# 1. Helping pupils think

‘Thinking about thinking’, or meta-cognition, is a powerful means for helping pupils understand and recognise the ‘deep’ features of particular kinds of problems, and how to solve such problems.

The first step towards such thinking is to give pupils the opportunity to talk about the problems they are trying to solve and how they are trying to solve them. When pupils are explaining their thinking, it is important to listen and not dismiss any ideas.

There are many different ways of solving mathematical problems (see Resource 1). You may be surprised at how many other ways pupils find, other than the way you may have expected them to use.

## Case Study 1: Listening to pupils’ voices in mathematics

Nomonde in South Africa reminded her pupils that, when they go home from school, there isn’t only one way to get home: there are many possible ways. Some are shorter, some longer, some safer, some more interesting. She told them it was the same with mathematics problems – there is often more than one way to get to the right answer, and looking at the different ways might be interesting.

Nomonde put the following questions on the board.

1. Sipho has 24 stones. He gives 9 stones to a friend. How many stones does he have left?
2. Thembeka eats 7 sweets every day. She has 42 sweets. For how many days does she have sweets?
3. The teacher buys 25 packets of crayons. There are 12 crayons in each pack. How many crayons does she have?

Next she asked the pupils to answer the questions using any method they liked. She gave her pupils ten minutes to answer the questions. She checked their answers and then asked one or two to explain how they worked out each question.

Nomonde listed these methods to find the answers and made a note of which methods were most popular. She reminded her pupils about the different routes to school.

## Activity 1: Helping pupils think

Try this activity yourself first, preferably with two or more colleagues. Then try it with your pupils.

Split the class into groups of four or five and ask them to take turns to explain carefully to each other how they worked out their answers.

Next, ask the groups to make a list of the strategies used, then ask these questions:

• Did you all have the same answer?
• Did you all work it out in the same way?

How many different ways can your group find to work out a correct answer for each question?

List these on the board.

Explain how important it is to your pupils to try different ways to solve problems to help their mathematical thinking.

Section 3: Ways to solve number problems

2. Identifying different types of problem