In this way one can explore a problem. It provides a way of finding the most elegant solution. By exploring a problem, one comes to understand the problem and the concepts and tools used to solve the problem. Each step of a problem requires a verbal statement of the reason for the step. The more challenging a problem is, the greater is the need for the verbal statement.
Verbal statements form probes to locate information in one's knowledge space.
Mathematically, the solution consists of an organized, self-driven approach to solving simultaneous equations. Typical word problems consist of several conditions which must be satisfied simultaneously. For this reason problems in all subjects across the curriculum are solved in the same way. The words change, the symbols change, the ideas change but the problem solving process remains the same. The diagrams above illustrate an essential feature of a problem solution.