Mathematical problem
From Wikipedia, the free encyclopedia
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 games.
Mathematical problems are used on all levels of mathematics education 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, solving the simple problem "Adam has five apples and gives John three. How many has he left?" may prove more difficult for some beginning students than calculating 5 - 3.
[edit] Formal definition
Formally, a mathematical problem is a tuplet (S, C( ), r) where S is a set of objects, C(s) is a condition (or conditions) such that for every s∈S, C(s) is either true or false (in other words, that C(s) is well formed). The solution to the problem is a series of steps that lead to finding r∈S that satisfies C(r).
