Mathematical Disciplines Research Articles

Медиакомпетентность в системе научно-исследовательской работы студента

The article describes the experience of forming the media competence of a future engineer when students perform research work. The methodological basis of the research includes competence-based, personcentered and system-activity approaches. The research methods are: analysis of scientific literature, defended dissertations of media educators, generalization of practical experience in the implementation of media education technologies, observation. The authors of this article consider media competence as the key competence of an engineering and technical specialist. This is due to a number of reasons. Firstly, under the conditions of modern society, the role and importance of the engineering education system, as the engine of the national system of the innovative economy of Russia, is increasing. Secondly, the digitalization of society poses the problem of the correspondence of professional education to the needs of employers. Thirdly, the co-evolution of the information and educational space makes the task of forming and developing the media competence of future engineers urgent, which is the subject of media education research. The authors consider the essence of the concept “media competence”, which is the subject of research, and then present the authors’ definition of the notion “media competence of a future engineer”, which forms the basis of the study. Relying on a competence-based approach, integrating media education and research activities, the authors reach their aim within Irkutsk State Transport University, where the student’s research work is provided for in the curriculum and is one of the important stages in the training of a young specialist. Carrying out the leadership of the research work, the teachers of the Department of Mathematical Disciplines resort to the help of traditional and non-traditional forms of scientific work. The methodology of organizing and managing the student’s research work is carried out in several stages. The first stage of starting work is the choice of a leader and type of work, the selection of a research topic for a student. The next stage is the organization of the process of introducing media education into educational activities, regardless of the choice of the type of work. The further stage is directly the work of the research participants, which is considered on the example of the types of work: an essay, an abstract, writing an article and making a presentation at a conference – this is the final stage. When working in any direction, the researcher has to resort to the help of a media text, to consider different points of view on the chosen research problem. There is a high probability of encountering unverified information. Therefore, one of the tasks of the leaders is to teach research participants to choose verified, reliable information from a huge stream of media texts in order to apply it to research in order to fill and enrich their scientific work. The process of forming media competence is quite protracted, it requires regular monitoring by the leader and diagnostics. The expected result of all this work is the media competence of a future engineer being formed.

Математическая дисциплина мысли в свете фундаментальной онтологии Хайдеггера

The key question in the mathematical discipline of thought is the question of the foundations of mathematics. To a large extent, this question boils down to the question of logic, which is guided in the construction of the architec­ture of mathematics (N. Bourbaki). Most mathematicians, with the exception of intuitionists, rely in their work on classical, extensional, logic, expressed through mathematical terminology. Here is the construction of axiomatic systems, and methods of their formalization, and metamathematics. Since this approach to the foundations of mathematics reveals the incompleteness of any mathematical system, including in itself, at least, elementary arith­metic, then this leads to the conclusion (K. Gödel) that the logic used in mathematics is insufficient to claim to substantiate the mathematical disci­pline of thought as such. The article shows that this deficiency can be filled when creating a complementary dialectical logic, the central operation of which is the operation of dialectical negation, called privation. Privation is borrowed from the fundamental ontology of Martin Heidegger, together with its inherent images of Being and Nothing.

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.

The experience in teaching mathematical disciplines using information technologies

The presented material is devoted to the long-term experiment on the introduction of computer technologies in the process of teaching students of technical (and not only technical) specialties and lectors in various courses and disciplines at MAI. The experiment was carried out in teaching completely different courses, such as: combinatorial analysis, operations research, computational mathematics, as well as in the course of information technology, designed to improve the qualifications of teachers.

Embodied mathematical practices in (re)designing board games in a linguistically diverse classroom

ABSTRACT In this article, we discuss embodied mathematical practices in the context of learners’ board game (re)design activities. By focusing on redesigning a board game as a pedagogical approach, rather than designing one from scratch, we intended to limit the vast creative design possibilities and engage learners more deeply with the discipline of mathematics. We conducted a design-based research project in a culturally and linguistically diverse Canadian school. Our video analysis identified embodied discourses wherein a student with limited English language proficiency came to be a designer of a board game, while meaningfully engaging in mathematics learning. Our findings demonstrate how the conversations between a newly arrived immigrant student and the teacher in the process of redesigning an existing board game helped the student fully participate in the classroom practice, maximizing the available cultural and linguistic resources.

