Библиографическое описание:

Косыбаева У. А., Сыздыкова Н. К., Утебаев И. С., Шаяхметова М. Н., Саткаримов А. А. Formation and development of mathematical abilities of secondary school students // Молодой ученый. — 2017. — №5. — С. 502-504. — URL https://moluch.ru/archive/139/39132/ (дата обращения: 22.04.2018).

The acquisition of Kazakhstan state sovereignty was put before the society the task of instilling patriotism among the younger generation. The work of the school should be directed not adopted the people a certain amount of knowledge, and the objectives set foundational documents and projects in the field of education, i.e. upbringing of a patriot and citizen of Kazakhstan. The younger generation will determine the future of our Republic in the XXI century.

The message of the President of the Republic of Kazakhstan N. A. Nazarbayev to people of Kazakhstan «Strategy Kazakhstan-2050: new political course of the established the government», where the President said, «We have a lot of work to improve the quality of all parts of national education. By 2020 it is planned to provide 100 per cent coverage of Kazakh children from 3 to 6 years of preschool education. Therefore it’s important to give them modern programs and method of teaching, qualified personnel”. It also noted that it is necessary to educate ourselves and our children new Kazakhstan patriotism. It is primarily the pride of the country and its achievements. Our Leader notes that the knowledge and professional skills — key landmarks of modern system of education [1].

In secondary education it is necessary to pull the secondary schools to the level of teaching at Nazarbayev Intellectual schools. The result of teaching should be mastery of critical thinking skills independent research and in-depth analysis of information.

Each student has abilities and talents. In order to enable them to exercise their talents, them need smart guidance from adults. The tasks of the teacher using a variety of teaching methods, including games, systematically, purposefully to develop the mobility and flexibility of thinking, to stimulate the process of restructuring, shift of search activity.

Ability is not something once and for all determined, they are formed and developed in the learning process, in the process of exercise. In this, it is necessary to form, to develop the abilities of children and it is impossible to accurately predict how far it can go is the development.

Speaking of mathematical abilities as the features of mental activity, first of all, to point out a few common among the teachers of the misconceptions:

First, many believe that mathematical abilities are, above all, the ability to rapid and accurate calculation (in particular in mind). In fact, the processing ability is not always associated with the formation of a truly mathematical (creative) abilities. Second, many people think that mathematics is capable of preschoolers have a good memory for formulas, numbers, numbers. However, as pointed out by academician A. N. Kolmogorov, success in mathematics is least of all based on the ability to quickly and firmly to remember a lot of facts, figures, formulas. Finally, I believe that one of the indicators of mathematical ability is speed of thought processes. Especially a fast paced work itself has nothing to do with mathematical ability. The student can work slowly and deliberately, but at the same time, thoughtfully, creatively, successfully progressing in learning mathematics.

Identifying the causes of the successes and failures of the students, the teacher can determine the ability or inability to influence the activities of students and depending on this purposefully to plan future work. The essence of the experience is the activities of teachers in the creation of conditions for active, conscious, creative activity of students; to improve the interaction between teachers and students in the process of problem solving; development of mathematical abilities of schoolchildren and raising their diligence, efficiency, demands of himself.

First of all, it must be emphasized that to develop the mathematical ability of students should not only in the case when these abilities are already evident or when it is prepared for entry to mathematics University. Knowledge of mathematics is necessary for many professions and abilities can develop and later through systematic studies of mathematics, mastery of knowledge, skills and abilities in this area.

We must remember that mathematical ability must be combined with a deep and effective interest and aptitude for mathematics. Interested in mathematics the child is inclined to do it, persistently studying mathematics and thereby vigorously exercise and develop their abilities [2].

To implement the quality work on the development of mathematical abilities, the following innovative teaching products and educational activities:

‒ optional course «Unconventional and entertaining task».;

‒ use of ICT technologies;

‒ a complex of exercises for development of all components of mathematical abilities;

‒ a series of studies on the development of the ability to reason.

Development of skills is inextricably linked to the formation of interest in mathematics. Noticing the child's interest in mathematics, tendency to engage in it, necessary to fully develop these interests and aptitudes, to encourage children in this respect.If such interests and inclinations is to try to awaken them.

Overtime working provides an additional incentive for creativity, learning, development of their mathematical abilities. This gives you the opportunity to make available to students the assimilation of new types of tasks in less time and greater efficiency.

For the revival and development of interest in mathematics is important popular show (not just tell about it, namely to show) its value for engineering, physics and other branches of science, industry and agriculture. A good means of creating interest in mathematics by setting and solving practically important for the child tasks (to calculate the square footage is quite a complex shape, the volume of haystacks to make calculations of the model vehicle or glider, etc.) [3].

