Mathematical Training Research Articles

МАТЕМАТИЧЕСКАЯ ПОДГОТОВКА ШКОЛЬНИКОВ И СТУДЕНТОВ В РЕСПУБЛИКЕ ТЫВА В УСЛОВИЯХ ДВУЯЗЫЧИЯ

Statement of the problem. The article deals with the issue of the peculiarities of the formation of mathematical training of schoolchildren and students of the Republic of Tyva. The problem is caused by the bilingualism that has historically developed in the Republic: education at the university is conducted in Russian, while a significant part of students who have come from remote regions of Tuva do not speak Russian well, which complicates the acquisition of educational material.In this regard, the problem of developing a mathematics course for university students is actualized which would take into account the specifics of Tuvan-Russian bilingualism. The purpose of the article. The aim of the article is to provide guidelines for the development of an adaptive e-learning course in mathematics for engineering students, taking into account the level of Russian language proficiency by junior students. Methodology (materials and methods). The research methodology is based on the analysis of the features of Russian-Tuvan bilingualism, which affect the process of mathematical preparation of schoolchildren and students of the Republic from the standpoint of a competence approach and taking into account both the ethnopedagogical specifics of modern education and existing approaches in the field of adaptive learning in electronic educational systems. Research results. The issue of mathematical training of schoolchildren and students of Tuva has been analyzed from the standpoint of the Tuvan-Russian bilingualism historically formed in the Republic of Tuva. It is shown that the insufficient level of Russian language proficiency by junior students is a certain obstacle to studying mathematics at university. To teach future engineers mathematics it is proposed to develop and use an adaptive e-learning course in this subject, capable of taking into account, among other things, the student’s current level of Russian language proficiency. Conclusion. The author recommendations on the development of an adaptive e-learning course, which have the ability to take into account the level of students’ Russian language proficiency, proposed in the article, can be implemented when creating such a course focused on the formation of the mathematical competence of students – future engineers studying at Tuva State University.

МЕТОДИКА ПРЕПОДАВАНИЯ КОНЕЧНОЙ МАТЕМАТИКИ В ПЕДАГОГИЧЕСКИХ УНИВЕРСИТЕТАХ В СВЯЗИ С НОВЫМИ ТЕНДЕНЦИЯМИ РАЗВИТИЯ МАТЕМАТИЧЕСКИХ НАУК

There were introduced new methods of the teaching and instruction of the following parts of the Pre-calculus: (1) Binomial Series; (2) Trigonometry; (3) Partial Fractions. The problems introduced in the article for the Pre-Calculus Course in Finite Mathematics was developed by the author. These unabridged problems are developed within the new trends in the evolutions of the novelty of the syllabi in Mathematics due to the development of the Mathematics Sciences / Theory and Applications. These new trends in the Theory and Application of Mathematics Sciences have been added new demands to the newly revised textbooks and corresponding syllabi for the Mathematics Courses taught at the Junior two years Colleges and Pedagogical Universities.These newly developed problems are reflection of the Development of Mathematical and Engineering Sciences to offer great amount of learning conclusion/sequel to those who pursue a bachelor’s degree at the universities of the pedagogical orientation. The problems presented in the article here are developed and restructured in terms of the newly developed techniques to solve the problem in Finite Mathematics and Engineering sciences. Moreover, the techniques offered in the article here are more likely to get utilized in Advanced Engineering Sciences, too, within the content of the problems, which require to obtain finite numerical solutions to the Real Phenomena Natural Problems in Engineering Sciences and Applied Problems in Mathematical Physics.The aim of this present publication is to offer new advanced techniques and instructional strategies to discuss methodology and instructional strategies of the mathematical training of the students at the Pedagogical Universities. Moreover, these new teaching techniques and strategies introduced may be extended to the engineering sciences at the technical universities, too.The results and scientific novelty of the introduced methodology and learning conclusions and sequel of the new knowledge the students at the Pedagogical universities may be benefited from are in the following list of the learning conclusions, presented in the article here. The students of the pedagogical orientation may attain the mastery skills in the following sections of the combinatorics in Finite Mathematics subject:- The n! Combination of n different terms.- Evaluate the expressions with factorials.- Identify that there are -!!( )!nrnr various of combinations of r identical terms in n variations.- Identify and evaluate the combinatorial coefficients from the Binomial Theorem.- Identify and able to build the Pascal’s triangle of the binomial coefficients.- Utilize the Binomial Theorem to expand the binomial formula for any natural powers.- Utilize the Binomial Theorem to obtain the general formula for the n-th term of binomial expansion.- Utilize the Sigma Symbols in the Binomial Theorem for the n-th terms of the binomial expansion. 19- Generate the expansion for the power of the ex, where e is the base of natural logarithmic function y = f(x) = x.Practical significance: the methods of teaching and new teaching strategies offered here in the article alongside with the application of the new trends in the development of mathematical and mathematics education sciences can be useful for prospective and currently practicing teachers of mathematics. Moreover, the materials presented here in this article can be useful for the educational professionals in their professional development plans to improve the quality in education

