Course Of Higher Mathematics Research Articles

Design and implementation of flipped classroom approach for higher mathematics courses at medical colleges

This research focused on the design and implementation of the flipped classroom approach for higher mathematics courses in medical colleges. Out of 120 students, 60 were assigned to the experimental group and 60 to the control group. In the continuous assessment, which included homework and quizzes, the average score of the experimental group was 85.5 ± 5.5, while that of the control group was 75.2 ± 8.1 (P < 0.05). For the final examination, the average score in the experimental group was 88.3 ± 6.2, compared to 78.1 ± 7.3 in the control group (P < 0.01). The participation rate of students in the experimental group was 80.5%, significantly higher than the 50.3% in the control group (P < 0.001). Regarding autonomous learning ability, the experimental group spent an average of 3.2 hours per week on self-study, compared to 1.5 hours in the control group (P < 0.005). Other potential evaluation indicators could involve the percentage of students achieving high scores (90% or above) in problem-solving tasks (25.8% in the experimental group vs. 10.3% in the control group, P < 0.05), and the improvement in retention of key concepts after one month (70.2% in the experimental group vs. 40.5% in the control group, P < 0.01). In conclusion, the flipped classroom approach holds substantial promise in elevating the learning efficacy of higher mathematics courses within medical colleges, offering valuable insights for educational innovation and improvement.

Realization of the humanitarian potential of a higher mathematics course in the professional training of technical university students

Introduction. The next stage of globalization of relations is being formed – the creation of a digital economy, including smart manufacturing, smart finance, telemedicine, etc. The UNESCO Science Report: the Race Against Time for Smarter Development – Executive Summary, published in 2021, calls this phase the “fourth industrial revolution.” The development and basis of this revolution in the fields of science and engineering is directly related to digital technologies such as artificial intelligence, robotics, blockchain technology, which intersect with nano- and biotechnologies, and cognitive sciences. Scientific institutions and higher education systems are actively involved in this process as direct participants and as training institutions. Mathematical training is rightfully considered the methodological basis of most educational and special disciplines. The purpose of the study is to reveal the humanitarian potential of a higher mathematics course in the professional training of a technical university student. Materials and methods. In accordance with the provisions of the system-activity and information approaches, the authors have developed a questionnaire to identify preferences in realizing the humanitarian potential of the higher mathematics course at a technical university. Respondents are asked to rank the proposed six statements that characterize the mathematical preparation of students. 368 people took part in the survey, among them students of bachelor's degree (136 people), specialty (124 people), master's degree (78 people) and postgraduate studies (30 people) of St. Petersburg Mining University. The method of summarizing and grouping statistical observation materials was used. Results. The highest rating of 3.74 was occupied by the contradiction between the awareness of the leading role of mathematics in the development of logical thinking and at the same time the predominance of theoretical facts over their practical application in the university course of higher mathematics. This statement was noted as the most significant by 20% of students, 27% of undergraduates and 24% of graduate students. The other two, in terms of the severity of the contradiction, have a rating of 3.55 (mastering the content of a higher mathematics course is accompanied by objective difficulty due to the high abstractness of the subject) and 3.56 (insignificant inclusion of heuristic methods in the content of the course). In the context of constantly increasing requirements for the quality of engineering education, the problem of increasing the role of mathematical knowledge can be solved through didactic support of the educational and cognitive process in the classroom and as part of students’ independent work. In a multi-component educational activity, the basic dominants (spatial, logical, numerical and symbolic) are highlighted and the methodological features of their implementation in the student’s mathematical preparation are revealed. Conclusion. The humanitarian potential of the higher mathematics course presupposes a system of measures aimed at the priority development of intellectual and general cultural qualities of students. The realization of humanitarian potential involves the formation of a student's value attitude towards himself, the world around him and his activities in it. The realization of the humanitarian potential of the discipline in the training of a future engineer is possible through the organization of symbolic activities by means of practice-oriented tasks and educational cases of an applied nature.

