Using Group work In problem solving LSEF Problem Solving Conference KS4/Post 16 Using Group work In problem solving Beth Williams & Lynda Browne

Why use group work to develop problem solving skills? Provides positive opportunities for Risk taking Mathematical language development Peer coaching and support Gives the teacher the freedom to move around the class and make informal assessments Allows mixed ability learning Effective learning (Vygotsky) Mathematics in the ‘real’ world is rarely done in isolation

Rules for group work You are responsible for your own work and behaviour Preparation to work effectively in groups has to start from year 7 You must be willing to help any group member who asks None of the mathematics should be done in isolation You may only ask the teacher for help if everyone in the group has the same question If someone in the group can overcome an obstacle, they must help the rest of the group to overcome it too

Standard pitfalls in group work One person dominates by collecting all the pieces of information and taking control. Someone opts out by sitting back and letting the rest of the group solve the problem. The ability of students to successfully follow the rules will improve with reinforcement of them in each session they are used. Teacher led discussions about the purpose of each rule are essential.

One approach: pieces of the puzzle All about deductive reasoning Each group member is given information to share with the rest of the group Each group member has to make value judgements about the information they have The solution can’t be found without everyone's contribution Group assumes 'ownership' of the task Individuals retain personal responsibility within the group

Introduce the task The introduction sets up the tone of the activity Make links to previous work Revise key terms and mathematical vocabulary The activity should clarify and develop mathematical ideas introduced in previous lessons

Problem 1 – Find the pattern Form groups of 4 In a class this may be done randomly or involve some social engineering You may assign roles to each member of the group e.g. team manager, equipment manager, scribe, spokesperson This one is for everyone (KS4/Post 16) to get the idea.

Problem 1 – Find the pattern Each group should have a grid And a set of cards (20)

Problem 1 – Find the pattern The aim is to find the pattern from the description on the cards Shuffle and deal out the cards You may not show your cards to anyone else, even after you have revealed the information on it Each group member takes turns in reading out the piece of information that they think is most useful from their cards

Problem 1 – Find the pattern After reading a piece of information out, the group member retains the card. They may refer to it later but they shouldn’t just place it on the table for everyone to see. After each individual piece of information is given, the group must see if they can make any progress with the design If no progress can be made, the next group member reads out a new piece of information

Problem 1 – Find the pattern Once you think you have finished… Check the design fits all of the information. If you are convinced you have the correct solution, you can then see all of the cards. Try to find the fewest number of cards needed to uniquely define the pattern

How did your group get started? How did the group 'join' the clues together? What caused some difficulty? Which clue did you find most helpful? Did any group do it a different way? What might you do differently next time?

Further problems There are a variety of these problems to try KS3/GCSE and A level Select a task and try it out in your groups of 4

Where can these problems be found? http://www.furthermaths.org.uk Look in the resources menu for problem solving

bwilliams@clapton. hackney. sch. uk lbrowne@clapton. hackney. sch bwilliams@clapton.hackney.sch.uk lbrowne@clapton.hackney.sch.uk phil.chaffe@mei.org.uk