Mathematical Training Research Articles

Restoration and transformation of high-tech machine building industry by implementing the principles of the CALS-concept in the context of Industry 4.0 development

The object of this study was the processes of restoration and transformation of high-tech engineering using the principles of Industry 4.0 and CALS-concept. The problem of identifying ideas, concepts, tools and developing the principles of their application for the restoration and transformation of high-tech engineering has been solved. It is shown that the restoration of high-tech engineering, in countries affected by hostilities, is advisable to carry out using the CALS concept. The top priority CALS technology and systems have been identified. An opportunity to jump from Industry 2.0 to Industry 4.0. for countries in which mechanical engineering has suffered greatly as a result of hostilities has been shown. The principles of restoration and transformation of high-tech engineering by implementing the principles of CALS concept in the context of Industry 4.0 development have been developed. The infrastructure of the participants of the life cycle of machine-building products is proposed. A model for optimizing the production program of the defense-industrial complex has been built. The model takes into consideration the nonlinearity associated with the optimization of the production program, as well as the stochastic nature of changes in the model parameters. An adaptive approach is proposed that makes it possible to optimize the production program according to the model even for specialists without special mathematical training. The priorities of post-war reconstruction of high-tech engineering have been defined. This study will make it possible to transform and restore the machine-building industry destroyed as a result of hostilities as soon as possible. The condition for the practical use of this study is to stop the hostilities

TO THE METHOD OF STUDYING THE BASICS OF SPECIAL THEORY OF RELATIVITY

Special Theory of Relativity (STR) is a fundamental physical theory that underlies modern physics andhas enormous worldview potential. At the same time, in the process of teaching (studying) the elementsof STR in school and higher education institutions face a number of problems. These problems areprimarily related to the complex mathematical apparatus that describes it; consideration of imaginarymodel representations that do not really exist in nature; formation of the concept of “event” anddistinguishing under different initial conditions of the concepts of “relative”, “portable” and“absolute” movements, etc. In this regard, it is important to find ways to improve the methodology ofstudying the elements of STR, which is what this article is about.The article offers one of the tested options for studying the main provisions of the special theory ofrelativity in the general course of physics, which is taught in the programs of physical andmathematical specialties of pedagogical universities. The main approaches on which the proposedmethodology is based are the reference to the principle of conformity in the transformation of physicaltheories from their partial cases to more general ones. In this regard, the limits of application ofclassical Galilean-Newton mechanics in the plane of absolutization by this theory of categories of spaceand time, the simultaneity of events in a different frame of reference, the instantaneous transmission ofinteractions between bodies at a distance, etc. are analyzed.The physical meaning of Einstein’s postulates, which underlie the theory of relativity, regarding thespecial status of the speed of light propagation as a natural phenomenon is clarified. On the basis ofthese postulates, the formulas of the Lorentz coordinate and time transformations are deduced. Aconsistent, detailed derivation of the formula for the transition coefficient from the Galilean coordinateand time transformations (for the transition from one inertial frame of reference to another) to theLorentz coordinate and time transformations, which reflects their relativistic content, is given. Theestablishment of these formulas is based on the mathematical apparatus, which corresponds to the levelof school mathematical training of participants in the educational process. Based on the obtainedresults on the formulas of Lorentz transformations, the relativity of the concepts of “duration ofevents”, “time intervals”, “changes in size and shape of bodies”, etc. is demonstrated mathematically,if they are considered in reference systems that are in motion relative to each other.
 Keywords: classical mechanics; reference system; the principle of relativity; space-time invariant;coordinate and time conversion.

