Mathematical ability as a factor in the acquisition of mathematical knowledge, abilities, skills, competencies

Abilities are the individual psychological features defining success of performance of activity or a number of the activities irreducible to knowledge, abilities, skills, competences [1].

In the 60-70-ies of XX century, the study of psychology of abilities was divided into a number of private areas: the study of mathematical, technical, literary and other abilities, which became known by occupation, and not only on psychological grounds.

Particular interest in human abilities is due to the fact that they are one of the opportunities to acquire knowledge and skills. It is worth considering that many students have difficulties in mastering the transferred knowledge in a number of disciplines, in particular in mathematics [2, p. 462].

Therefore, the actual theme of the study of mathematical abilities and their impact on the level of mathematical knowledge.

Mathematical abilities-individual psychological features of human activity in the study and creative development of mathematics.

They are part of the structure of intelligence, as it is one of the determining factors. Intelligence is a mental ability that affects the performance of any activity, manifested in the quality, speed and accuracy of solving mental problems, in the pace and success of learning. Mathematical abilities, being a mental reality, interact with other factors. In structural models, they occupy different positions and are interpreted differently - as a group factor of intelligence, as a cognitive structural component, as an independent intelligence, etc. Mathematical abilities have always been the object of attention of psychologists as a key indicator of human intellectual abilities [3].

The structure of mathematical abilities consists of:

• *    ability to obtain mathematical information;

• *    ability to focus attention;

• *    availability of advanced mathematical memory;

• •    the ability to imagine;

• *    ability to process mathematical information;

• *    mathematical orientation of the mind;

• *    special style of thinking [4].

Useful, but not mandatory abilities can be: the speed of thought processes, computational abilities, good memory for numbers and formulas, abstract thinking, etc.

In the course of my work, I made the assumption that the level of mathematical abilities affects the level of mathematical knowledge.

The aim of the work is to reveal the influence of mathematical abilities on the level of mathematical knowledge.

A study was conducted to identify the level of analytical mathematical abilities (AMA) of first-year students in the field of "State and municipal management" of the RF presidential Academy of Sciences (18 people). The results were compared with the performance of students. The survey and psychological test "Analytical mathematical abilities", presented in four forms, were used for the research [5].

AMA refers to academic abilities, that is, first of all, they allow better assimilation of educational material, in this case – mathematics. This is due to the fact that these abilities are interdependent with IQ indicators.

As a result of the study, 11.2% of the total number of students tested have a high level of AMA. The average level is observed in 33.3%. Low-55.5%.

It is worth noting that the owners of high results are capable of analysis not only in the field of mathematics, but also in other heterogeneous problems. Holders of low results do not have such abilities, moreover, they are capable of unjustified and frivolous actions.

It should be noted that the performance of students is estimated as follows. Grade " 5 " in mathematics have 33.3% of the total number of students tested. This is almost 3 times more than the percentage of students with a high level of AMA. A rating of "4" have to 38.8% - a figure roughly equal to the percentage of examinees students who have an average level of AMA. Rating " 3 " have 27.7%. This figure is 2 times less than the percentage of students with low AMA.

Thus, we can say that there is a relationship between mathematical and analytical skills and the level of mathematical knowledge. It is necessary to take into account the subjective assessment of the level of mathematical knowledge, as well as factors such as motivation, interest, the desire to study mathematics.

Mathematical abilities, like any other abilities, are acquired. Therefore, it is important to strive to develop their inclinations, which are innate, to form from them certain abilities: you need to decide what a person wants to do, that it is interesting; based on the result of the first paragraph, to find out what abilities he needs to develop; begin to develop the necessary abilities, as well as to study and practice.

This work was carried out as part of the Competition of research works for students in the category "Education", organized by the HSE in 2018. Future specialists, bachelors, students of the Kaluga branch of Ranepa, taking part in government programs [6, p. 5], international, national conferences [7], competitions [8], demonstrating the successful development necessary for acquiring competences.

Sources used:

• 1.    Дружинин В.Н. Психология общих способностей / В.Н. Дружинин. – 3-е изд. – СПБ: Питер, 2008. – 368 с: ил.

• 2.    Формирование, оценка и развитие компетенций будущих управленцев в процессе изучения цикла математических и естественнонаучных дисциплин / Г.В. Хамер [и др.] // В мире научных открытий. 2014. № 51 (53). С. 462-474.

• 3.    Стоименова Я. Структура математических способностей учащихся начальной школы / Я. Стоименова// Вестник по педагогике и психологии Южной Сибири – 2013. №1-2. С. 30-47.

• 4.    Канин Е.С. Математические способности учащихся и их развитие / Е.С. Канин // Вестник Вятского государственного университета – 2013. № 21. С. 152-158.

• 5.    Психологический тест "Аналитические математические способности. Форма А" [Электронный ресурс] // А. Я. Психология (azps.ru): [web-сайт].– Режим доступа: http://azps.ru/tests/kit/chryad_a.html (28.10.2018).

• 6.    Hamer G.V. Management of health-saving educational environment of space / G.V. Hamer // Форум молодыхученых. 2017. № 11 (15). С. 3-7.

• 7.    Хамер Г.В. Радио как средство реализации информационнокоммуникативного спроса студенческой молодежи / Г.В. Хамер //

  Международный журнал гуманитарных и естественных наук. 2018. № 4. С. 76-78.

• 8.    Хамер Г.В., Корнеева Р.В. Модернизация муниципальной сельской библиотеки в Центр общественного доступа // В мире научных открытий. 2014. № 7-3 (55). С. 1176-1192.

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