Problem-solving

The child's attempts to solve a problem require him/her to call on many skills. Problems in mathematics have often been seen as textbook examples at the end of a section on a particular topic. Problems in life are rarely that simple, and there is often more than one way to find a solution.

Problem-solving experiences should develop the ability to plan, take risks, learn from trial and error, check and evaluate solutions and think logically. Discussion and acceptance of the points of view of others are central to the development of problem-solving strategies.

Problems can be classified in many ways. They can be presented concretely, diagrammatically or in written form. They can be open or closed. They can relate to one particular content area or include elements from more than one strand.

A written problem may be difficult to solve because of readability or because it has multiple steps to the solution procedure. Large and awkward numbers often frighten a child away from attempting a problem, and if the information is not presented in the order in which it is to be used some children just give up without trying. If children are taught to analyse the problem carefully and extract the relevant information they can often find that it is much easier to solve than it appeared at first.
Children need to develop problem-solving skills in general and to be confident in
their own ability to attempt a solution.

• children should be taught a variety of strategies and to experiment with applying the same strategy to different problems and different strategies to the same problem. These strategies will vary according to the age of the child
• the teacher will need to structure the problems given to the children so that they experience success
• re-reading of a problem by the child should be encouraged
• co-operative group work and class discussion of the results of a problemsolving exercise encourage the children to respect the ideas of others, to try different approaches themselves, to offer alternative solutions and try them out on the blackboard - giving the children problems with irrelevant information or with no solution possible because of missing information encourages them to analyse what it is they are being asked to do; for example, Jim has red hair. His sister gave him 50p. He bought a bar for 20p and a bag of crisps for 30p. Do you think Jim's sister was a kind girl? Although the numbers appear to add up, the child was not asked to operate on them. This type of exercise can be done orally and encourages a more critical approach to a problem
• children can invent problems for others to solve, and discuss the
  results.

Problem-solving strategies

Problem-solving strategies must be varied and the children given ample opportunity to try them out concretely, orally or in a written task. Many children fail at mathematics because their mathematical vocabulary is insufficient to cope with the terminology of problems. Development of the necessary vocabulary in a consistent manner throughout the classes must be stressed. Some strategies that can be taught to children are:

• constructing a model
• drawing a diagram to illustrate a problem
• making a chart or table of the information
• looking for patterns in a problem
• making a guess and testing it out
• breaking the problem down and solving each part
• writing a number sentence for the problem
• using appropriate equipment to solve the problem, for example balance, measuring instrument, calculator, blocks
• solving a simpler version of the problem, for example using smaller numbers.