But no single strategy works every time.effective problem solving skills. He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1 This is all well and good, but how do you actually do these steps?!?! We will articulate some useful problem solving strategies, but no such list will ever be complete.
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.
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.
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.For example: This strategy can be stretched when combined with other strategies such as looking for patterns or drawing a picture.By combining this strategy with others, students can analyze the data that is given to find more complex relationships.You will see that each strategy we have in our list is really only a summary of two or more others.1 Guess This stands for two strategies, guess and check and guess and improve. This is a strategy that would certainly work on the Farmyard problem but it could take a lot of time and a lot of computation.Because it is such a simple strategy to use, you may have difficulty weaning some children away from guess and check.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.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.It encourages students to organize information in a logical way and to look critically at the data to find patterns and develop a solution.Introduce a problem to students that will require them to make a table to solve the problem.