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If you are not careful, they may try to use it all the time.As problems get more difficult, other strategies become more important and more effective.On the other hand, it can also be cumbersome when used by groups, especially if a largish number of students is involved.
Strategies are things that Pólya would have us choose in his second stage of problem solving and use in his third stage (What is Problem Solving? So they are some sort of general ideas that might work for a number of problems. As speaking in riddles isn’t likely to be of much assistance to you, let’s get down to some examples.
To Pólya they were things to try that he couldn’t guarantee would solve the problem but, of course, he sincerely hoped they would.
But all children should be encouraged to use this strategy at some point because it helps children ‘see’ the problem and it can develop into quite a sophisticated strategy later.
It’s hard to know where Drawing a Picture ends and Drawing a Diagram begins.
This is because the participants are so engrossed in the mechanics of what they are doing that they don’t see through to the underlying mathematics.
However, because these children are concentrating on what they are doing, they may in fact get more out of it and remember it longer than the others, so there are pros and cons here. Generally speaking, any object that can be used in some way to represent the situation the children are trying to solve, is equipment.
In some problems though, where there are more variables, it may not be clear at first which way to change the guessing.2 Act It Out We put two strategies together here because they are closely related. In the Farmyard problem, the children might take the role of the animals though it is unlikely that you would have 87 children in your class!
But if there are not enough children you might be able to press gang the odd teddy or two. It is an effective strategy for demonstration purposes in front of the whole class.
In this site we have linked the problem solving lessons to the following groupings of problem solving strategies.
As the site develops we may add some more but we have tried to keep things simple for now.