Focus on...adapting 'team building' tasks
During August a discussion developed in the Secondary Forum about ‘cooperative learning’ tasks.
These tasks start from a variety of facts, which are printed on cards, about some object or situation. The cards are dealt out to the learners in a small group, who use the information together to solve a problem. The learners are not allowed to show their pieces of information to each other, so they have to talk to each other about what they each know.
The original version of this kind of activity was called Zin Obelisk. It was devised during the 1980s by Michael Woodcock – a past MP, director of several companies, consultant and writer of team-building manuals – as a team problem-solving exercise for business executives on team building courses. It has been used in this way on business management courses ever since, and can be found on many websites, for example Business Consultants Network and Baidu.com.
The kinds of question about the behaviour of people working in a group to solve the Zin Obelisk problem that are addressed on leadership-in-business courses are:
- what behaviour helped the group accomplish the task?
- what behaviour hindered the group in completing the task?
- how did leadership emerge in the team?
- who participated most?
- who participated least?
- what feelings did you experience as the task progressed?
- what suggestions would you make to improve team performance?
During an ATM conference the Zin Obelisk task was introduced to mathematics teachers soon after it had been published. Having themselves enjoyed what was then for most mathematics teachers a novel kind of activity, some conference participants took it back to their own schools and local authorities.
Zin Obelisk thus gave many students their first opportunity to try to cooperate in solving a problem as a group. The focus was on the social skills involved in sharing information, cooperating and contributing to the work of a group, rather than on developing mathematical ideas. That is why it became known as a ‘cooperative learning’ task.
Some teachers were, at about that same time, thinking about, discussing and trying to introduce into their classrooms, what John Mason had described in Expressing Generality in the Open University Update materials as a 'conjecturing atmosphere'.
Teachers saw in Zin Obelisk a task that put students in a situation in which the students, while endeavouring together to solve the Zin problem, might begin to understand that:
“The essence of working in a conjecturing atmosphere is…listening to and accepting what others say as a conjecture which is intended to be modified. Consequently, it is well worth noticing how you go about:
- developing and using a vocabulary which fosters conjecturing, (e.g. use words such as ‘I suggest that...’ or ‘Perhaps...’ rather than ‘No!’ or ‘That's right!’)
- listening to others and being listened to.”
You will find the Zin Obelisk task, slightly improved, at NRICH. Lincolnshire teachers adapted Zin Obelisk in order to reduce the number of ‘red herring’ statements. That version is called Workers of Zen.
The creator of Zin Obelisk was not a mathematics teacher. It is possible to design ‘cooperative learning’ tasks that have the same structure as Zin Obelisk but which provide rather more opportunities for mathematical learning.
It might seem to be a daunting challenge to invent a Zin-type task. But it isn’t hard if you go through the following process:
- imagine, or make a rough physical model of, an ‘object’, or draw a diagram
- write down facts that you ‘see’ about aspects of, and relations between aspects of, the ‘object’. You can include one or two questions that draw attention to facts
- decide what will be the goal of the task. It might be to reproduce the diagram that you drew, or to make a model. Or it might be to deduce a fact that is not immediately obvious – as in Zin Obelisk
- put everything away and don’t think about it for several days
- after a few days retrieve the list of facts, but don’t look at the diagram or model. Using only the facts, and any suggestive questions, in your list, try to reproduce the diagram or model, or deduce the fact that wasn’t obvious. Tick off the facts as you use them.
Olympic Podium (instructions, information sheet and cards) is a task created in this way that involves ratios and visualising three-dimensional objects. We also give the chain of reasoning that the task designer constructed when checking the list of facts. But if you are considering trying out this activity with your students you are advised to attempt the task yourself before looking at the author’s chain of reasoning – you or your students may find other more ‘elegant’ ways of reaching a ‘solution’ that satisfies the conditions!
A Logo (example logos, information sheet and cards) is another ‘cooperative’ task that was devised by going through the process described above. It is about properties of triangles and other polygons, and the aim is to produce an arrangement of shapes about which all the statements on the cards are true.
These tasks give students opportunities to suggest tentatively, and explore together, deductions, and discuss relationships between mathematical ideas, while finding out that a conjecturing atmosphere facilitates cooperative problem solving in particular, and learning mathematics in general.