## Stages of solving math problems

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- Published: Thursday, 31 March 2016 10:25

What are the stages of the process of solving a problem?

Upon receiving the task, the first thing to do is to understand what the problem is, what are the statements, what are its requirements, i.e., you have to analyse the problem, as said in the first chapter. This analysis constitutes the first step in the process of solving the problem.

This analysis must be somehow arranged, recorded. For this purpose, all sorts of schematic notations are used. Their construction is the second step in the process of solving the problem.

An analysis of the problem and the construction of its schematic notation are needed mainly to find a way of solving the problem. This search for the method of solving constitutes the third phase of the process of solving the problem.

When the method of solving the problem is determined, it needs to be implemented. This will be the fourth stage of the process of problem solution: the solution implementation (presentation) phase.

After the solution is implemented and presented (in a written or oral form), you must make sure that the solution is correct, that it satisfies all the requirements of the task. To this end, a solution check is carried out, which is the fifth stage of the process of solving the problem.

In solving many problems, besides this check, you must make a study of the problem, namely to establish conditions under which the problem has a solution and, moreover, how many different solutions does it have in each particular case; the conditions under which the problem has no solution, etc. All this is the sixth step in the process of solving the problem.

Upon making sure that the solution is correct and upon performing the study of the problem, if necessary, you need to clearly formulate an answer to the problem - it is the seventh stage of the solution process.

Finally, for training and educational purposes, an analysis of the solution can be performed, in particular, you can determine whether there is another, more rational solution, whether it is possible to generalize the problem, what conclusions can be drawn from this solution etc. All this is the last, certainly optional eighth stage of the process of solving a problem.

The structure of the process of solving a problem depends on the nature of the problem and, of course, on the knowledge and skills possessed by the person who is solving the problem.

The proposed plan of the process of solving a problem is just an example. In actual solving these stages aren’t generally separated from each other: they are intertwined. For example, during the analysis of the problem, the search for solutions is also usually conducted. Moreover, the solution plan is determined not before implementing the solution, but in the process. Then the search for a solution is limited only to finding the idea of a solution. The order of stages may also vary.

Of these eight stages, five are indispensable, and they are present (in one form or another) when you solve math assignment. They are the stages of problem analysis, search for the method of solving, the solution implementation, solution check and response formulation. The remaining three phases (schematic notation, problem analysis and the final analysis of the solution) are optional.