Методика расчета коэффициента корреляции Фехнера и Пирсона, и их области применения

Research relevance in this article is shown in tabular form the calculation of correlation between fixed assets and the volume of commercial products. Using the properties of average values, Pearson’s formula was changed, which made it possible to simplify the calculation methodology. The aim of the research is to study and analyze the correlation coefficient of the mathematical and statistical indicator, the relationship between factorial and effective indicators that are found in the socio-economic life of society. Research purpose is to study and analyze the correlation coefficient of the mathematical and statistical indicator, the relationship between factorial and effective indicators that are found in the socio-economic life of society. Research methods: the article uses the correlation dependence and the statistical relationship of two or more random variables, while changes in the values of one or more of these quantities are accompanied by a systematic change in the values of another or other quantities. Research results can be used in the practice of teaching the course of statistical analysis in medical, biological, biophysical and economic specialties in universities. Conclusions: correlation coefficients are relatively easy to calculate, their application does not require special mathematical training. Combined with the simplicity of interpretation, the simplicity of the coefficient application has led to its widespread use in the field of statistical data analysis.

The limitations, dangers, and benefits of simple methods for testing identifiability.

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

Педагогические условия практико-ориентированного обучения математике студентов естественно-научного профиля

The article reveals the methodology for the implementation of practice-oriented activities of students in the study of mathematics at a university. It is noted that at present, it is relevant to introduce pedagogical technologies into the educational process that ensure the achievement of students' personal educational results in the course of specially organized educational and cognitive activities. In this aspect, the work emphasizes that the creation of a practice-oriented educational environment of the university, as a pedagogical condition for the implementation of the requirements of the Federal State Educational Standard, contributes to the introduction of new knowledge into the educational process that is significant for vocational training and the formation of practical experience of their use to solve problems not only in the professional field of activity.
 The relevance of practice-oriented learning lies in a significant increase in the effectiveness of training based on a system of selection of educational material that helps students assess the significance, practical relevance of acquired knowledge and skills.
 The demand for mathematical knowledge is beyond doubt, it is necessary in almost all areas related to the natural sciences, technical and engineering professions, and economics.
 The relevance of practice-oriented teaching of mathematics is increasing in the context of the dominance of the competence-based approach, which combines the intellectual and practical components of learning in education. Mathematics, by virtue of its specificity, the fundamental nature of the content, becomes the basis for the natural-mathematical training of future specialists. It is emphasized that in the digital era, which most vividly reflected the connection of mathematics with natural, technical and many other sciences, as well as growing high-tech processes, automation and robotization of production, it is important to ensure the advanced nature of the mathematical training of students at the university, including the natural sciences. In the context of the stated research topic, the problem field of research is determined, which consists in resolving the contradiction between the need for a scientifically grounded selection of the content of the mathematics course for students, identifying the methodological features of its teaching and the spontaneously developing practice of teaching mathematics to students of the natural sciences.