Професійна спрямованість математичної підготовки студентів технічних спеціальностей у контексті фундаменталізації освітнього процесу

The article examines the peculiarities of mathematical training of future technical specialists in the context of fundamentalization of the educational process. The study of the definitions of fundamentalization, mathematical preparation was carried out, the main characteristic features of mathematical preparation, proposed by the researchers of the problem of mathematical preparation, were singled out. An analysis of the work of scientists dedicated to the selected research problem was carried out. It has been established that the mathematical training of future technical specialists is a dialectical combination of formed mathematical skills and abilities for their applied application and the direct process of forming these skills. The fundamentalization of mathematical training is considered to be the concept of improving mathematical training, in which basic mathematical invariants are selected for their further application in professional activities. To implement the approach of professional orientation of mathematical training of students of technical specialties, it is recommended to take into account the peculiarities of the construction of the course of higher mathematics and courses of special disciplines in order to enable the integration of educational material, as well as the organization of the educational process in higher education institutions. Based on the analysis of educational programs for students of various specialties of the Vinnytsia National Technical University, a conclusion was made about the difference in program results in mathematics for students of the same lecture stream. On the basis of which it is proposed to unify tasks of professional content. Examples of professional tasks from the "Theory of Probability" section are given.

The usage of stochastic matrices while learning the topic “Eigenvalues and eigenvectors of a matrix” in the course of Higher Mathematics

Abstract The article looks into teaching students mathematical modeling during the mastering of the topic “Eigenvalues and eigenvectors of a matrix” in the Linear Algebra. The modeling is based on the usage of matrices built based on Markov chains. The analysis of the researchers’ papers shows that the usage of matrices of this type can be implemented while teaching students of different university specialties. The analysis of the prerequisites for the involvement of stochastic matrices in the consideration of students has helped to determine additional concepts and theorems that should be considered while learning “Eigenvalues and eigenvectors of a matrix”. The theorem on the presence of stochastic vectors in a stochastic matrix can serve as a formula for systematizing problems that can present applications of eigenvalues and eigenvectors of the matrix in real-life situations. The results of the experiment conducted using the developed system of problems for students of different University specialties show the improvement of skills provided by mastering the topic “Eigenvalues and eigenvectors of a matrix”.

DEVELOPMENT AND IMPLEMENTATION OF THE TEACHING METHODOLOGY OF THE HIGHER MATHEMATICS COURSE BASED ON PRACTICE

The teaching of higher mathematics has traditionally focused on theoretical concepts, which often creates a gap between students' understanding of the subject and its practical applications. This article explores the development and implementation of a teaching methodology for the higher mathematics course based on practice-oriented learning. The objective is to bridge the gap between theory and application, improving students' problem-solving skills and enhancing their ability to apply mathematical concepts in real-world situations. By integrating practical activities, case studies, and applied projects into the curriculum, this methodology fosters deeper comprehension and equips students with valuable competencies for their future careers.

The Analogy Method as an Element of Research Work of Junior Students

The article explores the possibility of increasing the efficiency of research work within the framework of lectures and practical classes for junior students. We have identified a contradiction between the potential of research work in the development of students’ research competencies in the process of teaching junior students and the insufficient development of productive methods for introducing research tools in addition to skills in working with sources of information and methods of conducting experimental work. We are talking about tools that allow you to identify objects of research, put forward and formulate hypotheses, test hypotheses, etc. The solution to the problem is realized through the developed methodology of lectures and practical classes, containing elements of intellectual tools of scientific activity in a systematic connection with the subject methodology. The method of analogy has been chosen as a specific tool for scientific activity. A system for assessing the levels of mastering the skills of intellectual tools of students’ scientific activities has been developed and an experimental test of the effectiveness of the developed methodology has been carried out. These methods, implemented for a higher mathematics course for non-core specialties, as well as algebra and mathematical analysis courses for mathematical and IT specialties, can be transferred to other disciplines of the theoretical cycle. This is the practical significance of the study. Keywords: research activity, levels of research activity, analogy method, research methodology

