Study Of Mathematical Disciplines Research Articles

ИСПОЛЬЗОВАНИЕ МУЛЬТИМЕДИЙНЫХ РЕСУРСОВ В ПРАКТИКЕ ПРЕПОДАВАНИЯ МАТЕМАТИКИ

The article is devoted to the study of the effectiveness of the process of implementing multimedia resources in the practice of teaching mathematics as an important pedagogical problem in the conditions of the modern information society. The information and educational space based on the active use of multimedia technologies is, on the one hand, a subsystem of the traditional educational process, on the other hand, an independent educational and cognitive structure that contributes to the formation of a creative personality, the activation of educational activities based on innovative software products, thanks to which classes become more visual and meaningful. An equally important direction in the modern information and educational environment is the provision of software for students to independently comprehend the theoretical material in mathematics and its application in solving practical problems. The article presents ideas for the use of didactic techniques, forms and methods for improving the educational activities of students, discusses the possibilities for developing the cognitive activity of schoolchildren based on information and communication technologies, their creative potential and fostering interest in the study of mathematical disciplines.

Methodical solutions for improving the effectiveness of studying mathematical disciplines by students of cyber security and computer sciences

The paper considers the influence of graphic methods of summarizing on the effectiveness of teaching mathematical disciplines. Emphasis is placed on the works of modern specialists in this field. The main points of traditional note-taking, its style, form, structure are analyzed, as well as the shortcomings and influence on the perception and assimilation of the material. The essence of various methods of modern graphic note-taking: scribing and sketch noting, their main components, which influence the improvement of memorization of new information, are revealed. Examples of the introduction of graphic note-taking in the course of mathematics during the study of elements of linear algebra and analytical geometry, namely: curves and surfaces in space, material on the theory of matrices and determinants, systems of linear algebraic equations, its effectiveness in the perception and assimilation of the material, are demonstrated. The given examples clearly show the difference between scribing and sketchouting. A fragment of the survey of students majoring in cyber security and computer science was demonstrated. Its analysis was carried out and positive and negative responses were presented both graphically and in percentages, survey questions were given. A conclusion was made regarding the importance of implementing modern note-taking methods in the study of mathematical disciplines. The opinion of modern participants in the educational process is considered when planning the educational trajectory in the future.

Mathematical education at a technical university: Motivational aspects

Introduction. The spread of digital technologies in all areas of life is associated with the acquisition of a prestigious profession related to the field of information and communication technologies and the influx of students to these specialties. However, level of motivation among these students is significantly different. They simply do not have significant knowledge about the profession and do not realize, for example, the need to study such an abstract discipline as mathematics. This is due to the increased motivation and interest of students in the study of mathematical disciplines.Purpose setting. The article deals with the problems of motivation of undergraduate students in the study of mathematical disciplines in a technical university.Methods and methodology of the study. The main methods of the research are analysis, generalization of published materials, personal observation and experienced authors in teaching the discipline "mathematical student analysis" based on first-year students of the Faculty of Automation and Computer Engineering of the Novosibirsk State Technical University.Results. The authors see one of the possibilities to increase interest of students in the introduction of extended survey lectures, the purpose of which is to convey to first-year students all serious fundamental mathematical training, linking such training with the chosen specialty and pointing out the impossibility of replacing it with the study of "fashionable" trends, for example, in the computer industry. The authors pay special attention to the analysis of the level of training of school graduates. It is noted that one of the reasons for the low motivation of students to study at a technical university is their weak mathematical training, which does not always correspond to relatively high USE score in specialized mathematics, which allows them to enroll in universities without exams.Conclusions. The level of motivation largely determines the effectiveness of training specialists, therefore, one of the tasks of a university teacher is to purposefully form motivations aimed at professional adaptation and professional development of students.