Formalization of tasks generation for complex of interactive web-tests on math

The approach to the formalization of the generation of problem situations applicable to the development of tutoring programs consisting of many tasks is considered. The main errors arising during the software-based generation of parameters are specified. Mathematical modeling of parametrical generation algorithms examined by examples of tasks that make up complex tests on mathematics for secondary schools. The parametric generation method proposed in the article allows getting the large quantitative variations in task problem situations. Thereby, every learner will get a personal unique set of tasks. The structure and functionality of web-tests complex consisting of tasks generated via the proposed method are described. The subject of research in the article is the process of computer training in mathematics. The goal is to develop a method for task generation for mathematical disciplines. Tasks. Research and analysis of the set of mathematical problems. Parameterization of each task and development method and algorithms for automated generation parameters with the determination of incorrect combinations of parameters or problem situations that have no solution. Estimation of borders of admissible for approximate answers. Evaluation of the user solution of a single task and a sequence of tasks. The general objective of the work is to make the software product consisting of a sequence of mathematics tasks. The software should have an extended user interface for the graphical presentation of various problem situations in various mathematical topics. The program must be accessible via the Internet. The following results were obtained: developed methods and algorithms of task generation, which provide correct problem situations and unique parameter sets for each user; described the program complex structure and developed the software system of mathematical web-tests provides two levels of difficulty. Conclusion. The scientific novelty lies in the development of the method of task generation for interactive web tests on the mathematics and its computer implementation with the possibility of graphical representation of tasks and checking of tasks correctness.

PROFESSIONAL COMPETENCIES FORMATION IN THE STUDY OF HIGHER AND APPLIED MATHEMATICS DISCIPLINE

The article considers modern pedagogical approaches and teaching methods that are based on the principles of motivation and are able to increase the interest of students in obtaining mathematical knowledge, skills and abilities. The purpose of the study is to analyse different approaches to the formation of professional competencies in the study of the discipline «Higher and Applied Mathematics». Timing of the study: 2018 - 2020. The results of the annual testing of first-year students of Kyiv National University of Trade and Economics to determine their attitude to the discipline and satisfaction with the learning process were used as an information base. The analysis of the change in the level of mathematical training was carried out by comparing the results of the initial and final tests, which were conducted at the beginning and end of the academic year. Analytical data obtained from the results of the study involving students, suggest that the use of a combination of modern pedagogical approaches and methods significantly increases motivation and arouses interest in studying the discipline. The tendency to more thorough knowledge was observed for almost all categories of students, regardless of their level of preparation. Students, getting into new realities, begin to learn mathematical material consciously and develop the ability to apply the acquired knowledge in professional activities. Given that the learning process at the university requires constant modification of the content and methods of teaching, the importance of the teacher's personality as a factor in the development of student's personality is emphasized. Key words: applied orientation, professional competencies, higher mathematics, methods.

An Introduction to the Technical Committee on Animal Bioacoustics

Animal Bioacoustics as a field of research involves the study of sound in non-human animals. The range of this field is wide and includes all aspects of sound production and reception, communication and associated behaviors, acoustic ecology and effects of noise/sound, and passive and active acoustic methods for monitoring individuals, populations, habitats and ecosystems. Members of the Technical Committee on Animal Bioacoustics (TCAB) come from diverse backgrounds, including those with training in biology, ecology, engineering, mathematics, oceanography, physics, and psychology. Many TCAB members also participate in the activities of other ASA Technical Committees including Acoustical Oceanography, Engineering Acoustics, Noise, Psychological and Physiological Acoustics, Signal Processing, and Underwater Acoustics, reflecting the interdisciplinary nature of the field. This talk will highlight some of the popular and emerging areas of research in Animal Bioacoustics.

The role of expertise in the aesthetic evaluation of mathematical equations.