Modeling of Additional Professional Educational Programs to Overcome Subject Deficits of Mathematics Teachers

Modern challenges of the system of mathematical training of schoolchildren cause the growth of subject professional deficits of a mathematics teacher. However, the question of how to identify and level these deficits remains open. This makes it possible to state the problem of research, which consists in finding effective methods for overcoming the subject deficits of a mathematics teacher. The purpose of the article is to determine a modern approach to modeling additional professional educational programs for overcoming subject deficits of mathematics teachers and to develop a structural-meaningful model of an additional professional educational program “Subject deficits of a mathematics teacher”. Methodology. The methodological basis of the study was a competency approach as the basis for structuring the professional competencies of a mathematics teacher; a variable-modular approach as a constructive basis for structuring the model of an additional professional educational program; a systematic approach as the basis for diagnosing the professional deficits of a mathematics teacher; professional standard of a teacher (Module “Subject training. Mathematics”), the requirements of the federal state educational standard for the mathematical training of students in a comprehensive school. Methods of analysis of special literature and regulatory documents, pedagogical modeling and design were used. Study results. The conceptual foundations of modeling an additional professional educational program to overcome the subject deficits of a mathematics teacher have been identified. A structural model of the additional educational program “Subject deficits of a mathematics teacher” is presented. Conclusion. A distinctive feature of the additional educational program presented in the article “Subject deficits of a mathematics teacher” is that it consists of modules that design the continuous process of professional growth of a mathematics teacher in the context of targeted, personalized assistance to practicing teachers, through the selection of variable program modules.

Establishment of interdisciplinary connections between mathematical disciplines in the context of high-quality professional training of a future cybersecurity specialist

The problems of qualitative training of a specialist in the specialty 125 "Cybersecurity" are considered in the work. The importance of the aspect of mathematical training is emphasized. Factors that ensure proper professional training of students and the formation of their defined MES integrated competence. The international experience of training cybersecurity specialists is reviewed. It is noted that in most US universities, the course of discrete mathematics, the course of algorithms and their mathematical implementation at the bachelor's level is a mandatory part of obtaining a degree in computer science.

Designing a didactic fairy tale as a key to advanced Physics and Mathematics training in primary schools

The relevance of the chosen research topic stems from its development outcomes, which aim to resolve contradictions between society's needs for personality-oriented training in Physics and Mathematics basics at comprehensive secondary school and the insufficient basic (necessary and sufficient) conditions to provide this in primary grades. Teachers also lack a structured and academically supported method of immersing pupils in a didactic fairy tale atmosphere. The primary goal of the study is to present the author's conceptual vision of the essence and principles of didactic fairy tale creation in order to transform it into a basic instrument for teaching Physics and Mathematics to 1st–4th-grade students.

Didactic fairy tale designing as a key to proactive training of Physics and Mathematics at primary schools

Relevance of the selected research topic is due to its development results aiming to resolve contradictions between society’s needs for personality-oriented training of Physics and Mathematics basics at comprehensive secondary school and the inadequate basic (necessary and sufficient) conditions to provide this in primary grades. Teachers also lack for a systematic and scientifically substantiated practice of immersing their students into the didactic fairytale environment. The research primarily aims to reveal the author’s conceptual vision of the essence and principles of didactic fairy tale designing in order to convert it into a basic tool of Physics and Mathematics training to 1st – 4th grade pupils.

