# Problem Solving Strategy

When this happens the students will be able to make the problem more simple by dividing it into smaller and easiest steps, such as rewording the problem using smaller numbers.

These strategies are really useful in helping to solve maths problems.

This is because I know how." 35 years later I still have that table, although it now plays a different role in our household.

There is nothing specific to mathematics in George Polya's four stages of problem solving: To these I can add considering special cases as a stepping stone in understanding the problem; seeking an analogous or related problem; splitting the problem into smaller ones (which may be also regarded as moving to Polya's second stage.) Generalization is the opposite of specialization and is often throws revealing light on the problem's true nature. However, details of implementation are, of necessity, field specific.

I found a detailed classification in an article by Murray Klamkin, cited below.

I added a few, and for some have not yet come across suitable examples. I would very much appreciate comments and additional examples. The most common way to approach a problem is by identifying a general class to which the problem belongs and using a method (if such exists) that is applicable to the problems of that class."...small solved and unsolved problems lead to larger solved and unsolved problems which in turn lead to important mathematical results." Murray S.Klamkin "Each problem that I solved became a rule which served afterwards to solve other problems." Descartes Solving problems is an activity not unique to mathematics. Check the working out and make sure that your solution is actually answering the question.When students use this strategy, they will make a reasonable guess, based on the information that they have been given and then check to see if their guess is correct The guesses should get closer and closer to the answer, until the correct answer is found.I found one new plain table of suitable dimensions in a carpenter shop for a price that in my estimate would not even cover the cost of materials.To my pointing that out the owner replied, "That's OK.There are strategies of problem solving that are applicable to solving problems in any human endeavor.But every field and every situation call for specific knowledge and specific habits of mind to apply to solving problems.Students just need to work out what the events were that occurred previously.Sometimes the problem is too difficult to solve in one step.

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