There is a notion that mathematical equations can be considered aesthetic objects. However, whereas some aesthetic experiences are triggered primarily by the sensory properties of objects, for mathematical equations aesthetic judgments extend beyond their sensory qualities and are also informed by semantics and knowledge. Therefore, to the extent that expertise in mathematics represents the accumulation of domain knowledge, it should influence aesthetic judgments of equations. In a between-groups study design involving university students who majored in mathematics (i.e., experts) or not (i.e., laypeople), we found support for the hypothesis that mathematics majors exhibit more agreement in their aesthetic judgments of equations—reflecting a greater degree of shared variance driven by formal training in the domain. Furthermore, their judgments were driven more strongly by familiarity and meaning than was the case for laypeople. These results suggest that expertise via advanced training in mathematics alters (and sharpens) aesthetic judgments of mathematical equations.

Methodology for Identifying Subject Professional Deficits of Mathematics Teachers

Modern challenges of the system of mathematical training of schoolchildren lead to an increase in subject professional deficits of a mathematics teacher. Monitoring the teacher’s professional deficits allows them to be leveled in a timely manner, thereby improving the quality of the educational process. However, the theory and method of identifying them has not been studied much. This makes it possible to state the problem of research, which consists in determining the conceptual basis of the methodology for identifying subject professional deficits of a mathematics teacher. The purpose of the article is to develop a methodology for identifying subject professional deficits of a mathematics teacher. Methodology. The methodological basis of the study was a competent approach as the basis for structuring the professional competencies of a mathematics teacher; a systematic approach as the basis for diagnosing professional deficits of a mathematics teacher; federal state educational standard for higher education in the field of training “Pedagogical education”; professional standard “Teacher (pedagogical activity in the field of preschool, primary general, basic general, secondary general education. Module “Subject training. Mathematics”, the requirements of the federal state educational standard for the mathematical training of students in a general education school). The study used methods of analyzing special literature and normative documents, pedagogical modeling and design, mathematical processing of information. Results of the study. The basic principles of the methodology for identifying subject professional deficits are formulated and substantiated: expediency, diagnosticity, systemicity and advance. Based on these principles, the authors developed a methodology for identifying subject professional deficits of a mathematics teacher. The example shows the main stages and results of diagnosing subject deficits of a mathematics teacher in the field of combinatorics and probability theory.

Mutual Integration of Information and Mathematical Training for Engineers in the Digitization Era

The article is devoted to the study of the development of interdisciplinary integration on the example of the disciplines «Computer Science» and «Mathematics» in training future engineers in the digitization era. It is considered the trends and directions for development of engineering education at the world level, among which a special role is given to the CDIO approach for implementing interdisciplinary training of future engineering personnel on the base of student-centered learning. It is revealed that information and mathematical modeling is the system-forming factor in the integration of knowledge in Computer Science and Mathematics. It is proposed a classification of IMM on the basis of which it is possible to create integrated educational and practical tasks with interdisciplinary content. In the experimental part of the research methods of questionnaire, survey, experiment are involved. In order to realize mutual integration of information and mathematical training the authors developed the scheme of implementation of the models in independent work of students throughout the entire training at ecosystem of technical university. It is defined student-centered learning technology and it is formulated the methodological recommendations for its implementation of the processes of mutual integration of the disciplines in the process of its teaching to students of engineering specialties of universities

The Opinions of Mathematics Teacher Candidates Who Have Received a STEM Training on STEM and the Activities they Designed in the Class

This study has been conducted to investigate the opinions of mathematics teacher candidates on science, technology, engineering and mathematics (STEM) training and the activities designed by them. It has been carried out using the case study method, which is one of the qualitative research patterns. In this study, semi-structured interview forms and activity cards have been used to gather data. While semi-structured interview forms served to elicit teacher candidates’ opinions on STEM, activity cards were employed to ask them to design an activity in which they could put their training on STEM into practice. The study has been conducted with 34 senior mathematics education students and the data obtained have been analyzed using the content analysis method. It has been concluded that mathematics teacher candidates have positive views on STEM training. The activities designed by the candidate teachers can be categorized under four categories, which are interdisciplinary, the engineering field it is related to, the preferred method and the activities that are not suitable for STEM. Teacher candidates should be trained on how to integrate STEM education into their lessons. Stem activity examples should be presented to teacher candidates for applicability. Keywords: Mathematics teacher candidate, stem, activity, training, opinion

The early history of computer-assisted mathematics instruction for engineering students in the United States: 1965-1989

The article discusses ICT development issues in teaching mathematics to engineering students in the United States. The nature of trends in the convergence of information systems in higher technical education and other tendencies in the United States are described in the article. The primary historical stages of computer-assisted mathematics training for engineering students in the United States are defined. The study of historical sources has allowed six stages to be recognized. The use of ICT for teaching mathematics is examined at each stage. It demonstrates the inconsistencies and key elements of using ICT to teach mathematics to engineering students. This article covers the first three stages (1965-1989) of computer-assisted mathematics training for engineering students in the United States.