Освітня складова проблем кадрового забезпечення рику інформаційних технологій

The problems of insufficient supply of qualified personnel for Ukrainian IT enterprises and the industry as a whole have been studied. The interrelation of regional indicators of specialists in the field of training and the quality of graduates of IT specialties of formal higher education is analyzed. The studied problem in the coming years will be exacerbated by: reducing the quality of mathematical training in secondary education, in particular related to quarantine measures caused by the COVID-19 pandemic and the destruction of a significant part of the infrastructure, including an educational infrastructure in a number of regions of Ukraine caused by the military aggression of the Russian Federation, as well as the forced emigration of school-age youth. The connection between the availability of a sufficient number of specialists in the specialty and the number of high-quality institutions of higher education that provide specialized educational services in the reagion is analyzed. The proposals to the heads of IT enterprises and institutions of higher education, which train future IT specialists, unite projects, are substantiated, namely: to create joint centers for the development and updating of curricula and programs; to conduct free refresher courses for scientific and pedagogical workers; to create laboratories for high-quality information support of the educational process; to provide financial support to the technical base of the institutions of higher education. These measures can enhance the provision of quality educational services through integration, rather than coexistence, of formal and non-formal education. Reforming specialized higher education is becoming an urgent need. Success requires the involvement of practitioners in the educational process on the one hand and the involvement of research and teaching staff in the development of projects occupied by IT companies in the region. The top management of the companies with the highest qualification for staffing all age categories of the IT market of Ukraine needs to monitor the feasibility of investments in the development of non-formal "post-academic" education and pay attention to the need to involve educators from the basic level. The results of the study indicate low labor mobility. The vast majority of graduates of IT specialties are looking for a job in the regions where they received higher education, or move to the capital Kyiv. The only exception among all regional centers in the city of Ternopil. Based on the analysis, recommendations for the top management of Ukrainian IT companies are formulated. In case you need to quickly increase the size, the most attractive is Kyiv and Lviv. However, the location in Kyiv is a competitive environment that affects the high cost of doing business. As a result of the large-scale invasion and destruction by the Russian occupiers of KhNU. Karazin and a number of other educational institutions, in the coming years the widespread development of IT business in the Kharkiv region is becoming unpromising. The authors of the study suggest that IT business management should pay special attention to Ternopil. In Ternopil, due to the activities of the IT cluster and its cooperation with the Free Economic Zone, the number of IT specialists is quickly increasing and low competition between companies leads to a lower cost of doing business

USING PARTIAL SEARCH AND SEARCH TRAINING METHODS IN THE PROCESS OF STUDYING MATHEMATICAL COURSES IN AGRICULTURAL UNIVERSITIES

The need to provide agricultural students with knowledge of mathematics, skills and abilities necessary for mastering professional courses, successful professional activities, including research, requires adjusting the content of the mathematical training of future agricultural specialists, which, in turn, requires the use of specially selected methods teaching mathematical courses. At the same time, domestic pedagogy lacks research on the definition of teaching methods, which are based on in the process of studying mathematical disciplines in agricultural universities. The purpose of the study is a theoretical substantiation of the need to use partially search and search methods, on which the process of studying mathematical courses should be based, taking into account the requirements of the agro-industrial complex, and demonstrating the application of these methods with examples. Research methods: theoretical (analysis, systematization and generalization of pedagogical and psychological research, legislative and regulatory documents), empirical (pedagogical observation of the educational process, analysis of work experience). It is noted that in order to promote the formation of research knowledge, skills and initial research experience of agricultural students, special attention is paid to partially exploratory (heuristic) and exploratory (research) teaching methods. It is demonstrated that the use of a partially search method of teaching contributes to the transition of knowledge into persuasion, forms the ability to independently acquire knowledge, contributes to the development of logical thinking, and fosters interest in research activities. When applying the search method in the educational process, students show initiative, independence, creative search in research activities, and the development of the ability for creative activity occurs. Examples of using partially search and search methods are given. Conclusions are drawn about the need to use partially search and search methods in the process of studying mathematical courses in agricultural universities.

Interrelation of levels of mathematical literacy in conditions of distance learning

Mathematical literacy and knowledge play a significant role in the formation of competencies. The purpose of the study is to determine the levels of mathematical literacy and their dependence on the type of thinking and the level of creative abilities in a distance learning environment. The research objectives are as follows: assess thinking (by type) and creativity; assess mathematical literacy; and determine the relationship between the level of mathematical literacy and thinking/creativity indicators. In line with this, it was established that the ratio of the spread in the values of the dependence of mathematical literacy on the basic forms of thinking (objective, symbolic, sign) is high. In practice, the study findings can become a starting point for further research in the field of critical thinking or may be applied during the development of mathematics training courses for students.
 
 Keywords: correlation analysis; creativity; mathematical literacy; regression analysis; school; thinking skills.

