The task is ... Mathematics: tasks. Answer task

Since at present in most countries of the world there is a reform of mathematical education, the problem of setting tasks in the school course of mathematics has become the main and very important in the development of teaching. The ability to solve problems is the most vivid characteristic of the state of education. How today does the student and teacher understand this goal in the school course of mathematics?

Teaching students

Practically all the pupils of the school think that when the correct solution is found, and the received answer of the task coincides with what is offered in the textbook, their work is over, we can forget about the problem.

A student or teacher does not take into account the fact that the role of each task is reduced to developing orientation skills in problem situations, to increase knowledge, experience. If you do not pay attention to the actualization of the acquired knowledge, the process of mathematical thinking is violated, which contributes to a decrease in the development of skills.

But before you deal with this issue, you need to find out what the task is and what its role in training is.

What is the task?

This term has several interpretations. Let us consider one of them, applied to mathematics. Here The task is A problematic situation (a question) that requires solution through the use of certain skills, knowledge, reflections. This is the goal that lies within the framework of the problem situation, what needs to be achieved, and the condition and requirement.

Thus, to solve the problem - this means to transform this problematic situation or to reveal that such a reconstruction in these conditions is impossible. Here it is important to define the process of solving the problem as a mental activity aimed at achieving the goal.

Task Format

In each mathematical problem, it is customary to identify the components of the situation, the rules of transformation, the desired goal or output. The solution itself can be set in different ways:

A) as the formation of relations between the components of the situation (for example, when it is necessary to find out which of the items is heavier);

B) as the final state of the situation (for example, collecting a puzzle);

C) how to obtain new knowledge (for example, the solution of an example).

The role of the task in training

Since the task is a problem situation, which requires a solution, its role in teaching a person is very important. So, with its help the theoretical question is illustrated - it is studied, its contents are explained. Through simple exercises that are performed according to the pattern that the theory gives, the assimilation of the studied fact is achieved. The task and the solution of it form in the students the ability to navigate in new situations, collect information for the performance of other tasks or study new sections of science, as well as knowledge of reality.

Learning Objectives with Tasks

The task is a tool used in teaching, designed to motivate and motivate students, to form a concept of a mathematical model in them . Correctly put, she reveals the modern teaching methodology, because her decision serves many purposes of learning. For example, tasks (grade 7) can be used to study a new topic or to control (self-control) knowledge, develop interest in mathematics. The main thing is that they serve to familiarize the student with search and creative activity, development of his thinking and logic.

Task and solution

The solution occurs in four stages:

1. Understanding the conditions of the task, as well as its individual components.
2. Building a solution plan.
3. Implementation of the plan in practice and all its details.
4. Final check of the decision, revision for the purpose of mastering the material, revealing what may be useful in the future when mastering other tasks.

To get the right solution, it is necessary to clearly represent the entire situation proposed in the problem. It is necessary to find out what is given, what to find. It is recommended to sketch a visual drawing, this will help to identify possible solutions. The mathematics of the problem is posed by those that are solved by logical thinking, the scheme allows you to visually see the right direction.

Hint system

In order to optimally activate the thinking activity of students, it is recommended to use a didactic method called the "Hint system". This technique consists of secondary tasks or questions that give the right direction to the thought stream, making the solution search orderly. The solution of tasks requires the presence of combinational abilities, that is, the ability to make the right choice in conditions of oversaturation of knowledge. This search and selection should be purposeful. The choice will be much faster and easier, if you turn to a suitable analogy. For example, you can ask the question: "Where did something similar happen before?" Using the analogy method for solving tasks, it is recommended to change their wording. Apply this technique best at the initial stage of solving problems. If it is here that we can compare this task with those that were solved earlier, then the similarity of the conditions and methods of solution directs the students to the right path, develops the appearance of fruitful ideas in drawing up a solution plan.

Methods for solving mathematical problems

Since the problem is a question (situation), which requires a solution, then to find the right answer to the mathematical problem means to reveal the sequence of the positions of mathematics that are used to derive the correct result. To date, there are several methods for solving mathematical problems:

1. Arithmetic. The answer lies at the expense of performing mathematical operations on the numbers that are given in the task. So, one and the same problem can often be solved using different arithmetic methods, which differ from each other by the logic of reasoning.
2. Algebraic. The answer lies in the composition and solution of the equation. First, they separate the quantities and establish a connection between them, then they enter the variables, denoting them with letters, making up the equation with their help and solving it. After that, check the solution and write down the answer.
3. Combined. This method includes both an arithmetic and an algebraic method for solving problems.

Summarizing

A mathematical problem is a problematic situation, which is solved by using mathematical techniques that require certain skills and knowledge. Tasks are divided into simple and composite, depending on the number of actions. When the solution of the task involves the use of only one action, it is a simple task. In the case of using more than two actions, it will be a matter of compound tasks. But both of them can be solved in several ways.

Solving one task in different ways is very useful, since in this case different mental operations begin to work, for example, analysis, generalization, comparison, and others. This, in turn, positively affects the development of mathematical thinking in students. To correctly solve the task, it is necessary to analyze and synthesize the problem situation, reformulate the problem, find an inductive method for solving it, using analogies and forecasting. Always remember that any task is solvable, you only need to find the right way, using the knowledge, skills and skills that come in the learning process.