Software Support for the Higher Mathematics Course at the Technical University

The paper addresses the challenges of training modern engineers in mathematical disciplines. It emphasizes the need for graduates to possess theoretical knowledge and be capable of using modern software solutions for efficient mathematical calculations. The article discusses the importance of incorporating mathematical software into higher education to enhance the teaching of mathematical disciplines. Explores the potential benefits and challenges of using mathematical software in the learning process, such as the need for coordination among teachers and the importance of familiarizing students with the interfaces of mathematical packages. The paper recommends using specific mathematical software packages, such as Scilab, for scientific and engineering calculations. It also highlights the necessity of guiding students in understanding the practical applications of mathematical software in solving complex mathematical problems. Furthermore, the paper addresses the issue of preventing students from inappropriately using online calculators for tasks, emphasizing the importance of mastering theoretical foundations before utilizing mathematical software packages. The paper generally advocates for a balanced approach that incorporates both traditional theoretical exposition and practical application of mathematical programs in higher education to promote effective teaching and learning of mathematical disciplines.

APPLIED DIRECTION OF THE STUDY OF HIGHER MATHEMATICS BY STUDENTS OF PROFES- SIONAL PRE-HIGHER EDUCATION

The article substantiates the need for a practical, professional focus of studying the course of higher mathematics by students of professional pre-higher education institution. The aim of the article is to highlight the ways of implementing the professional orientation of the content of mathematical disciplines in the education of students in various specialities of vocational higher education. Modern requirements for the development and reform of higher education require an increase in the professional competence of a bachelor’s graduate in each field of knowledge, the ability to creatively approach and find the solution to emerging professional tasks. Therefore, teachers of higher mathematics have the task of reorienting the teaching of the academic discipline with the use of professional problem solving. The purpose of the article is to highlight the ways of implementing the professional orientation of the content of mathematical disciplines in the training of students of professional pre-higher education in various specialties of the college. In connection with the rapid development of science and technology, the training of competent, competitive, and highly qualified specialists requires a high level of skills in applying mathematical apparatus in professional activities. Mathematics is the basis of studying physics, technology, general technical and special disciplines. At present, mathematical education has a significant impact on the formation of professional qualities of a modern specialist who is able to navigate the directions of development of modern science and methods of learning about the world around them, predict the impact of human production on society and the environment. Modern mathematics is used in the study of economic, humanitarian, biological, physical, technical and other phenomena. This is done by building a mathematical model. It takes into account all essential connections within the phenomenon. Under mathematical modelling we will understand the method of researching processes or phenomena by building their mathematical models and researching these processes. The applied direction of solving problems by students of various specialties is oriented towards future professional activity. This is an effective means of increasing learning motivation, and developing mathematical and professional competences. The results of the research are examples of practical problems of various sections of higher mathematics for students of economic and technical specialties. The applied nature of the given problems aims to combine the study of higher mathematics with special training of future bachelors and to give them the opportunity to gain experience in solving production problems, and to increase their professional competence. This is very important in times of fierce competition in the labour market. Conclusion. Practical skills and the ability to use the mathematical apparatus when solving applied, profession-oriented problems increase the motivation of students of higher and pre-higher education, and aid students to study other courses of professional disciplines, and do coursework and diploma projects, which will contribute to the maximum use of mathematical methods in the educational course of higher education mathematicians in the future professional activity. The obtained results open up prospects for further research in the following directions: development of methods of formation of skills to solve applied problems by students of various specialties, as well as strengthening integration links between fundamental and profession-oriented courses.

Design and Construction of Ideological and Political Micro-platform for Higher Mathematics Courses

This article focuses on the design and construction of an ideological and political micro-platform for higher mathematics courses. It actively builds a micro-platform for ideological and political teaching in higher education courses through two aspects: platform design and construction and the design of ideological and political elements of advanced mathematics. The project team will improve the "Basic Mathematics Knowledge of Economics and Management" Library" WeChat public platform to explore the establishment of a learning platform with the construction of course network resources and interactive integration of mathematics courses as its main modules. The goal is to truly understand students' learning status through communication between students and teachers at different stages, establish a new method system for the organic integration of advanced mathematics courses and professional courses, and form a new situation of teacher-student and teacher-teacher interaction. To serve the construction of application oriented high-level universities.

