UNPACKING THE NATIONAL CURRICULUM Shirley Clarke suggests ways to set up practical maths problems to help children understand concepts and knowledge
PROMPTS FOR REAL-LIFE PROBLEMS
1. WHAT DO YOU THINK THE ANSWER WILL BE?
2. WHAT EQUIPMENT WILL YOU NEED AND HOW MIGHT YOU FIRST TRY TO SOLVE THE PROBLEM?
3. TRY IT OUT, RECORDING ANYTHING IMPORTANT
4. IF IT DIDN'T WORK, DECIDE WHAT YOU WANT TO CHANGE AND TRY OUT YOUR NEW IDEA
5. STOP WHEN YOU ARE HAPPY WITH YOUR ANSWER
6. HOW DID YOUR ANSWER COMPARE TO YOUR PREDICTION?
Real life" problem-solving is an essential aspect of the mathematics curriculum. Problems such as "How many people will fit in the hall?"; "How much will biscuits for the class cost?"; "Which are people's favourite drinks?"; "Which class has the longest journey to assembly?" provide opportunities for children to apply their skills to the real world rather than learning them without application. These problems imply that the child must "select the materials and the mathematics", focusing on finding his or her own methods.
It takes courage, however, for a teacher to "let go" and allow a child to find common sense ways of solving the problems. Their first attempts at open-ended problem-solving usually result in what might appear to be very long-winded methods, but this is the important part; by finding their own methods first, they are making "human sense" of the problem and really getting to understand the concepts of addition, subtraction, multiplication, division and so on.
It is the teacher's role to suggest refinements (for instance, pointing out how rounding up to 10 makes it easier, suggesting that it might help to create a chart), but these need to come after they have their own clear understanding of the concept involved.
In my own classroom, I found it helpful to structure these kinds of problems so that children were kept on task and so that I could see what was going on at various points. The stages seem appropriate (see box), and can be presented as a class poster (regardless of the age of the children).
I found these are useful prompts to break up what could be a daunting task. It means that children only have limited things to think about as they begin to solve the problem. It also gives the teacher a chance to see how they are thinking (for example, "Have a look at the maths table and talk about how you are going to do it. That should take about 10 minutes. Then come to me and tell me what you are going to do.") Children used to this approach become more independent and confident about the processes they need to go through.
Apart from cross-curricular books from the Islington-based BEAM Project (Be A Mathematician, 0171 457 5535) - Journeys, Celebrations, Birds and Flight and Our School - and the ideas in the HBJ scheme (published by Collins), it is rare to see "real life" problems in commercial publications. There tend to be lots of pure maths problems or investigations, like "the growing patterns of squares", which are excellent maths activities but have no link with real life.
However, real-life problems are quite easy to make up because they tend to start with open questions like "How far? How long? How heavy? How much?" If you are planning a topic on volume and capacity, for instance, it is important to make sure you have some questions like "How much lemonade do we need for everyone to have two cups each?", so that the maths becomes meaningful.
Linking the mathematics with your main class topic will serve the same purpose (for a topic on health: "How much liquid do most people drink in a day?"). These types of problems help to emphasise the connections between the different areas.
I remember teaching maths topics without real-life problems so that, given volume and capacity again, the children would do endless filling of various containers: finding out how many cups filled a bucket, and thimbles a cup, and so on. I found that a few months later, when we returned to volume and capacity, everything seemed to have been forgotten. It was no wonder really - what sense did it all make? I noticed a significant difference in children's ability to remember, and therefore really understand concepts and knowledge, after I introduced real-life problems as well as skill-based activities.
Shirley Clarke is lecturer in assessment, guidance and effective learning at London University's Institute of Education