EDUCATIONAL AND SCIENTIFIC LABORATORY OF INNOVATIVE EDUCATIONAL SOLUTIONS IN PRIMARY EDUCATION: PEDAGOGICAL TRENDS AND CREATIVE IDEAS

The experience of educational and scientific laboratory of Innovative educational solutions developed on the chair of primary education, natural and mathematical disciplines and teaching methods of PNPU named after V. G. Korolenko has been generalized and its brief haracteristic activity has been presented. The basic principles of the laboratory functionality which determine its place and role in the system of training specialists in the field of primary education have been distinguished. Emphasis is placed on the fact that the laboratory is an open platform for creating the preconditions for an effective combination of education, science and innovation. It has been pointed out that the laboratory environment meets the modern requirements of the new Ukrainian school regarding the organization of the educational space for junior students. The model variants and their use methods of the primary classroom hubs equipping built on the principles of pedagogical ergodesign have been illustrated.

Determining the STEM Discipline Identities of Female Students

Different meanings can be attributed to STEM education, which is the trend approach of recent years, by societies and individuals. In order to understand the STEM approach in the mind of the individual, it is necessary to learn the perspective of STEM education or STEM disciplines. It is necessary to determine the STEM identity of female individuals, especially because of the differences between men and women who prefer STEM professions or their perspectives on STEM disciplines. In this research, it is aimed to determine the identity of the disciplines of Science, Technology, Engineering and Mathematics in female individuals. Within the scope of this aim, 125 female students studying child development were reached. Data were collected online with a short-answer form. In this form, the reasons for being a scientist, technologist, engineer or mathematician were asked. As a result of the analysis of the data, it is understood that almost half of the participants stated that they wanted to be scientists and engineers, and nearly half of them stated that they could be technology experts. In addition, it was determined that very few of them believed that they could be mathematicians. When the reasons for these data are examined, it is understood that they determine their identities in these disciplines due to reasons such as love, interest, curiosity, research, intelligence, willingness, and using their imagination. Likewise, it is understood that they cannot choose these disciplines due to reasons such as fear, anxiety, competence and unwillingness.

Distance educational technologies in teaching mathematical disciplines to students of pedagogical universities

The global pandemic of 2020 and 2021 was a turning point for the higher education system. Higher educational institutions should be ready to switch to a distance learning format at any time. This article attempts to discuss the problems that arise in teaching mathematics to students of a pedagogical university when introducing distance educational technologies and recommendations for solving these problems. To that end, a survey was performed conducted at the Faculty of Physics and Mathematics of the Mordovian State Pedagogical University. The research process comprises theoretical methods (studying and analyzing scientific, methodological, and educational literature). As a result, the analysis of modern distance educational technologies for students ' communication with a teacher is presented and the problems of transition from traditional to distance learning are identified. Some recommendations on health care in the distance learning format of mathematical disciplines are highlighted.

ПРОЄКТНІ ІННОВАЦІЇ В СИСТЕМІ STEM-ОРІЄНТОВАНОГО НАВЧАННЯ СТУДЕНТІВ ТА УЧНІВ

The concept of STEM implementation in the educational sector of Ukraine as a means of forming and developing skills of research and engineering, invention, entrepreneurship, early professional self-determination, popularization of scientific, technical and engineering professions is analyzed. One of the indicators of readiness of future specialists for innovation is their ability to create innovative projects independently. Therefore, the problem of development and use of innovative STEM-projects to ensure the education of scientific and applied (professional) direction is relevant. The purpose of the article is to outline the concept of innovative activity of students and pupils, to determine the criteria of efficiency of project activity in the system of STEM-oriented learning on the example of the developed STEM-project. As an example, we consider the STEM project, which can be performed on the basis of a modular set of “Smart Home”. The purpose of the technological STEM-project “Smart Home” is the interest of pupils and students in innovative technologies, natural and mathematical disciplines, development of critical thinking, ability to apply scientific and technical information, formation of competence approach and professional mobility, motivation to consciously choose a future profession. The modular set implements the current functions of the “Smart Home” system and is a model of a two-storey building with a garage. The set is developed on the basis of block-modular technology. Each design is an independent technical solution implemented using microcontroller platforms, sensors, servos and other components. Pupils or students under the guidance of the teacher independently assemble the structure, guided by the methodological materials and technical characteristics of the project. In the process of work, they process theoretical material, install electronic components, study technologies for programming microcontroller platforms, perform full configuration of all components and mechanisms of the structure. Key words: STEM-direction, innovation, programming, design activities, platforms Arduino.