Organization of research activities of cadets of fire-technical specialties in the process of teaching mathematics

The article considers the issue of the formation of research competencies of future fire and techno sphere safety engineers in the process of teaching mathematical disciplines. It is proposed to organize the research activities of cadets, taking into account the principles of practice-oriented teaching. The methodological basis of the research is based on the key provisions of a practice-oriented approach to teaching mathematics, modern methods of scientific and pedagogical research, requirements for the level of development of research competencies among future rescue engineers. The structure of the research activity of cadets in the process of teaching mathematics is presented in the form of four components: motivational, cognitive, activity-based, reflexive. The characteristics of each component from the point of view of practice-oriented learning are given. The types of research activities that contribute to the formation of research competencies of cadets of fire-technical specialties in teaching mathematics are indicated, the goal and educational tasks of performing each type of activity. Requirements for the subject matter, the content of term papers and research work in teaching mathematics to future fire safety engineers are formulated. The examples of assignments for the course work in the discipline "Probability theory and mathematical statistics" are given. A fragment of tasks for research work in higher mathematics for cadets of the specified specialties is presented. The specifics of assessing the level of formation of cadets' readiness for research activities in the study of disciplines of mathematical training cycle are indicated. Incentive and operational criteria are dominant. Based on the results obtained, the goal of the practice-oriented research activity of cadets of fire-technical specialties in the process of teaching mathematics was formulated. The conditions that favor the formation of practice-oriented research competencies of a fire and techno sphere safety engineer in the study of mathematical disciplines are indicated.

Using the Mathematica package in teaching mathematical disciplines

This article analyzes the capabilities of the Wolfram Mathematica computer system, examines the feasibility of using its tools in the study of mathematical disciplines. The authors propose and demonstrate by examples a methodology for building a training course based on the integration of the methods of the discipline being studied and their implementation in the Mathematica environment. The paper explores the practical significance of including the Mathematica toolkit in the training course, which makes it possible to mathematically model various processes in modern society, demonstrate the solution of mathematically complex problems using the built-in functions of the package, as well as provide visualization of analytically obtained solutions.

Interactive methods of teaching mathematics, contributing to the formation of competencies in students of the field of training Agronomy format

The article outlines aspects of the formation of general professional competencies (GPC-1) through the study of mathematical disciplines; reveals the features of the methodology for the application of tasks (tasks of profile content, task case, task-situation), which are the main means of assessing the formation of the corresponding indicators of achievement of competence: ID-1, ID-2, ID-3, etc. The work analyzed educational publications in mathematical disciplines for the presence of tasks for an objective assessment of the level of formation of general professional competence (GPC-1), the problem of developing the content of criteria and assessment tools for formation of general professional competencies. The authors provide examples of tasks in the disciplines of Higher Mathematics and Mathematics and Mathematical Statistics, designed to form skills in identifying and defining a problem, choosing research methods, analyzing, interpreting the result and transferring fundamental knowledge into the language of professional activity.

COMPUTER ORIENTED TRAININGS FOR THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS FOR FUTURE TEACHERS OF COMPUTER SCIENCE

Introduction. The problem of using computer-based teaching aids in mathematics is very relevant today, especially for future computer science teachers, that are not interested in traditional teaching methods. Since the choice of teaching methods and tools, as well as forms of organization of the educational process are closely related, the implementation of computer-based approaches to learning requires the development of appropriate methods and teaching aids. Purpose. The main purpose is a theoretical substantiation of introduction of computer-oriented means of teaching probability theory and mathematical statistics of future teachers of computer science Methods. During the research such general theoretical pedagogical methods were used as analysis of scientific and scientific-methodical literature on this issue, analysis of educational programs, curricula, textbooks and manuals; generalization and systematization, comparison, classification. Results. The use of modern computer-based tools for teaching probability theory and mathematical statistics to future teachers of computer science are considered and theoretically justified. The main types of classes using computerbased learning systems, including computer-based lectures, computer-based practical classes and laboratory-practical classes using software are considered. The use of some software tools and programming languages in the teaching of this discipline is considered and theoretically substantiated. The combination of traditional and computer forms of education allows to intensify educational and cognitive activities in the study of mathematical disciplines, including theory of probability and mathematical statistics by future teachers of computer science. Originality. The paper considers and theoretically substantiates the use of computer-based tools in the educational process in in the teaching of theory of probability and mathematical statistics by future teachers of computer science. Conclusions. The use of computer-based tools for teaching theory of probability and mathematical statistics for future computer science teachers provides a number of methodological and methodological advantages over traditional teaching, enhances cognitive activity and improves the level of practical and professional training.

