Ofsted conference

OFSTED SUBJECT CONFERENCES FOR TEACHERS MARCH 2002

Problem solving allows children to engage in the processes of mathematics. In particular it is a means of stimulating children's curiosity and catching heir attention. Problems can facilitate the learning of new concepts, provide a vehicle for transferring concepts and skills to new situations or present a meaningful device for practising computational skills. Before the conference, the delegates asked children in their schools why problem solving is important in mathematics. Responses show that children in these schools see problem solving as an important component of the curriculum. Many children clearly gain pleasure from problem solving activities, seeing them as a challenge that is not just about right and wrong answers.

The following are the points that delegates felt were pertinent to the effective implementation of problem solving, reasoning and communication in mathematics:

• Ensure that starting points are accessible to the children. In the planning of problem solving work, focus on intended outcomes rather than activities. Each child should have a goal to achieve with equal value placed on their work, despite ability;
• The problems chosen need to build on children's own interests and their own ideas and questions;
• Problem solving is a two way process. It tests the applications of learnt skills but also can initiate new learning;
• Consider what you need to teach the children to do when faced with problems. In particular, model solving one or two problems using a framework for problem solving and how to break down a multi-step problem into its various parts;
• A group of children working together on a problem make more progress than individuals working separately. Collaborative working enables children to spark ideas from one another and to discuss thoughts and hypotheses;
• Different methods of grouping children should be employed including grouping by ability and by friendship groups;
• Well chosen problems provide pleasure and satisfaction as new situations are explored. Problems also allow children to encounter difficulties; a significant part of the problem solving process is to find ways of over-coming these. A great deal can be learned from unsuccessful attempts, providing teachers build strategies that children can employ when they become stuck;
• It is important to build a climate which encourages children to share their work with teachers and with each other. Much of this will be through talk and discussion;
• Problem solving tasks allow children to find their own perfectly acceptable ways of presenting written work. Where necessary, children can be helped to simplify overly complex and long-winded written recording through showing them more conventional forms;
• It is a good idea to allow children to decide for themselves what resources and equipment to use to solve problems. Providing equipment is often restricting - as children become experienced at problem solving they also become confident about choosing equipment. It is, however, important to build competence and confidence and this means making suggestions such as "would xxxx be of use?" or in putting out a carefully selected range of equipment from which children can make a reasoned choice;
• Children need the experience of evaluating their own work. The teacher can help this by sharing the learning goals with them and then using carefully framed questions to guide children to make their own judgements about the strategies they have used and the work they have produced;
• During plenary sessions, review together one or two questions, possibly the most difficult, taking the children through the problem solving framework, discussing different methods used to solve problems and commenting on the appropriateness and efficiency of the methods chosen. Alternatively, allow children to work with a different pair or group to discuss whether there is agreement about answers and to explore the range of mathematics used to solve the problems.