MATHEMATICAL COMPETENCES AS A BASIS OF PROSPECTIVE ENGINEERS TRAINING IN HIGHER TECHNICAL EDUCATIONAL INSTITUTIONS

The article analyzes theoretical and methodological basics of formation of mathematical competences as a key condition of training prospective engineers in higher technical educational institutions. The study considers the problem of prospective engineers’ mathematical training implementation based on the competence approach aiming at future activity in industrial production field on the level of world standards. On the basis of the analysis of modern concepts essence, purpose, and management of prospective engineers’ training in higher technical educational establishments from the perspective of the competence approach realization are reconsidered. Mathematical education is considered as a basis for the training of technical specialists. Despite the fact that the issue of professional development of higher technical educational institutions students was given considerable attention in the research of the scientific community, the problem of forming their mathematical competences remained insufficiently covered and was not the subject of a dedicated special research. The aim of the article is to study the theoretical and methodological foundations of prospective engineers’ mathematical competences formation as a basis for their professional training. Theoretical research methods were used during research, namely: study and analysis of psychological-pedagogical, legal and special literature on the researched issue; analysis of state educational standards, programs, textbooks and teaching materials. The specifics of teaching mathematical disciplines in higher technical educational institutions are determined. The basic techniques and principles of realization of the competence approach in education are reviwed. The stages of prospective engineers’ professional competence formation are characterized. The article focuses on personal values of a prospective engineering specialist in the process of professional competence formation. Procedural, technological, logical, research and methodological components of mathematical competence of technical specialists are described. The article proves on the effectiveness of prospective engineers’ mathematical competences formation in order to train highly qualified specialists of technical field in higher technical educational institutions.

Possibilities of using information technologies in teaching mathematics (on the example of a functional-graphic method for solving equations)

The article is devoted to the methodology for the formation of a functional-graphic method in students using information technologies. The article describes the theoretical foundations of teaching the functional-graphic method for solving equations; methodological recommendations for the formation of students' actions that are adequate to this method with the use of software. To study the possibilities of using information technologies in teaching mathematical disciplines to students, to determine their effectiveness, the study was conducted at the Faculty of Physics and Mathematics of the Mordovian State Pedagogical University named after M. E. Evsevyev. The research process involved theoretical methods (the study and analysis of scientific and methodological, educational literature). Empirical methods were also used – monitoring the educational activities of students, the professional activities of teachers, surveys of the specified contingent were conducted.

Examination of the electronic educational resources accessibility on the university Moodle platform

The purpose of the article is to assess the accessibility of electronic educational resources (EER) published in the university Moodle Learning Management System (LMS). The analysis involved 22 EERs in mathematical and information technology disciplines, located in the Moodle LMS of the V. I. Vernadsky Crimean Federal University. The examination algorithm included analysis using the Web Accessibility Evaluation Tool (WAVE) and expert analysis of web accessibility using visual, auditory and manual methods based on 89 checklist attributes. In the result of the analysis, multiple accessibility errors of the Moodle platform and the EERs hosted on it were found. The most serious platform problems include: lack of compatibility with text browsers; errors of reproduction by screen readers; errors of content reproduction on mobile devices. The list of accessibility errors made by the authors of EERs includes: incorrect design of hyperlinks (22.7 % of the EERs); lack of subtitles (13.6 %), transcripts (22.7 %), synopses of video lectures (27.3 %); lack of alternative descriptions for figures (68.2 %); time limit for tests (9.1 %); lack of special markup for mathematical notation (36.4 %) and program code (13.6 %), etc. Results of the survey show need in training of EERs’ authors in technologies for developing accessible educational web content. It is advisable to familiarize web developers deploying an LMS at universities with the basics of web accessibility, LMS accessibility functions and modules in order to select the most suitable platform, determine and install the required set of accessibility tools. Before launching all EERs should be subject to mandatory examination for compliance with the web accessibility guidelines.