PROSPECTS OF THE MOBILE APPLICATIONS USE IN THE PROFESSIONAL TRAINING OF FUTURE TEACHERS OF MATHEMATICS

The relevance of the problem under consideration. The use of modern developments in the field of mobile digital technologies will intensify the process of teaching professional disciplines in the system of pedagogical education of future teachers of mathematics, which encourages the study of the specifics of using mobile applications in the training of future teachers of mathematics. The purpose of the study is to reveal the possibilities of introducing mobile applications in the process of teaching mathematical disciplines to future mathematics teachers. Research methods. Theoretical (analysis, systematization and generalization of pedagogical and psychological research, curricula for future teachers of mathematics) and empirical (pedagogical observation of the educational process, questionnaires) methods. Results of the research. By mobile learning we mean the process of creating a mobile educational environment with the use of mobile technologies for access to educational resources, implemented in face-to-face and distance forms. Active use of mobile educational applications leads to changes in the content of education, learning technology and in the relations between the participants of the educational process, allows to individualize learning, make it more adequate to the abilities of students. According to the survey results, the least attention in the study of mathematical disciplines is paid to applied mobile applications for mathematical calculations, but specialized programs and applications installed on mobile devices make them real assistants to teachers of mathematical disciplines and students of mathematical specialties. Our survey shows that the mobile application PhotoMath is the most popular among students when studying mathematical disciplines. We analyzed the possibilities of using the mobile application PhotoMath in the study of mathematical analysis by students of pedagogical universities.

DEVELOPMENT OF PRINCIPLES AND MEANS OF DIAGNOSTICS OF COMPETENCIES FORMED WHEN STUDYING DISCIPLINES OF THE MATHEMATICAL PROFILE IN STUDENTS OF TECHNICAL SPECIALTIES

The state of solving the problem of formation of mathematical competencies in the study of mathematical disciplines in technical students is clarified. Approaches to the diagnosis of mathematical training of students in the process of teaching mathematical disciplines at the university, which provide continuous, objective and timely information about the current level of mathematical training of students, as well as gaps and shortcomings in the formation of mathematical competence.
 The goals of diagnostics are formulated, which should reflect the structure and content of mathematical competence as a result of mathematical training. In the structure of mathematical competence, in accordance with the content of mathematical activity, it is appropriate to consider: possession of heuristic methods of finding solutions to problems; possession of methods for solving problems; knowledge of methods of mathematical modeling, application of mathematics in other areas.
 The analysis of prospects of application of automation of process of estimation of knowledge of students on the basis of computer testing is carried out that gives the chance to receive the full information on process and results of mathematical preparation of students, increase of motivation of their cognitive activity, development of reflection and skills of self-diagnostics.
 The advantages and disadvantages of using automated knowledge control systems are considered. With the help of such systems the differentiation of educational material is carried out, the interrogation providing objectivity of diagnostics of knowledge is carried out, results of training of students are fixed. Automated systems are focused on in-depth assimilation of information individually by each student.

Formation of general professional competencies among students of agricultural universities through mathematical disciplines

The article describes the aspects of forming general professional competences (GPC-1) through the study of mathematical disciplines; reveals the features of the methodology for the application of problems (profile content problems, case tasks, problem-situations), which are the main means of assessing the formation of the corresponding indicators of competence achievement: AI-1, AI-2, AI-3, etc. The work analyzes textbooks on mathematical disciplines for the presence of problems for objective assessment of professional competence formation level (GPC-1), the problem of the development of the criteria content and assessment tools for formation of professional competences is identified. The authors give examples of problems in the discipline of Mathematics and Mathematical Statistics, designed to form skills for identifying and defining the problem, choosing research methods, analyzing, interpreting the result and transferring fundamental knowledge to the professional activity language.

