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For other uses, see Problem (disambiguation)

A problem is a situation that is hard to deal with. The word comes from a Greek word meaning an "obstacle" (something that is in your way). If someone has a problem, they have to find a way of solving the problem. The way to solve it is called a solution.

Examples[change | change source]

"John has locked his car keys inside his car so that he cannot get at them. John has a problem".

Social examples[change | change source]

We can also talk about a child with "behaviour problems". That would mean they act in ways that hurt and upset other people or themselves or cause too much disruption.

Sometimes people describe the ways in which people with learning difficulties and autism interact with their own bodies and the environment as behaviour problems because they find it disturbing, but this is controversial. These do not cause hurt and are not meant to cause upset but are seen as self-expression or self-soothing by the adult or child acting in these ways- such as rocking themselves or repeated actions like moving doors and drawers or echoing the movement in the environment, such as the movement of a flag in the wind. The argument is that it is other people's problem if self-expression or self soothing that hurts no-one is something which other people find disturbing.

"Communication problems" are when people struggle to talk in a way that helps and feels good. Communication problems come from many kinds of problems, body problems such as with the ears, learning and mental problems, being in a new country or an ethnic minority or using special science words. For example a person who is deaf has communication problems because he cannot hear the spoken words most people use, but this is different when he is in an environment where everyone can use sign-language well, or if he can speak and others allow him to lip read. Those with developmental delay or learning disability or learning differences or speaking in a second language may be said to have "communication problems". Problems in relationships in families and between friends are often called "communication problems". People who must work together but use different words, for example science words and simple words, to talk about the same things, they are also said to have communication problems.

Entertainment examples[change | change source]

Some problems are made up for fun. These are like puzzles. Some of them can be solved with logic, others can be solved by trial and error or by a heuristic.

Mathematical examples[change | change source]

Here is an example of a mathematical problem: "John is three times as old as Mary. In three years time he will be twice as old as Mary. How old are John and Mary?" The answer to this problem is that John is 9 and Mary is 3.

Children often like to give one another problems that can be solved by "lateral thinking". This means using the imagination rather than strict logic. Here is an example:

"Peter, Ruth, Samuel and Jessica live in the same house. Peter and Ruth went out. When they returned they found Jessica lying dead, surrounded by glass. They were sure Samuel had done it. Why did they not call the police?" The answer is: Samuel was the cat and Jessica was a goldfish.

A well-known example of a problem that cannot be solved is that of squaring the circle – how to get a square that has the same area as a given circle, using geometry.

Sources on problem solving[change | change source]

These are classic works on problem-solving:

  • Duncker, Karl 1945. On problem solving. APA Psychological Monographs 58.
  • Gordon, William J.J. 1961. Synectics: the development of creative capacity. New York: Harper.
  • Polya, George 1945. How to solve it: a new aspect of mathematical method. Princeton University Press.
  • Wertheimer, Max 1959. Productive thinking. New York: Harper. New and expanded edition (first edition was 1945.
  • Simon, Herbert A. & Newell, Alan 1972. Human problem solving. Englewood Cliffs, NJ: Prentice Hall.

Most of these deal with well-formulated problems. There are also a number of books on the psychology of thinking, which is obviously a large part of problem-solving:

  • Bolton, Neil 1972. The psychology of thinking. London: Methuen. ISBN 0-416-70450-6
  • Wason P.C. & Johnson-Laird P.N. 1972. Psychology of reasoning: structure & content. London: Batsford. ISBN 0-7134-0347-0
  • Novick L.R. & Bassok M. 2005. Problem solving. In K.J. Holyoak & R.G. Morrison (eds) Cambridge handbook of thinking and reasoning. Chapter 14, pp. 321-349. Cambridge University Press.

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