USE OF COMPUTER TOOLS TO DEVELOP MOTIVATION OF STUDENTS TO STUDY MATHEMATICS: CRITERIA OF EFFICIENCY

The article considers the problem of development of cognitive activity of students in mathematics lessons. The peculiarities of the use of the formative system of assessment in the process of teaching mathematics with the use of computer tools in the context of the tasks of personality-oriented learning. The main risk factors for increasing the mathematical anxiety of students are identified. The pedagogical factors of motivation development and increase of interest in learning, development of mathematical thinking and reduction of mathematical anxiety due to the development of methods to increase the clarity of learning and cognitive activity of students related to the use of computer tools are substantiated. The criteria are substantiated and the indicators of assessment of the development of cognitive activity of students of 7‒9 grades of gymnasiums in the process of teaching mathematics with the use of computer tools are distinguished: motives of students learning at school; interest in studying the study of mathematics (algebra and geometry); success in the study of mathematics (algebra and geometry); motivation to study mathematical disciplines; mathematical anxiety. A method of assessing the impact of the use of computer tools to study certain topics and sections of mathematics in grades 7‒9 in general secondary education, which will increase the motivation of students to study the subject and reduce the level of mathematical anxiety of students. The results are presented and the dynamics of the indicators of the experimental influence of the use of computer interactive tools on the motivation of students to study mathematics is analyzed.
 Keywords: personality-oriented learning; mathematical disciplines; mathematical anxiety; pedagogical conditions; mathematics teaching aids; motivation to study mathematics; interactive computer learning tools; success in the study of mathematics.

The experience of implementing STEM-education in the study of natural and mathematical disciplines by students of pedagogical specialties

This article describes the necessity of introducing STEM-teaching ideas into the educational process of the students of pedagogical specialties in terms of the overall need for forming a creative and imaginative personality. The plan of project activities, which can be used during the self-study of natural and mathematical disciplines is shown. The paper demonstrates the motivation of students to research activities due to the accumulation of a well-tested theoretical basis and experimentally obtained material.

Three Foci of Mathematic Teachers' Considerations in Evaluation of School Students' Achievements

As part of efforts to improve the quality of mathematics' teaching and evaluation, we examined the focus of math teachers' considerations in evaluating students’ achievements, as well as the links between these focuses, regarding differences between students and the validity and reliability of assessment methods and examinations. Based on the categorization of issues that concern math teachers while assessing their students, a self-report quantitative-questionnaire was constructed and validated. The questionnaire included three foci of consideration for mathematics evaluation: considerations regarding evaluating learners, considerations regarding the choice of assessment methods, and assessment considerations that are unique to mathematics; positive, high, and significant were found between them. The main conclusion is that math teachers aspire to evaluate their students on the basis of a broad picture, that considers the needs of students studying mathematics as a unique discipline, the available assessment methods and their ability to adapt them to a valid and reliable assessment in mathematics, and the overall need to focus on the challenges and difficulties which are unique to assessing the discipline of mathematics. The findings also strengthen the claim that assessing math learning has unique considerations that are distinguished from assessment considerations in other disciplines.

Forms and Means of Information and Communication Support for Students of Mathematics in the Pedagogical Institution of Higher Education

The article is devoted to the forms and means of information and communication support for students of mathematics in the pedagogical institution of higher education. The main purpose of the article is to define and characterize the forms and means of information and communication support for teaching mathematics in a pedagogical institution of higher education. To achieve this goal, the authors used the following research methods: analysis and generalization of scientific and methodological sources, government documents on the research topic for theoretical justification of the problem, modeling, synthesis of data. The results. The introduction to this article presents a theoretical analysis of educational technologies, in particular, highlights the «information technology» and defines the essence of this concept. The authors define the pedagogical goals of the use of information technology, as well as provide a classification of pedagogical software. The article highlights and substantiates computer training programs used in higher education institutions in the study of some disciplines, which by their purpose are divided into control (tests, questionnaires, etc.), reference and information (databases, dictionaries), modeling and electronic textbooks. In the process of analysis, the means of information and communication support for teaching mathematics in a pedagogical institution of higher education are identified: computer training and control programs (electronic textbooks, workshops, test systems, simulators), expert systems, electronic libraries, telecommunications, e-mail, teleconferences) and multimedia systems. Conclusions. The authors proved that spreadsheets and integrated mathematical packages can also be widely used in teaching students of mathematical disciplines. Integrated mathematical packages such as Matlab, MathCad, Maple, Mathematica are singled out and briefly described. It is noted that one of the leading types of ICT is computer telecommunications, in the system of mathematics education the use of the following types of computer telecommunications as teleconferencing, e-mail, electronic bulletin board and other Internet capabilities is quite possible. So, modern MultiMedia tools allow you to create a variety of information environments that increase the level of emotional perception of information, and to develop the ability to implement various forms of independent activities for information processing.

