Drawn into the subject
The National Numeracy Strategy recognises the importance of solving number problems from the earliest years. Children need opportunities to use and apply their in-creasing mathematical knowledge and skills in meaningful situations throughout the key stage. Successful problem-solvers, it seems, have not only mathematical skills, but also a range of strategies that they can apply consistently. Children who are good at problem-solving always make sure they have understood the problem, they organise and apply their knowledge, and then check that their answers make sense.
These strategies can be taught, informally, alongside maths skills and knowledge, beginning in reception. The importance of talking about maths cannot be over-emphasised. Familiar songs and rhymes used to develop counting skills can be turned into simple problem-solving situations. Take the well-known rhyme "Five currant buns in a baker's shop". Have five children at the front of the class to be the "buns" and call out different children to come to the shop and buy a bun. Asking the children to predict how many buns will be left each time encourages them to "have a go" in a non-threatening situation - and they can easily check if they were right by counting. Encourage the children to think about the situation mathematically by saying something like: "Yes, you are right, four take away one leaves three."
Similar informal situations can be developed and continued in Year 1 using favourite story books, television programmes or CD-Rom. The Channel 4 maths programme, The Number Crew, creates problem situations for its characters, then puts the viewers in the role of the expert. The presenter asks: "How can Bradley solve the problem? What would you do?" This approach encourages children to use whatever skills and knowledge they have to solve new problems and gain confidence in their ability as problem-solvers. Use everyday opportunities in the classroom to create problems which the whole class can talk about and decide how to solve. Link the talk to mathematical symbols by asking the children to make appropriate number sentences using number and symbol cards. The cards can be large enough for a few children to hold up at the front of the class, or the size of playing cards which can be used on the table.
Many teachers find that children who seem confident answering questions orally, and who can use number facts and mental strategies with ease when discussing problems, are often unsure when presented with written problems. For example, a child who knows three and two make five can still find the following written questions difficult: 3 + ? = 5 ? + 2 = 5 By the end of the key stage all children are expected to be able to tackle a wide range of written problems. Teachers are concerned that some children don't perform as well with these as they do when working orally.
One way to help these children is to link their developig reading and writing skills with problem-solving situations. Writing stories to illustrate number sentences is very effective. Early in their first term in Year 2, some children at Smawthorne Lane Infant School in Castleford had been looking at the operations of addition and subtraction. Their teacher then asked them to write and illustrate a story problem using one of the operations.Their work was put up on display.
Billy's writing and illustration, for example, concerned adding up cats: four cats in a basket. Seven more came. There were 11 cats.
And Jessica: 10 cats on a wall and five went away. How many are left? Five cats are left.
Darren illustrated addition with: 80 cats on a wall and 80 more come. How many altogether? 160.
Ryan thought about conkers: 50 conkers by a tree. 50 dropped off. How many altogether? 100 conkers by the tree.
The children enjoyed the experience. They were keen to read out their stories. Hopefully, when presented with similar written questions in end of key stage tests, they will know which operation to use.
Write a selection of problems on the board. Include some two-stage problems and some involving measures and money. Tell the children you want them to work on the problems individually for a few minutes and do as many as they can. Afterwards, you will want them to talk about the problems and explain how they solved them. Some children may need help. When most have done as many as they can, start the discussion, going through the questions one by one, concentrating on those which the children found most difficult.
Understanding the problem * Emphasise the importance of reading the problem correctly;
* ask the whole class to read out the question aloud;
* encourage individuals, particularly the poorer readers, to have a go;
* help the children to recognise mathematical words;
* present similar problems in different formats.
Deciding which operation to use * Talk about how the children know which operation to use;
* discuss the effect of using inverse operations;
* ask the children to estimate to get a rough idea of the answer;
* demonstrate using practical apparatus if appropriate.
Calculation * Ask different children to explain their method;
* collect answers from several children before saying which is correct;
* discuss different methods and ask the children to decide which are more efficient.
Checking the answer Tell the children to:
* re-read the question;
* ask themselves: "Have I answered this problem?";
* check their work by doing the calculation another way, or using an inverse operation.
Encourage a positive attitude towards solving problems. Have a corner of the classroom where children can find interesting puzzles to explore and talk about when they have time. And have some maths problems which pupils can take home to share with parents.
Marjorie Gorman is a primary and advisory teacher, and co-author with Alan Wigley of'Success in Mental Arithmetic' (Ginn)