Strategies for Improving the Teaching Quality of Higher Mathematics Course under the Background of New Engineering

Strategies for Improving the Teaching Quality of Higher Mathematics Course under the Background of New Engineering

Research on Teaching Quality Evaluation Model of Higher Mathematics Based on Hierarchical Analysis Approach

Abstract The teaching quality of higher mathematics courses plays a pivotal role in the cultivation of students’ quality and the improvement of their abilities. In this paper, information entropy is added to the hierarchical analysis method to improve it and then combined with the fuzzy synthesis method to construct a model for evaluating the quality of mathematics teaching. The higher mathematics teaching course at a university is selected as the research object, and the constructed model for evaluating the quality of higher mathematics teaching is applied to the teaching of higher mathematics in classrooms. The evaluation index system for higher mathematics teaching quality is established by combining relevant literature, and the improved AHP is used for weighting. Then, the index data is collected through questionnaires to analyze the differences and assess the teaching quality of different genders and majors and then to propose strategies to improve the teaching quality of higher mathematics. The significant effects of teaching methods (0.184), teaching effectiveness (0.176), and teaching content (0.170) on the teaching quality of higher mathematics were revealed. The quality of teaching higher mathematics in the sample universities is located at a good level with scores between 8 and 9 on each evaluation index, with the best performance of 8.934 for teaching content. The evaluation model for higher mathematics teaching quality established by the research has validity and feasibility.

Research of Online and Offline Blended Teaching of College Mathematics

The traditional teaching model faces significant challenges in the era of information technology, while the blended learning model that integrates information technology and educational instruction has become an undeniable trend. Blended learning, which combines online and offline elements, can achieve complementary advantages to a greater extent, effectively enhancing the quality of teaching and promoting students' competence. This article explores the blended learning model, using higher mathematics courses as an example.

FEATURES OF TEACHING HIGHER MATHEMATICS IN THE CONTEXT OF FUTURE PROFESSIONAL ACTIVITIES OF TECHNICAL UNIVERSITY STUDENT

Peculiarities of teaching a higher mathematics course at a technical university for engineering students are considered. Methods of algorithmic learning, problem-based learning, and research learning are analyzed in the context of the future professional

МЕТОД ПРОЕКТОВ КАК СПОСОБ ОРГАНИЗАЦИИ ЦЕЛЕВОГО ДИСТАНЦИОННОГО ОБУЧЕНИЯ В ТЕХНИЧЕСКОМ ВУЗЕ

The presented article is devoted to the problems of distance learning in the target areas. The article discusses in detail the problems of university distance education. By distance learning in this article, we will understand learning with the help of information technology. Distance learning is defined differently by different authors. With such training, the teacher perceives the students as an impersonal mass and has no way to assess the degree of understanding of the proposed material. The main purpose of the study was to consider distance learning for students who entered the university in the target areas of various divisions of the Russian Railway. The authors of the article consider the problems of distance learning of students in target areas at the Samara State University of Railways on the example of teaching higher mathematics. One of the methods of organizing targeted university distance learning is proposed, the project method. With the help of the project method, we propose to solve professionally oriented tasks when teaching students in the target areas in the course of higher mathematics. It is this format of education that is most promising. The approbation of this approach to teaching target students in a distance format has shown the effectiveness of the proposed teaching method.

