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UDC 374.45
Salomova D.H.
The teacher of the academic lyceum
TashPMI
EMERGING METHODS OF TEACHING MATHEMATICS
Annotation: This article discusses the methodological systems of teaching mathematics
Key words: education, method, visual method, cognition
Саломова Д.Х.
Преподаватель академического лицея
ТашПМИ
ЗАНИМАТЕЛЬНЫЕ МЕТОДЫ ПРЕПОДАВАНИЯ МАТЕМАТИКИ
Аннотация: В данном статье рассматривается методические системы обучения математике
Ключевые слова: Образования, метод, наглядней метод, познание
Operating with "ideal" objects, reflecting the properties of mathematical techniques and the laws of the material world, combined with abstraction from the inessential properties of the objects in question, mathematics in its concepts and statements expresses the most profound and general properties of reality.
The process of cognition and the process of teaching students expresses the independent discovery of mathematical facts of truths; therefore, the scientific methods of mathematical research simultaneously serve as the methods of students' educational work.
The problem of teaching methods is expressed in the question "how to teach?", For which it is necessary: 1) to find out why it is being studied, what knowledge and skills pupils should acquire as a result of studying; 2) to conduct a logical-didactic analysis of what is being studied (the structure and features of the content of instruction; the presentation in a school textbook); 3) to know the object of training (the level of mental activity of students, the amount of knowledge and skills necessary for training in this content).
There are traditional and modern teaching methods. Traditional methods are aimed at teaching ready-made knowledge and learning activities of students is of a reproductive nature, and is not conducive to effective development. Externally, the traditional method manifests itself in a well-known form, when the teacher presents the educational material with the use of various means of visualization, and the students perceive the educational information, memorize and reproduce it at the request of the teacher. The student's learning activit y is reproductive, and the main result of the training is the assimilation of a sum of facts. The developing effect is very low, because no active student activity.
Modern methods that are not contrasted with traditional ones are focused on learning activities for the independent acquisition of new knowledge, on learning cognitive activity, including the following components: 1) general logical methods
of thinking (induction, deduction, analysis, synthesis, analogy, synthesis, abstraction, specification, classification); 2) special techniques of mental activity that form the basis of mathematical methods of knowledge (a method for constructing mathematical models of processes; methods of abstraction inherent in mathematics; an axiomatic method); 3) knowledge system.
The assimilation of mathematical knowledge and the level of mathematical development of students is always checked through the ability to solve problems. Training methods focused on the development of active cognitive activity of students require teaching them to look for and describe general methods (algorithms) for solving classes of problems of the same type by analyzing and summarizing ways to solve private problems belonging to these classes.
Training methods allocated by the source of knowledge:
Verbal teaching methods: story, conversation, lecture, which are held for the entire class.
Signs of the story:
• involves oral narrative presentation of educational material;
• used in the presentation of educational material familiarization;
• not interrupted by questions for students;
• allows you to communicate the maximum knowledge with minimal time;
• involves the use of such methods as presentation of information, activation of attention, acceleration of memorization; logical methods of comparison, comparison, allocation of implicit, summarizing;
• characterized by a lack of independent knowledge of students, limited elements of search activities;
• complicates feedback (the teacher does not receive sufficient information about the quality of learning, can not take into account the individual characteristics of all students).
Types of the story: story-introduction, story-presentation, story-conclusion.
Efficiency is achieved by having a well thought out plan, choosing the most rational sequence of disclosing the topic, successfully selecting examples and illustrations, maintaining the proper emotional tone of presentation.
The effectiveness of the conversation depends on the selected questions that govern the conversation. When the material is divided into semantic parts, the process of asking questions that help students move from one part to another is simplified; an example is the analysis and solution of a textual problem.
Visual teaching methods:
a) the method of illustrations - involves the display to students of various illustrative aids (maps, drawings, diagrams, paintings, photographs, graphics, tables, models);
b) the method of demonstrations - involves the demonstration of dynamic manuals, natural objects, movies, filmstrips, videos, slides, various instruments and equipment in action.
In particular, the "Shatalov reference signals" can be referred to the method of illustrations.
Efficiency is achieved when: 1) a good overview of visual aids; 2) setting a learning goal, a clear allocation of the main when demonstrating benefits; 3) skillful combination of the word and showing the means of visibility, the implementation of the orientation of students' actions towards the achievement of the educational goal with the help of means of visibility; 4) attracting students to find the desired information.
Practical training methods:
in mathematics they are connected with constructions, measurements, calculations, production of visual aids, execution of drawings of figures that most fully meet the condition of the problem; written exercises (training and commented), laboratory and practical work, work on a computer on training programs; group work.
Methods of learning, determined by the level of cognitive activity of students.
These include:
1) reproductive: teaching methods, which are based on verbal, visual and practical methods;
2) problem search method of learning: problem statement of educational material, heuristic conversation, research method.
3) methods of independent work:
a) work with textbooks and other literature;
b) independent written work (held for almost every lesson for 7-15 minutes; the first - on the topic - of educational and corrective nature, allowing to establish operational feedback; only good marks are given in the journal, and satisfactory marks - on request; subsequent ones - the controlling character with all grades in the journal);
c) independent problem solving;
d) independent work with devices;
e) independent observation;
e) independent performance of arbitrary tasks.
Methods of scientific knowledge in teaching mathematics.
These include:
1) logical methods of knowledge: induction, deduction, analysis, synthesis, comparison, analogy, generalization, specification, modeling, classification, proof;
2) empirical methods of knowledge.
Observation, description, measurement and experiment, which are not characteristic of mathematics. The history of the development of mathematics suggests that empirical methods played an invaluable role in the emergence of mathematical knowledge, the development of mathematics as a science, an independent theoretical discipline. School education in mathematics to some extent repeats its historical path of development. The use of visual aids and TSS implies the use of various empirical methods that help avoid passive
contemplation, intensify the actions of students, and engage them in purposeful work.
Task. Find all such positive integers, the square of which ends with the number 7.
Finding a solution to this problem implies a small numerical experiment and the formulation of a hypothesis in the process of summarizing the data.
The measurement method is applicable to finding solutions to planimetric problems when we perform an instrumental study of the drawing of this figure. Measurement: the conclusion about the sum of the internal angles in an arbitrary triangle, for which students are asked to cut out acutely angular, obtuse triangles from paper, measure the angles of their angles with a protractor and find their sum: za+zb+zc = 180° Experience: using tabular data or marked points on the coordinate plane, determine the type of function: A) y=x
E) y= I x I
B) y=-x2
Observation: prime and composite numbers; formulate definitions. Is the number 1 simple?
3) mathematical methods of knowledge:
a) the method of mathematical models. Mathematical model - the description of any class of real world phenomena in the language of mathematics. The simulation method makes it possible to apply the mathematical apparatus to solving practical problems. The concept of numbers, geometric shapes, equations, inequalities, functions, derivatives are examples of mathematical models.
The method of mathematical modeling in the educational process has to be resorted to in solving any problem with practical content. To solve such a problem by mathematical means, it must first be translated into the language of mathematics (to build a model), using abstractions of identification, idealization, generalization.
References:
1. Abramova, IG. Problems of achieving the basic standard of mathematics / IG Abramova // Secondary professional education. - 2008
2. Dzhanaberdieva S.A. EMERGING METHODS OF TEACHING MATHEMATICS // International Journal of Applied and Fundamental Research. -2014
