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This also makes them more interesting and relevant to the children.
In actual fact, the best teaching approach is probably some combination of the two.
Most of the problems used in problem solving have more than one solution.
There is very little difference between a child using the Scientific Approach to problem solve and a mathematician using it to do research.
Hence through problem solving, children get a much better feel for what mathematics is actually about than they get in the more traditional type of teaching.
Even apparently relatively weak children may have ideas that turn out to be fruitful.
Sometimes though, it can take a little work on the your part before the consequences of some ideas are seen. It is important to point out at this stage, that though we are concentrating here on mathematical problem solving, many of the strategies and techniques that are used in mathematics are used in any type of problem.This is partly because they involve some detective work, which most people enjoy.It’s also partly because we all enjoy getting the answer after having struggled with a problem.The four stages of problem solving due to Pólya (in What is Problem Solving?) are quite general steps that can be applied to any problem whether mathematical or not! Traditionally, mathematics has been taught to individuals working by themselves. But there are other reasons for it to be part of the mathematics curriculum.The following are some reasons that are frequently suggested as to why you should include problem solving in your maths programme. Currently much credence is being given to a theory of learning called constructivism.(We say more about this in the 'Reporting Back' section of Organising the Teaching of Problem Solving.)Positive attitudes.Because the children seem to enjoy the problems, and get quite involved with them (we have seen children work through their breaks in order to settle a problem), it helps them to gain a positive attitude towards the subject.Over time, and from seeing what other children have done, you should be able to develop and extend the range of strategies that the children have at their disposal.So, starting with the members of your own class in mind, problems can be found that can give every child in the class the chance of making some progress toward a solution, either on their own or with the assistance of others in their group.