There are, of course, many ways to organise children into groups. Unless the teacher has specific reasons for doing otherwise, a random mix method is best for this type of co-operative problem solving.
Random Mix by the Cards
Here is one way to achieve a random mix of pupils using a pack of ordinary playing cards. To form seven groups of four children, use all four card suits from one (Ace) to seven. Shuffle this pack and have each child choose a card. All the sevens form a group, all the sixes form a group and so on.
This type of problem solving activity is well suited to developing and clarifying mathematical ideas that have already been introduced in other lessons. Therefore, in introducing the task to the class, the teacher can make links to previous work. If the mathematical vocabulary contained in the problem is of particular concern, then key terms should be revised.
The groups are formed and each child in a group is given one clue card. To maintain 'ownership' of the piece of information, the child may not physically give away the clue-card, but must be responsible for communicating the content to the group. Each pupil's role is now to work within his/her group to solve the puzzle, following the set of work rules. The teacher must also take care to follow these rules, and not take back responsibility for the task by interfering with the problem-solving processes or offering help before being asked by the whole group.
As always, it is advisable to have an extension question ready for a group that finishes before the others. It is also useful to have one or two 'extra' clues ready. These can be used to allow the inclusion of an extra group member, to give help to a group that is 'stuck', or to assist 'checking' when a group thinks it has finished the task.
- It is important for groups to report on their problem-solving processes as well as confirming the correctness of their end product. The teacher can use questions focus on particular issues and highlight points that have been observed during the session. For example:
(More than one answer is possible until Clues E & F are incorporated)
Each group needs a handful of sticks, all of the same length - such as matches, ice-cream or lolly sticks, or drinking straws. The aim is to arrange some of the sticks to make either a single shape or shapes-combinations (depending on the level of complexity).
The clues in this type of problem are non-verbal. In the example below, the squares are cut up by the teacher and each member of a group-of-four is given three pieces marked with the same letter. The aim is for the group to make four complete squares.
Each group needs a set of digit cards (two or three copies of the digits 0-9) and a template of the algorithm, in this example a two-column sum
Burns, M. (1992) About Teaching Mathematics, Maths Solution Publications: California Erickson, T. (1989) Get It Together, EQUALS: University of California.
Gould, P. (1993) Co-operative Problem Solving in Mathematics, Mathematical Association of N.S.W. Australia. ISBN 0-7310-1371-9 (Available through the Australian Association of Mathematics Teachers Catalogue code MAN466 - http://www.aamt.edu.au/ )