The mathematical ability of the student to be diagnosed through testing, both in paper and in electronic form. Scientists have proved that there are many factors that affect the deterioration of mental abilities, for example, old age, prolonged inactivity, physical abnormalities. However, there are a number of ways that help to maintain intellectual abilities at a good level.

  1. Regular brain training, solving the problems and examples in mind, perform calculations without computing devices.
  2. Solving crosswords and puzzles.
  3. Special computer programs that are designed to improve brain performance (very popular in America).
  4. Developing a hobby (playing bridge, learning foreign languages, etc.).
  5. Exercise.

During the theoretical study of the problem, I was conducted research on formation of students, and the development of mathematical abilities of schoolchildren in the process of solving mathematical problems. In experiment took part students of 5 «b« class (the class of 28 students) school of Zhambyl of Karaganda. The stages of the experimental activities:

  1. preparation and determination of the level of mathematical ability based on observations.
  2. The ascertaining stage of the experiment is to determine the level of formation of mathematical abilities.
  3. A formative experiment — the creation of necessary conditions for the development of mathematical abilities.
  4. Control experiment — definition of efficiency of forms and methods for facilitating the development of mathematical abilities.

All materials jobs will be added to the master thesis. For observations were selected characteristics, which are most clearly manifested:

1) the ability to consistently correct logical reasoning;

2) resourcefulness and ingenuity in the study;

3) flexibility of thinking;

4) the ability to shorten the reasoning process;

5) the ability to switch from direct to a reverse train of thought;

6) the development of figurative-geometric thinking and spatial concepts.

Very useful if students will try first to solve these problems in mind, and then proceed to a written decision. Tasks are not only useful, but they are interesting and students usually with great enthusiasm and tenacity to solve them.

In the second phase, carried out diagnostics of development of mathematical abilities. This test was used. Qualitative analysis of the test showed the main reasons for the difficulty of the test run. Among them:

a) the lack of specific knowledge in solving problems (not able to determine what actions solve the problem, they can’t write the solution of the expression (7 people — 25 %);

b) lack of formation of computing skills (10 people — 36 %).

In stage 3 investigated mathematical abilities and identified the following levels using the game «guess the touch». Student closes eyes and gets an object that can feel. The object is to have such dimensions that the student had the opportunity to study it as a whole. There is a certain amount of time (5–15sec). After this time the student needs to say what it was and why he decided to. In the game you can use different kinds of fabric, similar to the shape of fruit (apples, oranges, peaches), geometric shapes, and more. Each correct answer is awarded a chip.

In the last stage to determine differences in growth and development of children's ability activity was conducted on the material assignments the «logic problems» by the method of A. Z. Zach. Identified the following levels of ability to reason:

high level — solved problems № 1–10 (contain 8 characters).

middle level — solved problems № 1–8 (containing 14 character).

low level — solved problems № 1–4 (contain 6 character) [4].

Comparison of results of works, the quality of teaching in mathematics lead to the conclusion that with increasing level of mathematical ability increases the success in learning mathematics. The results of the competitions show that students with a high level of mathematical ability confirm your level.

We have sought to ensure that the student has independently learned to see a problem, formulate it, to explore the possibilities and ways of its decision. The research method is characterized by a high level of cognitive independence of pupils. The lessons we organized independent work of students, giving them the problematic cognitive tasks and tasks.

Such activities raise the level of mathematical abilities of most students, increase productivity and creative activity. For most students the level of mathematical abilities, develop all components of mathematical abilities.


  1. The message of the President N. A. Nazarbayev to the people of Kazakhstan «Strategy — Kazakhstan 2050" http://strategy2050.kz/ru/page/message_text
  2. Formation of interest in the doctrine at school students / under the editorship of A. K. Markov. — М: Education, 1986. — 192 pages.
  3. Mathematics. 5th class. Tasks for training and development of pupils. Lebedintseva E. A., Belenkova E.Yu.M.: 2013–104 pages.
  4. Zack A. Z. 600 game tasks for development of logical thinking of children / A. Z. Zac, Publishing house: «Academy of Development» 1998–192 pages.
Основные термины (генерируются автоматически): mathematical abilities, mathematical ability, mathematical ability confirm, mathematical ability increases, mathematics, students, development, high level, ) abilities., Kazakhstan «Strategy Kazakhstan-2050, Kazakhstan state sovereignty, new Kazakhstan patriotism, Kazakhstan N. A., mental abilities, intellectual abilities, new political course, younger generation, fast paced work, critical thinking skills, Nazarbayev Intellectual schools.


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