Markets for Flexibility: It Don’t Mean a Thing If It Ain’t Got That Swing [Book Review

This book proposes a new wholesale electricity market design paradigm, with a focus on North America, for centrally managed electricity markets that are based on the novel concept of swing contracts. The author, a professor at Iowa State University, has been working on electricity market design and agent-based computational economics for many years. Her extensive academic, research, and industry experiences, as well as her training in both economics and mathematics, make her highly qualified to provide fresh thinking in this important area. The book proposes the adoption of swing contracts between the system operator and relevant resources to provide flexibility. This flexibility is represented in the form of future availability of dispatchable power paths (“reserve”) with prespecified physical attributes and economic attributes (for pricing purposes). The book contains rigorous mathematical descriptions of the proposed mechanism and implementations.

ОСОБЕННОСТИ ИСПОЛЬЗОВАНИЯ АКСИОМАТИЧЕСКОГО МЕТОДА ВВЕДЕНИЯ ЭЛЕМЕНТАРНЫХ ФУНКЦИЙ ПРИ ОБУЧЕНИИ БУДУЩИХ УЧИТЕЛЕЙ МАТЕМАТИКИ В ВУЗЕ

Abstract. The concept of the development of mathematical education in the Russian Federation focuses on the importance of teaching mathematics as a system-forming factor in human education, the development of his cognitive abilities, logical thinking. At the same time, the problems that exist in the field of mathematical training of schoolchildren are also indicated. In this regard, the problem of improving the quality of professional training of future teachers of mathematics becomes relevant and significant. In the modern specialized school, the axiomatic approach in teaching mathematics is traditionally used to present the geometry course. It should be noted that in order to achieve subject learning outcomes that meet the requirements of educational standards, it is advisable to use formalized methods for studying other mathematical sections. The purpose of the work is to present the features of studying mathematics at a university using the axiomatic method of introducing elementary functions in the professional training of teachers. Observation, surveys, questionnaires, conversations with trainees were used as the main research methods; Elements of statistical analysis were used to process the experimental data. The author has developed diagnostic tools for assessing the level of formation of the main components of the methodological competence of future teachers of mathematics. The results of studies conducted with students of pedagogical areas of study of Pitirim Sorokin Syktyvkar State University (profile "Mathematics"), and their statistical analysis showed the effectiveness of using the axiomatic method in the process of developing the methodological competence of future teachers. The methodology for teaching future teachers of mathematics the axiomatic approach for introducing elementary functions, developed in an experimental study, has been successfully introduced into the educational process of the university.

Analysis of Mathematics Lesson Planning Framed by the Teachers’ Pedagogical Content Knowledge

<p style="text-align: justify;">Lesson planning is considered to be an important and efficient tool for effective teaching and learning process. Preparations of effective lesson plan requires teachers to be competent in the pedagogical content knowledge (PCK). This study investigated how the mathematics teachers’ PCK impact their competences on designing effective lesson plans. Twelve in-service mathematics teachers from public secondary schools in Unguja-Island (Zanzibar) of Tanzania were involved. The data were collected using the reviewing of the teachers’ mathematics lesson plan documents and teachers’ interview. The data were analyzed in both quantitative and qualitative mode based on the lesson plan framework guideline (LPFG) and the criteria for better planning of the sections jointly with PCK abilities indicators. The percentage average of occurrence of the sections in the teachers’ designed lesson plan (DLP) and the percentage of occurrence of different category within the sections of the DLP in relation to the criteria were determined. Also, the challenges faced by the teachers in their DLP were identified. The result of the analysis revealed that the PCK competences of mathematics teachers are not good enough to impact their DLP, as some of their designing lesson plan sections were occurred inconsistently. Also, the implementation of PCK competences for effective mathematics teaching found to be at developing stage, as some criteria related to it were not clearly observed in their DLP. The study recommends the demand of in-service training for mathematics teachers on the implementation of teachers’ competences particularly PCK in the lesson plan designing for effective classroom practices.</p>

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.