DEVELOPMENT OF THE ELECTRONIC TEXTBOOK FOR THE HIGHER COURSE OF MATHEMATICS ACCORDING TO THE PROGRAM MACROMEDIA FLASH 8

This article discusses the ways of organizing the educational process for the course of higher mathematics at a university independently or jointly with a teacher through an electronic textbook, the use of effective methods and techniques used in the preparation of the program and training.When compiling an electronic textbook, a model was developed using the Macromedia Flash 8 program. When choosing a design with an interface from individual methods, the social method was used, and when it was introduced into the educational process, control methods were used. As a result of the research, a large-scale electronic textbook was compiled using various methods. During the research work, several possibilities of an electronic textbook were identified, designed to facilitate the teacher's lesson progress, and the student to comprehend the material provided as effectively as possible.During the preparation of the program, ways of further integration into Windows were developed.All formulas used in the course of higher mathematics have been saved as a separate reference.The first scheme of the program with a total volume of 8043 kilobytes is fully working. The developed electronic textbook can be used as a methodological guide when studying a course of higher mathematics, as a theoretical basis for creating an electronic textbook for future teachers of mathematics.

ЧИСЛОВЕ МОДЕЛЮВАННЯ ЯК ОДНА ІЗ СКЛАДОВИХ ФУНДАМЕНТАЛЬНОЇ МАТЕМАТИЧНОЇ ПІДГОТОВКИ ІНЖЕНЕРІВ

The article investigates the problem of mastering the skills of numerical modeling by students of engineering specialties while studying the course of higher mathematics. Much attention is paid to the formation of creative thinking of students in the process of learning mathematics. The main components of the methodological system using SCM in lectures, practical and individual classes. Using SCM MathCAD, Maple and others, the student can abstract from the technical details of programming, features of the operating system and focus on analyzing the features of such concepts as conditionality of the problem, stability of the method, evaluation of calculation results. Professional orientation of training future professionals with good personal qualities and is seen as creative, full of modern knowledge in mathematics and computer science. The given examples of tasks can be used for independent solution by students with a high cognitive level. Forming  of maintenance of course of higher mathematics is offered to carry out in such directions: strengthening  of role  of numerical  methods  and  their  realization after dopomogo of SKM; the use of mathematical design is during untiing of the applied tasks; capture students mathematical semantically professional by knowledges, necessary for the analytical  and numerical design of practical engineerings tasks, creation of own libraries of user of software products. Main abilities and skills which can be formed for students during computer-integrated employments after higher mathematics and elements of numerical design are selected: ability to use necessary programmatic facilities in the environment of SKM; ability to compare results in the different forms of presentation (analytical and graphic presentation); ability to use new possibilities, which are given computer technologies, based on the use of environment of SKM; ability to design programmatic facilities of the first in the environment of SKM; ability to design in the environment of SKM programmatic facilities of the first level of complication for untiing of educational and subject tasks.

Teaching and Practice of Ideological Politics in Higher Mathematics Course —Based on Teaching of “Law of Large Numbers”

Higher mathematics; Law of large numbers; Ideological and political education

ЗАСТОСУВАННЯ СКМ MAPLE ДЛЯ ПОБУДОВИ 3D ГРАФІКІВ В ЗАДАЧАХ ОБЧИСЛЕННЯ ОБ’ЄМУ ФІГУР

Every year the number of works devoted to the search for methods and techniques for introducing computer mathematics systems for teaching higher mathematics is increasing. The main place among them is occupied by the Maple computer mathematics system, which is one of the leaders in universal systems and allows the user to use an intelligent environment for mathematical research. This paper emphasizes that the most valuable developments of a theoretical and applied nature on the use of computer mathematics systems in teaching higher mathematics should include materials related to improving visibility, as well as the formation of students' skills and abilities in solving typical problems of higher mathematics. The problems of introduction and adaptation of the Maple computer mathematics system in the educational process of the institu-tion of higher education in teaching the course of higher mathematics are considered. The use of the Maple computer mathematics system provides an oppor-tunity to optimize the educational process and activate the organization of students' independent work to consolidate the educa-tional material. The paper adapts the use of the Maple computer mathematics system graphics package capabilities to build 3D graphics in order to improve clarity in the tasks of calculating the volume of a spatial figure. Part of the mathematical apparatus and the developed code fragments in the Maple computer mathematics system make it possible to automatically obtain the line of intersection of graphs of functions, build the corresponding surfaces and figures when solving typical problems of higher mathematics. The paper substantiates the need to design educational problems of a new type, taking into account the need to use modern information and communication technologies for solving them, in particular Maple computer mathematics systems.