Цели и формы организации самостоятельной работы бакалавров экономики в системе прикладной математической подготовки

Цели и формы организации самостоятельной работы бакалавров экономики в системе прикладной математической подготовки

ФОРМУВАННЯ ІНТЕЛЕКТУАЛЬНОЇ ТЕХНІКИ СПЕЦІАЛІСТА НА ОСНОВІ МАТЕМАТИЧНИХ КАТЕГОРІЙ

Досліджено основні типи та рівні математичної компетентності, що застосовуються до вивчення математичних дисциплін в економічних ЗВО. Актуалізовано питання науково-технічного і соціально-економічного розвитку сучасного суспільства, удосконалення і повної реалізації в повсякденну практику новітніх комунікаційних технологій (ІКТ), використання яких дозволяє значно збільшити ефективність комп’ютерних процесів: систематизації, збирання, опрацювання, аналізу, зберігання, узагальнення, пошуку, передавання і подання різноманітних даних і відомостей. Запропоновано шляхи та умови ефективного впровадження в навчальний процес нових ІКТ для підвищення якості знань і рівня підготовки майбутніх фахівців-економістів. Проаналізувавши теоретичну і практичну частини математичної підготовки майбутніх спеціалістів фінансово-кредитної сфери діяльності, виділено основні функції застосування комп’ютерних технологій в освіті: організація пізнавальної діяльності методом внутрішнього і зовнішнього моделювання; створення нових методик освітнього процесу; своєчасні корекція і контроль системи освітніх дій; моделювання спільної діяльності викладача і студента. Застосування систем комп’ютерних технологій у ході вивчення математичних дисциплін суттєво підвищить математичну освіченість студентів в економічних ЗВО.

ФОРМИРОВАНИЕ ТВОРЧЕСКОГО ПОТЕНЦИАЛА СТУДЕНТОВ ТЕХНИЧЕСКОГО ВУЗА

Based on the analysis of scientific literature, the concepts "creativity" and "creative potential" for technical university students are considered and clarified, as a complex psychological process, which must be developed in the process of activity, stimulated by a problem or a contradiction. The analysis of scientific research provided an opportunity to highlight the components of creative potential. Comparing the components of the professional competencies of a future engineer and the components of the technical university students’ creative potential, the authors showed that the ability of a student to realize his creative potential is possession of a high level professional competence. To achieve the goal of the study, will apply a competence-based approach during the teaching process. Considering the possibilities of mathematical disciplines, as a means of forming the future engineer creative potential, tasks were selected to search for mathematical patterns and their choice was justified. During the educational process psychological and pedagogical conditions were used, which, according to the authors, contribute to the achievement of the research goal. To identify the state of formation of students creative potential, an experimental study was carried out. Samara State Technical University was chosen as the base of the research. The results of the study confirm the effectiveness of the identified psychological and pedagogical conditions for the formation of students creative potential in the study of mathematical disciplines.

FORMATION OF THE PROFESSIONAL COMPETENCE OF STUDENTS OF ECONOMIC SPECIALTIES IN THE STUDY OF MATHEMATICAL DISCIPLINES

The urgency of the problem of formation students’ professional competence is caused by the change of the educational paradigm of higher education, a rapid upgrade of scientific and technical knowledge. An important criterion for the competitiveness of a specialist is his competence in various fields, including the mathematical one. Therefore, our article is dedicated to the problems of the development of professional competence of students of economic specialties in the study of mathematical disciplines. The purpose of the article is to show how the construction and analysis of the future specialists’ mathematical models in the tasks of the professional field influence on the development of individual components of professional competencies. Theoretical: analysis of pedagogical, psychological and special literature in order to substantiate the necessity of formation graduates’ professional competence of economic higher educational institutions; generalization of the results of domestic and foreign research of this problem. Empirical: pedagogical observations, conversations with teachers and students about the role of mathematical models in the implementation of the applied orientation of teaching of mathematics in the system of higher economic education. The results of the study indicate that teaching of mathematics in the economic higher educational institutions through the construction and analysis of mathematical models, which are created for the solution of applied problems, has considerable potential in the field of the formation future economists’ professional competences.