Providing quality mathematical training for students with different types of thinking and with different interests in conditions COVID-19

The aim of the study the article highlights that the process of teaching mathematics to non-mathematics students is complicated by the limited time of the educational process, low motivation of their cognitive activity, psychological barriers of students, assessment and self-assessment of their academic achievements, lack of non-standard tasks. Proposing ways to solve these problems will create conditions for enhancing the cognitive activity of such students in the process of learning mathematics in conditions COVID-19.

Pundits and Possibilities: Philosophers Are Not Modal Experts

ABSTRACT Wilfrid Sellars [1962: 1] described philosophy as an attempt to ‘understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term’. But it is distinctive of philosophy that many of us are interested not only in how the world is but in ways that it could be. That is, philosophy is concerned with facts about modality. Some of the most important arguments in philosophy hinge on modal premises, and philosophers have typically assumed special expertise in evaluating these modal premises. Replicating Goldvarg and Johnson-Laird’s [2000] study of modal illusions, we show that training in mathematics and not philosophy predicts success in overcoming such illusions (n = 395). This study is the first to test the modal expertise of professional philosophers directly. Our findings undermine claims to modal expertise. Philosophical training does not inoculate expert philosophers against basic mistakes in modal judgment.

Students' mathematical training for professional self-realization in a modern, inventive society

In the framework of their professional self-realization on the contemporary job market, the paper explores the issues with professionals' training for mathematics at universities. The structure of students' mathematical proficiency is taken into consideration, and its key elements are substantively presented (the ability to ask and answer questions in and with mathematics, the ability to deal with mathematical language and tools). The initial (ascertaining) step of the pedagogical experiment allowed for the establishment of the level of students' mathematical proficiency and formation in accordance with the predetermined structure. It has been demonstrated that students, both of mathematical and non-mathematical majors, lack the mathematical knowledge and abilities necessary to solve complicated issues, particularly those involving modeling in the context of future professional engagement. The following fundamental strategies for developing students' mathematical competence are supported: research-focused instruction, an interdisciplinary approach with a practical focus, and the use of digital learning environments and related resources. The implementation strategies for these techniques are described in the authors' optional course "Methods of formation of students' mathematical competence for the future successful career" for math specialist students. The research will continue with the introduction of the aforementioned discipline to the educational system, which will include the subsequent assessment of future teachers' readiness to employ the suggested methods in their professional work.

Science Teachers’ Remuneration and Their Job Performance among Government Aided Secondary Schools in Mbarara, Uganda

This study sought to investigate on Science Teachers’ remuneration and their Job Performance among Government Aided Secondary Schools in Mbarara District, Uganda. The study employed a descriptive survey research design. The target population was 126 science teachers and head teachers in seven government-aided secondary schools in Mbarara District. The study randomly sampled 96 science teachers and seven Head Masters using Yamens’ formula. A questionnaire and an interview schedule were used as source of data from the field. The study established that parent-teachers association (PTA) and Secondary Science and Mathematics training allowances were the most common allowances in schools under investigation. Extra teaching allowances, salary increment, duty allowance and overtime allowances were moderately perceived to exist. Remuneration motivated teachers in carrying out such school activities as to complete syllabus, to promote good performance and quality of teaching and to attend classes regularly. Therefore, the government through the ministry of education should ensure that science teachers are provided with attractive remunerations in order to sustain their motivation toward teaching.