APPLICATION OF IGS GEOGEBRA IN THE STUDY OF HIGHER MATHEMATICS BY STUDENTS OF TECHNICAL INSTITUTIONS OF HIGHER EDUCATION

Introduction. Recently, the use of various packages of computer mathematics systems to improve the efficiency of the educational process has become relevant, especially during distance learning. One of the most promising areas in the technology of higher mathematics is the introduction and development of interactive geometric environments, and, as a consequence, to identify effective ways to use them in the educational process. The use of software is especially relevant in higher mathematics classes. The above software packages help to perform calculations in a short time, allow you to build graphs of functions and three-dimensional bodies and more. Purpose. Possibilities of application of the interactive geometric environment GeoGebra for the purpose of the organization of research activity of students of technical specialties during employment in higher mathematics are considered Methods. The article substantiates the relevance of using the cognitive-visual approach in the process of teaching students of technical specialties of higher mathematics in institution of higher education, considers the essence of this approach, as well as its implementation in teaching higher mathematics using educational software products using interactive geometric environment GeoGebra Results. Possibilities of separate software products of professional and educational purpose are considered, advantages of the interactive geometrical environment GeoGebra are listed, the example of its use in the course of training of higher mathematics of students of technical institution of higher education is given, namely: possibilities of application for the purpose of organization of research activity of students. in particular, remote, and the use of second-order image curves, which allows the visualization of geometric objects under study. Also, the stages of the process of preparation for the application of the interactive geometric environment GeoGebra were identified. Originality. For the first time with students majoring in 151 Automation and Computer-Integrated Technologies, we used distance learning to study one of the problems of solving problems using the interactive geometric environment GeoGebra. Conclusion. Solving our geometric problems, performed using the interactive geometric environment GeoGebra, allows students to see not only the visual construction of geometric objects, but also to form elements of the algorithm for solving practical problems in analytical geometry and lay the foundation for calculation the length of the arc, the area of the figure, the volumes of bodies in parallel section and the body of rotation, the surface area of the body of rotation, which is discussed in the next section "Application of the definite integral". The dynamic capabilities of GeoGebra to study the change in the shape of the projections of the spatial curve when changing the parameters in the equations of surfaces. The use of GeoGebra to solve problems in the course of higher mathematics in technical free economic education increases the motivation and interest of students, creates conditions for the formation of research skills, prepares students for the effective use of ICT in their future careers.

К ВОПРОСУ О РАЗВИТИИ ПРОФОРИЕНТАЦИИ ПРИ ПОЛУЧЕНИИ ПРОФЕССИИ В ЖЕЛЕЗНОДОРОЖНОМ ВУЗЕ

Currently, career guidance activities are not given enough attention. We believe that these activities should be carried out for students of general education schools, starting from the eighth grade, so that students have the opportunity for self-determination within their future profession. The paper shows the possibility of preparing a modern specialist for professional activity by means of higher mathematics, namely, the introduction of professionally oriented tasks into the learning process. Problems of this type are understood as mathematical problems with practical content, revealing the applications of mathematics in various areas of work, which prepares for a future profession. In addition, the professionally oriented tasks proposed by the authors can be used as an effective tool to increase motivation in the study of the discipline "Mathematics". The presented article describes the need for the use of professionally oriented tasks in the process of studying at a railway university on the example of studying mathematics when studying in the specialty 23.05.03 "Rolling stock of railways", specialization "Locomotives" at the Samara State University of Railway Communications. Since some of the graduates who graduated from a railway university in the specified specialty begin their professional activities as an assistant driver, we will dwell in more detail on the description of the profession of a driver, considering it from the point of view of the need to gain knowledge from a higher mathematics course.