Mining and crafting a game to teach research methodology

Gamification is used in various disciplines to elucidate complex problems. These disciplines are typically the science, technology, engineering, and mathematics disciplines. It is not known whether gamification can be used to teach research methodology. MinecraftEDU was used to create games to explain the various concepts within research methodology. The purpose was to force students to engage with the theory and literature and create a game based on their insights. An analysis of the students’ feedback indicates that they preferred this method to more traditional lectures. Although they experienced initial problems with the MinecraftEDU environment, the overall experience was perceived as positive. The results indicate that gamification can be used to teach research methodology, but more research is needed to determine how game elements can be incorporated into a research methodology game.

Student ways of thinking in STEM contexts: A focus on claim making and reasoning

AbstractSTEM education should be grounded in our knowledge of how students think in STEM‐focused learning environments. However, little is currently known regarding specific types of thinking in these contexts. We explore the theoretical notion of STEM Ways of Thinking (SWoT) in interdisciplinary learning situations. Our primary focus is not on the curricular content of STEM education, but rather on the nature of the cognitive activity at play during STEM‐focused activity. We give particular focus to students’ claim making and reasoning during interdisciplinary STEM activity. Our framework focuses on the disciplines of science, engineering, and mathematics. While these disciplines have vastly different practices and epistemologies, we argue that claim making and reasoning provide an avenue for considering student thinking at their intersections. A brief literature review of SWoT is provided that illustrates trends and limitations amongst current theories and studies. After a detailed discussion of our own theoretical perspective of SWoT, we provide an illustrative learning segment to explore the explanatory and analytic power of our theoretical perspective. Implications of our work on curriculum and instruction are provided.

Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates

For scientists and engineers, the Laplacian operator is a fundamental tool that has made it possible to carry out important frontier studies involving wave propagation, potential theory, heat conduction, the distribution of stresses in a deformable solid and quantum mechanics. Knowing, understanding, and manipulating the Laplacian operator allows us to tackle complex and exciting physics, chemistry, and engineering problems. In this paper, contained in the Special Issue “Mathematics as the M in STEM Education”, we present an instructional derivation of the Laplacian operator in spherical coordinates. Our derivation is self-contained and employs well-known mathematical concepts used in all science, technology, engineering, and mathematics (STEM) disciplines. Our lengthy but straightforward procedure shows that this fundamental tool in mathematics is not intractable but accessible to anyone who studies any of the STEM disciplines. We consider that this work may be helpful for students and teachers who wish to discuss the derivation of this vital tool from an elementary approach in their courses.

The Instuments for the Development of Universal Logical Skills of Analysis and the Culture of the Transmission of These Skills in the Process of Professional Training of Mathimatics Teachers

General logical universal learning activities (analysis, synthesis, comparison, etc.) in studies of the theory of development of universal learning activities are often represented by generalized formulations such as «text analysis», «analysis of the formulation of a theorem», «synthesis of information», etc. This approach does not allow to evaluate the level of complexity of a cognitive action, to determine its specificity, and to distinguish the levels of possession of this cognitive action. The article deals with the approach to forming the general logical action of analysis, which is based on the concept of funding, developed by E.I. Smirnov, V.D. Shadrikov. The methodological principle of the research is associated with various aspects of the system-activity and competence-based approaches to the organization of teaching students of pedagogical specialties. The aim of the article is to develop an approach to the design of teaching tools aimed at the formation of the general logical action of analysis. Results. The article describes the preparatory stage of the implementation of the concept of funding general logical cognitive actions in the training of students of pedagogical direction. The approach to the level differentiation of cognitive action of analysis is proposed. The types of analysis and their manifestations in mathematical and socio-humanitarian disciplines are considered. In conclusion, the necessity of differentiating the analysis in the organization of funding of this action is justified.