ANALYSIS OF THE EFFECTIVENESS OF THE USE OF ADAPTIVE TRAINING PLATFORMS IN SECONDARY VOCATIONAL EDUCATION

The article considers the tasks and features of mathematics training for studentsof secondary vocational education. Special attention is paid to the need to solve the problemof adaptation of students to the conditions of study in college and the organization ofindependent work. In this regard, the authors propose to make wider use of the practiceof adaptive learning as innovative pedagogical tools. The article considers the concept ofthe effectiveness of adaptive personalized learning and suggests the directions by which itcan be evaluated. As an example, the experience of implementing an adaptive educationalcourse “Mathematics”, designed in the Articulate Storyline platform, is analyzed. The moduleis designed to organize and support adaptive learning of students of the Department ofInformation Systems by means of adaptive educational technologies. The results of thetraining are analyzed, and the possibilities of the Articulate Storyline platform in ensuringthe independent work of students are presented. The main part of the article is devotedto evaluating the effectiveness of e-learning using an adaptive educational platform. Withthe help of questionnaires and tools of the Articulate Storyline platform, an assessment ofthe educational result achieved was made, the degree of motivation of students to masterthe discipline of mathematics was analyzed, and the attitude of students to the process ofe-learning using an adaptive educational platform was investigated.

Evaluation of math anxiety and its remediation through a digital training program in mathematics for first and second graders

IntroductionMath anxiety severely impacts individuals’ learning and future success. However, limited is understood about the profile in East Asian cultures where students genuinely show high‐level math anxiety, despite that they outperform their Western counterparts. Here, we investigate the relation between math anxiety and math achievement in children as young as first and second graders in Taiwan. Further, we evaluate whether intensive exposure to digital game‐based learning in mathematics could ameliorate math anxiety.MethodsThe study first evaluated a group of 159 first and second graders’ math anxiety and its correlation with math performance. Subsequently, a quasi‐experimental design was adopted: 77 of the children continued and participated in multi‐component digital game training targeting enumeration, speeded calculation, and working memory. Post‐assessment was administered afterward for further evaluation of training‐associated effects.ResultsResults confirmed that math anxiety was negatively associated with school math achievement, which assessed numerical knowledge and arithmetic calculation. Furthermore, children's math anxiety was remarkably reduced via digital training in mathematics after 6‐week intensive remediation. Crucially, this math anxiety relief was more prominent in those with high‐level math anxiety. Although the children who underwent the training showed training‐induced math achievement and working memory enhancement, this cognitive improvement appeared to be independent of the math anxiety relief.ConclusionOur findings demonstrate that students can show highly negative emotions and perceptions toward learning even in high‐achieving countries. Auspiciously, the feeling of distress toward learning has the feasibility to be relieved from short‐term intensive training. Our study suggests a new approach of early treatments to emotional disturbance that can lead to permanent consequences in individuals.

Development of students’ scientific knowledge on computer modeling while teaching inverse problems for differential equations

Problem statement. Currently, the higher school provides students of physical and mathematical training areas with fundamental subject knowledge, forms professional competencies, develops creative abilities and creativity, teaches them to use modern computer technologies to solve applied problems. One of such academic disciplines, in which students are taught to use computer technologies in solving applied mathematical problems, is a training course called Inverse problems for differential equations. Such an academic discipline has been taught in some Russian universities in the form of elective courses since the 70s of the 20th century. The educational material of this training course includes advanced research results on inverse problems belonging to specialists from different countries, such as Germany, Italy, China, Sweden, Netherlands, Russia, Japan and other foreign countries. During the practical classes, much attention is paid to the use of computer simulation for the study of such applied problems. This circumstance implies the development of educational materials taking into account the professional training of university students, in which attention should be paid to the use of computer modeling in solving mathematical models of inverse problems. Methodology. The implementation of training of university students in physical and mathematical areas of training involves taking into account modern scientific achievements of world science in the field of inverse problems using computer simulation and implementing advanced pedagogical technologies in the classroom. Results. Students acquire scientific knowledge of computer modeling and master the wide possibilities of computer modeling in the study of inverse problems. Conclusion. The presence of scientific knowledge in the field of computer simulation and practical experience of its application for solving inverse problems gives students great advantages and opportunities to be successful specialists in the field of applied mathematics and to be in demand on the labor market in various spheres of human activity.