Mathematical problem
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A mathematical problem is a problem that can be solved with the help of mathematics.
The field of mathematical problems is closely related to the more light-hearted topic of mathematical puzzles.
Mathematical problems are used on all levels of mathematics eduction to teach students to connect between real world situations and the abstract language of mathematics, that is, to think logically.
Solving a mathematical problem involves three basic steps that is common to all types:
- Comprehend what the problem is asking.
- Abstract the problem, find a mathematical expression that represents the problem, and solve it.
- Understand what the solution means and implicates.
Usually mathematical problems are harder to solve than regular mathematical exercises even if the student has knowledge of the mathematics involved in solving the problem. For example, many lower grade students has no problem calculating 5 - 3, but when faced with the simple problem "Adam has five apples and gives John three. How many has he left?" they wouldn't know how to solve it, partially because of the stringent language employed in mathematical problems and partially because the student has difficulties visualizing the problem. Even harder are problems in which the student has to decide whether a given text contains enough information to solve the problem or not. Many students does not even consider the possibility that the problem might be a "trick". This problem for example, would leave many lower grade students confused:
- "A shepherd has 125 sheep and 5 dogs. How old is the shepherd?"
It is very likely that they would try to calculate an answer, even if the result would seem unlikely.