar approach in future CPS lessons.
Example 2: Five Steps to 50
Our project schools also explored the number activity Five Steps to 50
. In this activity, pairs of learners rolled a die to generate a two-digit number, such as 34. They needed to either add or subtract in steps of one, ten or a hundred to reach their target of fifty … but they were only allowed five steps to reach the target!
Choice of Task
This task is designed to be played in pairs and many of the learners really enjoyed this aspect of the activity. This was usually because there were two clear roles for the learners which they felt made it fair, one rolled the die and the other recorded their answers. They found that they often supported one another well without having the issues of trying to get heard within a larger group. They
also found it easier to stay on track when working in pairs and not get disturbed by others. The importance of carefully planning the modelling aspect of a lesson arose several times during discussions with teachers. They suggested that it was far better to carefully choose numbers which allowed their learners time to understand the activity rather than rely on rolling a die.
Level of Engagement
Five Steps to 50
is a very engaging problem, which might be regarded as a KS1 activity, but most of our teachers chose to use it with their KS2 classes. In most cases the teachers were keen to develop CPS skills, so decided to lessen the mathematical requirements by choosing a KS1 activity. This worked extremely well, and the task
often continued into break time. The classroom environment was also important for this CPS activity. Several of the teachers ensured that a range of useful resources such as number lines, Numicon and bead strings were provided on desk tops, with dice and wipe boards also easily accessible in most classes. In one Y6 class, a higher attaining pupil decided to use a hundred square to very
effectively represent which numbers he could, and could not, reach when taking five steps to fifty. His approach was quickly adopted by other members of the class, a lovely example of learning from one another's ideas (Figure 1).
‘Another way of thinking about this problem,’ the Y6 reflected, ‘ Is that you can move five spaces across or down.’
Can you follow his reasoning? It might help knowing that his class used a set of dice numbered from one to six.
Black = Works and can be rolled with a die
Blue = Works and can’t be rolled with a die
Red = Doesn’t work
Figure 1: Example of a colour-coded solution using a hundred square.
In most classes the teachers allowed the learners to choose a partner they thought they would work well with. Some of the teachers provided the pairs with recording sheets but most encouraged pairs to develop their own recording approaches.
Again, the teachers found that insisting each group member should be prepared to feedback to their class, ensured that everyone was motivated to support their group.
Most of the learners enjoyed working with partners but some were less positive about paired work for number challenges, they felt that number work was far better suited for individuals and would have preferred to work alone. When prompted, they admitted that a partner might be helpful if they got stuck.
More ideas for CPS activities
We hope that this short article has inspired you to consider introducing CPS into your own classroom. You can find Stringy Quads
, Five Steps to 50
and other CPS activities under the heading Being Collaborative
Luckin, R., Baines, E., Cukurova, M., Holmes, W., & Mann, M. (2017). Solved! Making the case for collaborative problem-solving.
Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior, 15(4), 375-402.
NRICH Team (2019). Low Threshold High Ceiling - An Introduction.