One thing employers value but which is not an explicit part of the curriculum is the capacity for working together, since this is the reality of much activity in the workplace. Mathematics often causes difficulties, so the capacity for individuals to be able to explain effectively to others and learn from their peers in turn, so that shared understandings can be developed, is an important skill. This can be fostered in the classroom by pupils working in different groups: independently as individuals, collaboratively with a partner, or in a small group on different occasions.
Working collaboratively includes talking about mathematics, evaluating their own and others’ work and responding constructively, problem solving in pairs or small groups and presenting ideas to a wider group.
Whether you choose independent, paired or group work for a particular activity will depend on the activity and what you want to achieve but, over time, pupils need opportunities to work in all three ways.
For example, in a unit of work on probability the teacher may ask pupils to work in pairs when collecting data in a practical exercise. He may then ask pairs to form groups of 4 or 6 to compare the outcomes, and to consider similarities and differences between sets of observations. This might culminate in a whole-class discussion where comparisons could be drawn between the data sets at group level, and on what could be seen from looking at all the observations as a single data set. Individual work on problems will also be a feature of the work in the unit, but without sharing the data collection out across the class there will be a strong case not to undertake any practical work because of the time involved, yet this will make the acquisition of deep understanding of random behaviour extremely difficult for pupils.
Group membership may need to change from time to time so that pupils experience working with different people. Sometimes groups will be of the same level of attainment, sometimes of mixed levels of attainment. Friends usually work together well, but it is also important that pupils learn to work together in the sort of arbitrary groups they will encounter later on in employment. On occasions, you may decide to form single-sex groups.
For some discussions, either you or the group may want to assign roles to particular members: e.g. leading the discussion, taking notes, drawing diagrams, leading the presentation, and so on. Pupils who are quick to suggest ideas may need to be asked to manage the discussion in order to let others contribute.
Some pupils find contributing to discussions difficult, and it may be useful to start the discussion in small groups within which each person has a number. Then in the whole-class discussion one representative from each group (the number being randomly chosen) can report on the group discussion and then the whole-class discussion can open out. This way, pupils see the process as transparent and they are not being ‘picked on’ at any stage, but everyone will contribute over time.
Having ready an extension activity to give to any group that reaches a conclusion quickly allows other groups time to fine-tune their thinking.