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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.
Guess and improve is slightly more sophisticated than guess and check.
The idea is that you use your first incorrect guess to make an improved next guess. In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. Children themselves take the role of things in the problem.
The on-looking children may be more interested in acting it out because other children are involved.
Sometimes, though, the children acting out the problem may get less out of the exercise than the children watching.
However, sometimes when children are completely stuck, guessing and checking will provide a useful way to start and explore a problem.
Hopefully that exploration will lead to a more efficient strategy and then to a solution.
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.
We have found that this kind of poster provides good revision for children. Through these links, children can see that mathematics is not only connected by skills but also by processes.
We now look at each of the following strategies and discuss them in some depth. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check.