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.
This proposes that we construct our knowledge through our experience rather than absorbing what we are told.
It’s also partly because we all enjoy getting the answer after having struggled with a problem.
And it’s partly because children enjoy having "ownership" of the problem. By working on a problem, children become involved with it and can get quite deeply involved with the mathematics that is both required to solve it, and that may be required to solve it. In the process of struggling with a problem, children can often obtain a fairly deep understanding of the mathematics surrounding the problem.
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.
Hence all children can develop from their current knowledge. Problem solving seems to employ problems that are implicitly interesting to children.Many teachers personalise word problems to include characters that the children in the class know.This also makes them more interesting and relevant to the children.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.Some of them have even expressed the opinion that what they were doing was not mathematics and have asked to do more problem solving instead of mathematics!Hopefully, every child in your class can find one approach that they can use to solve the problems that you present.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.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.Hopefully they begin to see that the subject is a live one, get some feeling for the way it is created, and see why certain things are done in certain ways.This understanding is often enhanced, when, in a whole class setting, teachers draw together the various threads from all of the children in the class.(We say more about this in the 'Reporting Back' section of Organising the Teaching of Problem Solving.)Positive attitudes.