A Survey of Computational Toxicology Approaches

Medications are a particular kind of chemicals that are considered essential for toxicity screening in contrast to those substances that contribute to the environment. In the development and production phases, toxicity is still the reason for a great number of candidate failures for new medicines. In-vivo work on the pharmaceutical industry, the in-vitro and animal trends of incompetence for correctly forecasting certain human toxicity, and the lack of accurate, high-thrown in vitro testing was obstructive in calculating toxicity. the development of computational toxicology structures has been encouraged by developing numerous omics techniques that have grown into several scientific areas, including genomics, proteomics, metabolomics, and transcriptomics. Computational toxicology is highly interdisciplinary. Researchers in the field have backgrounds and training in toxicology, biochemistry, chemistry, environmental sciences, mathematics, statistics, medicine, engineering, biology, computer science, and many other disciplines. This paper offers a historical perspective and current status for the computational approaches used at the assessment of toxicity. It presents examples of the expert systems, machine-learning approaches and web-based toxicity predictors.

Teacher candidates attitudes towards the stem and sub-dimensions of stem

The developments in science and technology have led to changes in the expectations of countries from the future and the individuals. In the 21st century, focusing on innovative approaches in the education system has become compulsory to raise individuals who question, find rapid and effective solutions to problems and who could think scientifically. One of these approaches is Science, Technology, Engineering and Mathematics (STEM) training. The aim of this study is to evaluate the relationship between STEM and STEM sub-dimensions. The study group consists of 204 teacher candidates from different departments of the Faculty of Education of Sakarya University during the academic year 2018/2019. To collect data, the attitude scale for STEM and the sub-dimensions of STEM were used in the study. One-way ANOVA was used in this correlation for parametric tests. According to the results of the study, there is a positive and significant relationship between STEM and all STEM sub-dimensions based on the data collected from teacher candidates. Keywords: STEM, sub-dimensions, teacher candidates

Educational Projection Systems, Levels And Prerequisites Of Mathematical Ontology OntoMathEdu

The developed educational projections, levels and prerequisites of the mathematical educational multilingual ontology OntoMathEdu are presented. Educational projection is viewed as the formalization of a certain system of subject training in mathematics. It is a subset of OntoMathEdu ontology concepts, which are structured at this stage of ontology development using two didactic relationships – educational level and prerequisites.
 Educational levels are allocated on the basis of the teaching standards of the corresponding education system, the relation of prerequisites is determined by the sequence of the studied concepts in a particular education system.
 The OntoMathEdu ontology defines two projections representing the educational systems of Russia and Great Britain. The algorithm for constructing an ontology through linking various projections allows it to be further replenished with new educational projections, which can later be used in the system of multilingual teaching of mathematics.

The mathematical competence of Olympiad participants as an indicator of the quality of mathematical training level

