# SOME FEATURES OF MATHEMATICS ABILITIES DEVELOPMENT FOR FUTURE CAREER PROBLEMS SOLVING

## Abstract

**Хузиахметова Р.Н. ^{1}, Хузиахметова А.Р.^{2}**

^{1 }Кандидат технических наук, доцент кафедры высшей математики, Казанский государственный технологический университет, ^{2 }Соискатель, ассистент кафедры высшей математики, Казанский государственный технологический университет

**О НЕКОТОРЫХ ОСОБЕННОСТЯХ РАЗВИТИЯ МАТЕМАТИЧЕСКИХ СПОСОБНОСТЕЙ СТУДЕНТОВ ДЛЯ РЕШЕНИЯ ЗАДАЧ БУДУЩЕЙ ПРОФЕССИОНАЛЬНОЙ ДЕЯТЕЛЬНОСТИ**

*Аннотация*

*В работе рассматривается новый подход к профессиональному обучению специалистов в Технологическом университете. Подход основывается на обучении не только теории математики, но и на возможности ее применения в прикладных предметах химических и технологических процессов. При этом предлагается использовать метрическо - компетентностный формат обучения студентов.*

**Ключевые слова: **профессионально-прикладная математическая компетенция**, **метрическо-компетентностный формат, система интегрированных задач.

**Khuziakhmetova R.N. ^{1}, Khuziakhmetova A.R.^{2}**

^{1} PhD in Engineering, Associate professor, Kazan State Technical University, ^{2 }Postgraduate student, Assistant, Kazan State Technical University

**SOME FEATURES OF MATHEMATICS ABILITIES DEVELOPMENT FOR FUTURE CAREER PROBLEMS SOLVING**

*Abstract*

*A new approach to the professional training of specialists at Technological University has been discussed in this paper with a view to teach mathematics not only as theory but also as the method for studying applied subjects in Chemical and Technological processes. The usage of metrics-competence approach is proposed.*

**Keywords:** professional-applied mathematical competence, metrics-competence format*, *systems of the integrated tasks.

The field of education is one of the most innovative industries. It is education that largely determines the competitiveness of the economy as a whole.The technological universities are designed to provide the fundamental nature and depth of education, strengthening its professional orientation.

An important element in solving this problem is a quality mathematics education. Mathematical knowledge serves as a methodological framework of the natural - scientific knowledge, as the basic ingredient of the most educational and special disciplines of Technological University. The growing influence of mathematics on the development of science and industry, expanding the use of this branch of knowledge, the process of mathematization of the major areas of human activity increase the value of the good education for every student.

A core measure of the skill level of the modern expert is his professional competence. Recently, the term has been more frequently appeared in our lexicon. In particular, the competent person is distinguished by the ability of the set of solutions to choose the most optimal, convincingly refute the false solutions, the ability to think critically.

Competence requires constant updating of knowledge, knowledge of the new information for the successful solution of professional problems in a given time and under given conditions. In summary, we can conclude that the primary purpose of training - the formation of the professional competence of the expert. Achieving this goal requires the development and implementation of an appropriate system for students training. [1]

It is generally recognized that the primary purpose of teaching mathematics at a vocational school is to learn to use mathematics to solve various problems that arise as a professional activity, as well as in practical situations, ie have professionally applied mathematical competence. This is possible if content of mathematics education is presented as a tool for solving applied professionally significant problems. The mathematical methods can be presented as such tool, the use of which may vary depending on the particular practical problem solving. That’s why the achievement of the main objective - the formation of professionally applied mathematical competence - is provided by the mathematical relationship and the training of students.

How to achieve this? What should be done to solve actual problem of interdisciplinary activity? We must build a didactic system of bachelor on the basis of professional problems using tasks base. A good example of this approach is the use of mathematics in solving practical problems in the scientific fields of chemical and petrochemical profile. The complexity and diversity of existing chemical production required the use of a fundamentally different approach to the mathematical description of the reaction rate and calculate the kinetic constants. This is due primarily to the fact that the kinetic equations that contain information about the basic laws of chemical transformations are the fundamental principle of the mathematical model of the chemical process.

Mathematically, the chemical reactions are described as stoichiometric and kinetic equations which, in terms of mathematical analysis, are written as a system of linear homogeneous algebraic equations. Additionally, equations that are combinations of two or more reactions might be presented. Such equations are called as linearly dependent equations. These equations do not provide additional information on the reaction system compared to those equations that form them. Any change in the concentration caused by the linear dependence of the reaction can be caused by reactions, which is the combination of this reaction is linearly dependent. Therefore, the equations of the original system of reactions must be checked for a linear relationship and it’s required to determine their number.

For finding the linearly independent reactions the usage of linear algebra elements is convenient, since the set of equations of chemical reactions can be mathematically considered as a linear space. This follows from the fact that the chemical equations are allowed to sum up and multiply by arbitrary factors, and again obtain the chemical equation. For such operations axioms of commutativity, associativity, etc. are valid.

This is just one example of the use of methods of higher mathematics in solving chemical problems, allowing to get results, the achievement of which in other ways is quite complex.

As per current education system in the universities students familiarization with the specialty starts only at the undergraduate period, while the formation of real ideas about the future professional activity should be carried out at all educational stages. Knowledge of undergraduate students about their future profession confined to academic disciplines and the general education of the general theoretical cycles that can not provide insight into future careers, especially if the course material of these disciplines is presented without any connection with the tasks of the specialty. Students not only do not feel the need for the study of general scientific and technical disciplines, but often do not see the connection, for example, between mathematics and their future profession. Meanwhile, acquired undergraduate students mathematical knowledge should be a means for solving the problems of other disciplines and future careers.

The ability to solve educational problems (competences) are supported by formalizing, performing and constructive capabilities of certain development level. The higher capabilities developed and knowledge learned, the more effective the training problem will be solved. [2]

To solve the problems based on modules, in which all learning material is divided, it is required to have abilities of different combinations: formalizing -performing abilities – to solve the problem student has to determine the analytical dependence and substitute the data in it; formalizing - constructive abilities - to solve the problem student has to build a mathematical model and choice the solution, but there is no need to bring the solution to the end result; constructive –performing abilities - solution of the problem requires the algorithm selection and evaluation completion; formalizing - constructive - performing - to solve the problem it is required to build a mathematical model and to select the algorithm, followed by the completion of calculations.[3]

All training material within each module is usually split into theoretical part (knowledge base) and practical part (learning problems base) - two interconnected databases. The depth of mathematical knowledge is evaluated by the completeness and integrity of this knowledge. Completeness of knowledge is a measure of the theory knowledge in the discipline "Mathematics" and the integrity of knowledge is a measure of the relationship of this knowledge. Tasks for the completeness and integrity verifications are generated in the form of tests. Theoretical questions are divided into two parts accordingly, and the completeness and integrity metrics are presented as a percentage. It should be noted that the completeness and integrity as the criteria for the development of knowledge should be read in conjunction with each other. Of course, each criterion gives some information about the degree of development of the material, but the full picture can only be obtained by considering these criteria together. Completeness and integrity is an organized knowledge base, which changes as per student's development.

In scope of the considering module the practical material is divided into 3 groups: tasks for formalizing abilities development; tasks for constructive abilities development; tasks for performing abilities development. In scope of every group the tasks are provided in increasing order of complication.[4]

The most difficult tasks for students are the tasks for formalizing abilities, with which help the connection with the future professional activity is performed. That’s why it’s more preferable to use in the tests the formalizing – constructive tasks with the increasing complication for the appropriate abilities development.

**References**

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