Mathematical modeling is used in solving numerous text. Already, pieced together from the equation, according to the text of a task is its algebraic (analytical) model. Drawing a shape specified in the geometric task, with marked on it data and search is also a geometric model of the task. But often the challenge helps and subject her to model (for example, a 3-d geometric shape, using model or image objects and objects that are defined in the task, etc.).
Great practical importance are methods of finding approximate values of the desired values.
All graphic techniques of calculation tasks give approximate solutions. But approximate solutions can be obtained and using numerical methods (for example, when solving quadratic equations formulas of their roots).
In geometry, approximate methods are used for the build. Examples of them serve to flatten the circle to build a square equal to this circle, divides the angle into equal parts, etc.
These are the main techniques for solving tasks at the rate of secondary school mathematics. Remains to emphasize that in practice the decision of tasks they are often combined.
One of the main aims of solving problems in school mathematics course and is to ensure the effective assimilation of each pupil the basic solution methods and techniques of teaching of mathematical problems.
General tips in solving math problems of student teachers. In order to learn how to solve problems, it is necessary to acquire experience to solve them. Rare students independently acquire this experience. It is the duty of the teacher is to help students acquire experience in solving tasks, to teach them to solve problems. However, the assistance of teachers should not be excessive. If the teacher a lot will help the learner, at a fraction of the latter remain nothing or too little work to acquire experience of problem solving. So the disciple does not learn how to solve problems. If the assistance of the teacher will be small, the apprentice well. may not learn how to solve the task.
The teacher should help the learner by Tips how to solve a problem or questions, replying to that pupil successfully solve the problem. Sometimes the teacher plays the task himself, asking questions and answering them. Students imitate him, gradually to solve tasks. But the option of learning requires more time and does not always lead to good results.
We can say that mechanical imitation teaching method not solving. Need questions and tips teacher student, causing developmental contract schoolchildren to help develop a creative approach to solving problems.
Such questions and tips should have commonality for various tasks, otherwise students learn to solve many tasks, and will learn to solve each task separately. At the same time, questions and tips should be natural and easy, must have its source of simple common sense.
They should assist the learner to a workable, but not shrill, help.
But some questions and tips teacher student learning is not sufficient to meet the challenges. We must not forget that the "math problem solving is art acquired practice".
Questions and tips student conditionally can be divided into four groups.
The unit issues, generally speaking, is not categorical. You may find that issues recommended for the first phase, will provide assistance and in the second phase, and featured for the second phase-the third and so on. in fact, stages of solving the math problem may not be strictly isolated from one another, there was a link between them, their unity is the process of solving the problem.
Formulated and further explains the questions and tips teacher student offered at every stage of solution of the problem.