*Third, in looking back and thinking a little more about the problem, children are often able to see another way of solving the problem.This new solution may be a nicer solution than the original and may give more insight into what is really going on.So a problem about three pigs may be changed into one which has any number of pigs. The answer to this problem will contain the answer to the previous three questions.*

*Third, in looking back and thinking a little more about the problem, children are often able to see another way of solving the problem.This new solution may be a nicer solution than the original and may give more insight into what is really going on.So a problem about three pigs may be changed into one which has any number of pigs. The answer to this problem will contain the answer to the previous three questions.*

These include the basic arithmetical processes and the algorithms that go with them.

They include algebra in all its levels as well as sophisticated areas such as the calculus.

On the other hand, we use "answer" to mean a number, quantity or some other entity that the problem is asking for. It is frequently the case that children move backwards and forwards between and across the steps.

Finally, a "solution" is the whole process of solving a problem, including the method of obtaining an answer and the answer itself.method answer = solution But how do we do Problem Solving? Pólya enunciated these in 1945 but all of them were known and used well before then. The Ancient Greek mathematicians like Euclid and Pythagoras certainly knew how it was done. In fact the diagram below is much more like what happens in practice There is no chance of being able to solve a problem unless you are can first understand it.

This is the side of mathematics that enables us to use the skills in a wide variety of situations.

Before we get too far into the discussion of Problem Solving, it is worth pointing out that we find it useful to distinguish between the three words "method", "answer" and "solution".If we have some sort of formula, or expression, for any height, then we can substitute into that formula to get the answer for height three, for instance.So the "any" height formula is a generalisation of the height three case. Then we get34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1We certainly got to 1 then. Well we can extend this problem, make another problem that’s a bit like it, by just changing the 3 to 5.With younger children it is worth repeating the problem and then asking them to put the question in their own words.Older children might use a highlighter pen to mark and emphasise the most useful parts of the problem.It will almost always be necessary to read a problem several times, both at the start and during working on it.During the solution process, children may find that they have to look back at the original question from time to time to make sure that they are on the right track.This is the side of the subject that is largely represented in the Strands of Number, Algebra, Statistics, Geometry and Measurement.On the other hand, the processes of mathematics are the ways of using the skills creatively in new situations. As such it is to be found in the Strand of Mathematical Processes along with Logic and Reasoning, and Communication.Pólya’s four stages of problem solving are listed below.1. This process requires not only knowing what you have to find but also the key pieces of information that somehow need to be put together to obtain the answer.Children (and adults too for that matter) will often not be able to absorb all the important information of a problem in one go.

## Comments Problem Solving Def

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