Ems Lord, Director of the University of Cambridge-based NRICH project, shares five key factors to consider when planning collaborative problem-solving (CPS) sessions using low-threshold, high-ceiling maths resources.
Have you ever attempted assembling flat-pack furniture with a friend or family member? How did it go? And are you still talking to one another?
Being able to work with others is a key life skill, but not always as straightforward as we might like. Whether we’re assembling furniture, putting up an extension or navigating our way to a holiday rental, we need to be able to work together towards a common goal and recognise our own responsibilities in achieving that goal. Moreover, developments such as driverless cars and drones signpost an increasingly automated environment in which those with strong group-working and problem-solving skills will thrive.
It is essential that we understand how to help learners develop collaborative problem-solving (CPS) skills alongside a sufficient level of challenge – planning lessons that will stretch more able learners while being accessible to all.

To this end, NRICH worked with 10 Cambridgeshire schools and the Cambridgeshire Maths Team in a project sponsored by Nesta. We shared existing low-threshold, high-ceiling NRICH resources with participants, who then adapted these to develop CPS in their own classes. After visiting each school, talking with teachers and running focus groups with learners, we identified five key aspects of CPS to consider when planning maths lessons:

1. Use low-threshold, high-ceiling activities 

First and foremost is the importance of low-threshold, high-ceiling (LTHC) activities and resources. These enable all learners to get started on a problem while also offering sufficient challenge. One of NRICH’s most popular LTHC activities is the Factors and Multiples Game, which challenges learners to work together to build as long a chain as possible. Be warned: it’s hopelessly addictive for adults too!
When choosing LTHC tasks, explore our free curriculum mapping documents for primarysecondary and post-16 provision.  

2. Get learners hooked

Engaging tasks are key for CPS sessions; learners must want to solve the problem. At NRICH, we aim to engage learners by designing activities which have a clear “hook” – such as the interactive challenge Got It! and the sports-themed activity Olympic Records
Got It! requires learners to pit themselves against the NRICH computer to be the first to reach 23. This challenging activity draws learners in and they often make multiple attempts at the problem. Several of our focus group participants said they later taught the game to older siblings and family members because they thought they could outwit them.
The group activity Olympic Records is particularly appealing to learners with an interest in sports, who can draw on their knowledge to support others to match sports to their graphs. It demands effective group work and a willingness to adjust initial responses once learners realise that gender is also an important factor.

3. Model individual roles and responsibilities

 A group is only as good as its individual members. Every member of the group must know what is expected of them during the task, and which roles belong to others. Individual learners should not dominate the session but should focus on filling their own roles while supporting others.
Card activities often work well in developing these skills; for example Shape Draw. Be clear about roles; which individual is responsible for recording the activity, suggesting the next shape or rolling the die? Make sure everyone knows their role and consider rotating different roles around the group. Teachers participating in our CPS project stressed the importance of modelling different roles for group members before embarking on the actual group work.

4. Develop skills for group communication

While knowing their own role is important, learners also need to be aware of the overall aims of the group. This changes the level of challenge for any task from merely cooperating to fully collaborating. In particular, all learners should be prepared to feedback to the wider class about their task.
Useful activities which offer a high level of challenge for older learners and the opportunity to feedback and explore different approaches include Steel Cables and  Kite in a Square. Younger learners might enjoy the challenge of Jig Shapes and Quad Match

5. Build in time for reflection

 CPS skills need time to develop. Timetables should allow for regular CPS teaching sessions, including time allocated for reflection. Building in this reflection time can be a challenge, as time is also needed to focus on developing the required mathematics and group-working skills – but the teachers in our project stressed that it was highly worthwhile.
Ask learners about how well they worked in a group. If they awarded themselves a score from 1 to 5, what would it be and why? Which areas of their group work do they need to develop further? From a teaching perspective, when will they get their next opportunity to work on those areas?
And for your own reflection… If your class attempted one of our tasks, how do you think they might cope? Which aspects do you anticipate offering the most challenges? More importantly, when are you planning to lead the next CPS session with your class?

Free webinar for NACE members

Ems Lord is running a free webinar for NACE members on 26 March, exploring effective approaches to develop collaborative problem-solving skills using low-threshold, high-ceiling maths resources. For details and to reserve your place, log in to our members’ site.

Further reading

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.

McClure, L., Woodham, E., & Borthwick, A. (2017). Using Low Threshold High Ceiling Tasks.
Ems Lord has been Director of NRICH since 2015, following a previous role leading one of the country's largest Mathematics Specialist Teacher Programmes. Ems has taught mathematics across the key stages, from early years to A-level Further Mathematics, and has worked in a variety of settings, including a hospital school. She’s supported schools as a leading mathematics teacher, local authority consultant and Chartered Mathematics Teacher, and has taught mathematics education on both BEd and PGCE teacher programmes. She is currently working on her PhD thesis, which explores approaches to improve support for those learning calculation skills, and is President-Elect of the Mathematical Association for 2019-2020.
Tuesday, March 5, 2019