Because now in most countries going reform of mathematics education, the problem of setting goals in school mathematics has become a major and very important in the development of teaching.The ability to solve problems in favor of the brightest feature of the state of education.As a student and teacher today realize this goal in school mathematics?
Education students
Almost all the students of the school think that when we find the right solution, and the answer is the same problem that is proposed in the book, their work is done, you can forget about the problem.
student or the teacher does not take into account the fact that the role of each task is to ensure, to develop skills in orientation in problem situations, to increase knowledge and experience.If you do not pay attention to the updating of the knowledge gained, it disrupted the process of mathematical thinking, helping to reduce development skills.
But before we deal with this issue, you must figure out what is the problem and what is its role in training.
What is the problem
This term has several interpretations.Consider one of them, applied mathematics.There task - it problem situation (question) that needs to be addressed through the use of certain skills, knowledge and reflection.It is a goal that is within the scope of the problem situation that need to be achieved, as well as the conditions and requirements.
Thus, to solve the problem - it means to transform this problematic situation or to identify that such a reconstruction in these conditions is impossible.It is important to define the process of solving the problem as a mental activity aimed at achieving the goal.
format problem
In every mathematical problem decided to allocate part of the situation, the rules of the transformation required purpose or output.The decision itself can be defined in different ways:
a) the formation of relations between both components of the situation (for example, when you need to figure out which one is heavier objects);
b) as the final state of the situation (for example, the collection of puzzles);
c) as the acquisition of new knowledge (for example, a solution of example).
role in training tasks
Since the problem - a problem situation that requires a solution, its role in human learning is very important.So, with the help of her illustrated by a theoretical question - studied, explaining its content.Through simple exercises that are performed on a template that gives theory achieved the assimilation of the facts.The problem and the solution it forms the students' ability to navigate in new situations, to collect information to perform certain tasks or to explore new fields of science and knowledge of reality.
learning objectives using the task
task - is a tool used in training designed to interest and motivate students to form their notion of a mathematical model.Properly delivered, it reveals a modern teaching methods, as its solution serves many purposes of learning.For example, the problem (Grade 7) may be used in the study of a new topic or control (self) knowledge development of interest in mathematics.The main thing they serve to familiarize the student with the search and creative activities, the development of his thinking and logic.
challenges and solutions
decision takes place in four stages:
- Understanding setting the conditions, as well as its individual components.
- Building Plan solution.
- Implementation in practice the plan and all its parts.
- ultimate test solutions, review with the aim of mastering the material, revealing what may be useful in the future for the development of other tasks.
To get the right decision, you need to clearly present the whole situation, as proposed in the task.We need to find that given that you need to find.It is recommended to outline a clear blueprint, it will help to identify possible solutions.Mathematics puts such tasks to be solved by logical thinking scheme allows you to visually see the right direction.
system prompts
to optimally activate the mental activity of students, it is recommended to use the didactic technique called "system prompts".This technique consists of minor tasks or questions that give the correct direction of flow of the thinking, making the search for solutions ordered.The solution of tasks requires the combination of abilities, that is, the ability to make the right choice in terms of knowledge of oversaturation.This search and selection should be focused.The choice will be much faster and easier, if we turn to a suitable analogy.For example, you can ask a question: "Where previously encountered something similar?" Using the method of analogy when solving problems, it is recommended to change their wording.Apply this technique is best in the early stages of solving problems.If it is possible to compare this task to those addressed above, the similarity of conditions and methods for solving guides students on the right track, developing the appearance of fruitful ideas when planning solutions.
methods for solving mathematical problems
Since the problem - it is a question (the situation), which requires a solution, then find the correct answer to a mathematical problem - means to identify the sequence of the provisions of mathematics, which are used to derive the correct result.To date, there are several methods for solving mathematical problems:
- arithmetic.The answer is due to perform mathematical operations on numbers that are in the job.So, the same problem can often be solved using different arithmetic methods, which differ in the logic of the argument.
- Algebraic.The answer is at the expense of setting up and solving the equation.Please allocate quantities and establish a connection between them, then the variables are introduced, indicating their letters up with them the equation and solve it.Then make test solutions and record the answer.
- combined.This process includes the arithmetic and algebraic method for solving problems.
Summary
mathematical problem - a problem situation, which is solved by using mathematical techniques that require specific skills and knowledge.The tasks are divided into simple and complex depending on the number of steps.When the decision involves the job application only one action, it is about a simple task.In the case of a two-step we will focus on constituent problems.But those and others can be solved in several ways.
solution of a task in different ways is very useful, because in this case begin their work various mental operations, such as eg analysis, synthesis, comparison, and others.This, in turn, has a positive effect on the development of mathematical thinking in students.To properly solve the task, it is necessary to conduct the analysis and synthesis of the problem situation, a reformulation of the problem, find the inductive method to solve it by using analogy and forecasting.You should always keep in mind that any problem is solved, you only need to find the right way, using the knowledge and skills that come in the learning process.