MATHEMATICAL TASKS AS A MEANS OF FORMING PROFESSIONAL COMPETENCIES OF FUTURE TEACHERS

An important result of the preparation of the future teacher of mathematics is the formed professional competences. The process of formation should be carried out systematically, starting from the first year. While studying at the university, the foundations of modern mathematical knowledge should be laid, the need for professional self-development and self-education should be formed. The purpose of the study: the development of tools that contribute to the formation and development of professional competencies of students, future teachers of mathematics, in the study of mathematical disciplines. The study analyzed the professional competencies of a mathematics teacher, the components of mathematical culture and established their relationship. The competencies that can be formed during the first year of study are defined. Identified the need to convert standard mathematical problems. Based on the research, a technology for creating special complex problems based on standard mathematical problems has been developed. Tasks consist of two parts: subject (mathematical) and professionally-oriented. Tasks can be used to form subject and professional competencies, diagnose their formation. The article presents the requirements for them, types and examples of tasks. The result of the assignments from the point of view of the formation of subject and professional competences is described.

Mathematics Teachers Training Problems in the Context of the of New Educational Standards Introduction

The article is devoted to the future mathematics teachers training problems. The problems range of this educational process is represented by the following components: applicants with a low level of mathematical training, insufficient hours for fundamental mathematical disciplines in curricula, reorganization of the educational process with a focus on expanding electronic content. The insufficient number of hours devoted to the study of mathematical disciplines leads to the fact that students do not form subject knowledge. The article outlines ways to eliminate problems in the future mathematics teachers preparation: the propaedeutic courses introduction, the structural and didactic schemes development in the main mathematical sections, the disciplines integration, the system use of practical tasks, the preparing students holistic model for the use of information and communication technologies creation. The results of the training teachers experience in one domestic educational institution of higher education are presented. In accordance with which, such components as sufficient pre-university preparation, integration of disciplines, schematization of mathematical content, creation of conditions for combining the logical and figurative components of the students’ mathematical culture, and informational competence of students become necessary in the structure of building the educational process.

Psychological problems with learning mathematical disciplines at the economics faculties

The paper analyzes some of the psychological problems of the economic faculties’ students arising in the course of study of mathematical disciplines. These problems are primarily related with the lack of students’ awareness, misconception about the calculation methods in their future profession, low motivation and performance, math anxiety, etc. They makeadditional difficulties which impede successful mastering of sophisticated material. Based on the experience of mathematical disciplines teaching, the paper provides some possible solutions to these problems with the lecturer who has to play an important role. The lecturer should orientate students towards serious and profound knowledge of economic and mathematical methods, create conditions for students’ active participation in the educational process and provide them with comprehensive assistance in overcoming difficulties.

RESEARCH PROFESSIONALLY ORIENTED-OBJECTIVES AS A MEANS OF DEVELOPING RESEARCH SKILLS

The FSES is a set of requirements to graduate. Military schools are no exception, and according to the state educational standard of higher military education future officer must successfully perform their duties and to perform certain professional activities, one of which is research. In this regard, we believe that future officer-graduate should have some search skills. Thus, we believe that the task of the teacher of military higher education institution is to use forms, methods and means of learning, contributing to the development of research skills of students. T he purpose of this article is to synthesize the research results, consisting in the application of professionally oriented research tasks in the educational process for the formation and development of research skills of students in the study of mathematical disciplines.