Teaching methods of solving mathematical problems

Problem solving is one of the main indicators of the level of mathematical development, development of educational material. Child from the first days of school meets the challenge.
If you carefully analyze the content of , you will see that it mostly consists of conceptualizing solutions to different kinds of tasks. It is thereforeschool mathematics natural that the tasks pays great attention and considerable training time.
Math problem solver is used for various training purposes: to generate motivation and interest in learning activities, students have to illustrate and clarify course material studied, students develop special skills for the development of logical thinking, to monitor and evaluate the results of their study, etc.
Unfortunately, less attention is paid to the formation of students ‘ overall approach the overall skills to solve any mathematical problems. The task itself is leaking on the basis of either mechanical trial and error followed by pinning accidentally found the correct solution or updating a system formed early operations. Private solutions to certain types of tasks, studied at the school, math problem solver may be soon forgotten, but here is a general skill, a common approach to solving any task must survive each graduate school for a long time, for life. Because this overall approach to solving any mathematical problems is, essentially, a model of a reasonable approach to solving any everyday, practical, technical and other tasks that will be ‘ routinely meet a person throughout his life. Because to live is to solve problems!
How to teach children to finding ways of solving the math problem? The issue is central in the learning problem solving. For the answer to this question in the literature suggested many practical techniques that make it easier to search for ways to solve the problem. However, the theoretical positions of relative finding solutions to tasks remain little developed.
Meanwhile, the vast majority of graduates and not master sufficiently the overall skill and met with the challenge of an unfamiliar or little familiar species, do not know how to approach it, what to start with a solution, and after several failed attempts to disclaim this, as they feel hopeless cases usually pronounce the infamous words: “we are not solved. The vast majority of students solving problems does not cause much interest, they passively belong to this process, and many of them prefer cheating from the Board or from a friend.
In many ways the character motivation depends on the Organization of the training process problem solving. Existing organization not internal contributes to a strong interest in this activity for most students.
Problem solving the work is somewhat unusual, namely mental work. And to learn any work must be familiar with the material, which will have to operate, the instruments that are used for this work.
Hence, in order to learn how to solve problems, it is necessary to understand what they are, how they are built up from component parts they are, what are the tools with which you are solving problems.
We want to ensure that students have mastered this activity, but not ‘ give them the necessary knowledge and skills to do so.
The majority of pupils and some teachers, as a result of the decision of a vast number of tasks view is emerging that there is a vast number of different techniques and ways of solving mathematical problems and understand. This diversity is very difficult.
Primarily, students should understand the following the general idea that underlies all of the methods and solutions: to accomplish a task, we must reduce it to one or more previously resolved tasks.
‘ Will be further understood by way of a set of actions to address specific tasks, and under the method — a common schema (algorithmic or heuristic), on the basis of which the constructed solutions to individual tasks.
From this point of view, all mathematical tasks should be divided into algorithmic, or standard, and heuristic, or custom. Algorithmic, or standard tasks are those for which. In mathematics there is a specific algorithm, and a way to solve the tasks consists in applying an algorithm to the conditions of the problem.
Teaching methods of the solution of these problems is well designed, and there is no need to discuss.
To the pupil could apply an algorithm to solve a specific task, it must, first, be able to articulate this algorithm of definitions, theorems, see his rule, formula, and secondly, he should be able to deploy this algorithm in a step-by-step program. This should be systematically teach students.
To address the same non-standard tasks students should themselves devise (compose) a way to deal with them.
To search and the invention of ways to solve such tasks were carried out by students for a particular plan wisely, they need to know and possess common heuristic methods for solving mathematical problems. These common methods should inform students gradually, illustrating them with a sufficient number of examples. Walk through these methods, you must come back repeatedly while meeting new challenges, where these techniques are used.