Introduction. The relevance of the research on the formation and assessment of the level of development of competencies in the mathematical educational field is due to the fact that the subject competence of the participant of the Olympiad predetermines his victory in the competition. And the Mathematical Olympiad, as a form of education, has potential not only for the formation, development, but also for determining the level of mathematical competence of its participants. The research problem is to justify the didactic potential of the mathematical Olympiad as a tool for determining the level of mathematical competence of school students. Aim of the study: to theoretically substantiate, develop and specify the content, indicators of mathematical competence of mathematical Olympiad participants Methodology and research methods. The methodological basis of the study is determined by: the activity and competence-based approaches to teaching; a retrospective analysis of psychological and pedagogical studies affecting the formation and development of key and subject competencies of schoolchildren; an analysis of the content of mathematical Olympiads; an analysis of the results of Kyrgyz Republic schoolchildren in international mathematical Olympiads; the study and generalization of the experience of juries of Olympiads. Results. The subject Olympiad forms a competence-based educational environment in which the levels of formation of key and subject competencies of its participants are most fully displayed. The competence-based approach to training in the Olympiad environment is characterized by the formulation of objectives from the point of view of the activity approach to the formed competence. Subject competence is leading in determining the quality of the student’s Olympiad activity. The mathematical Olympiad is one of the effective forms of both the formation and development, and the determination of the level of mathematical competence of its participants. The introduction of presented system for preparing schoolchildren for mathematical Olympiads, using model’s formation of mathematical, informational competencies in the experimental group, led to an increase in students' knowledge of the theory and practice of solving Olympiad problems in mathematics by 12,95%; the qualitative indicator of knowledge of the school curriculum in mathematics increased by 15,25%. The index of absolute indicators in the experimental groups in the theory of Olympiad mathematics was 53,12%, in the methods of solving Olympiad problems – 55,38%. In control groups, these indicators were 41,23% and 42,36%, respectively. The qualitative indicator of exam results of schoolchildren of the Olympic reserve turned out to be 19% higher. The results of the questionnaire survey participants of the Olympiads confirm the expediency of using technology for the development of critical thinking, the project method of teaching, ICT in the process of preparing for the Olympiads, contributing to the emergence of motivation to study an extracurricular course in mathematics in 68% of students, 42% of students showed a desire to participate in the Olympiads. The results obtained confirm our conclusions that the development of the mathematical competence of the participants of the Olympiads is successfully realized only in a situation of continuous Olympiad activity.

СОВРЕМЕННЫЕ МЕТОДИКИ ОЦЕНИВАНИЯ РЕЗУЛЬТАТОВ ОБУЧЕНИЯ МАТЕМАТИКЕ СТУДЕНТОВ ИНЖЕНЕРНЫХ НАПРАВЛЕНИЙ ПОДГОТОВКИ

Statement of the problem. To achieve the requirements for graduates of engineering fields of training, it is necessary to design and implement an educational process based on the integration of competence, activity and personality-oriented approaches in the context of using information and communication technologies. The improvement of procedure for assessing the results teaching mathematics is due to the transition to competence-based paradigm of education in the context of informatization, strengthening of the role of students’ independence in the educational process, need to solve new problems in future professional activities arising in connection with the development and renewal of the production base. The purpose of the article is to develop an assessment methodology in teaching mathematics for future bachelors of engineering training in the context of informatization of education and increasing role of their independence. The research methodology consists of the analysis of regulatory documents in the field of higher education, the requirements of educational standards, analysis and generalization of the available experience on the problem under consideration. The research is based on the theory of competence-based, activity-based, personality-oriented and systematic approaches, and informatization of education. Research results. The article describes the methodology for evaluating the results of teaching mathematics to students of engineering fields of training. In accordance with the criteria for evaluating the results of teaching mathematics, key indicators of the formation of each criterion are formulated and the levels of their manifestation are described. The potential of using diagnostic tools, including electronic educational resources, has been determined. Conclusion. The implementation of a systematic methodology for assessing the results of teaching mathematics contributes to improvement of the quality of mathematical training. The conducted diagnostics helps to identify gaps in the knowledge of students and adjust the teaching methodology, thereby increasing the motivation of students to study the discipline.

ПРОФЕССИОНАЛЬНЫЕ ДЕФИЦИТЫ УЧИТЕЛЯ МАТЕМАТИКИ И ИХ ПРИЧИНЫ

Statement of the problem. The reform of Russian education, which is in demand by the rapid technical development of all branches of production, is associated with the search for opportunities for appropriate changes in its content and methodological aspects. The general education school requires more and more from a teacher, thus creating a certain tension in terms of the growth of professional deficits among teachers. The purpose of the article is to determine the main approaches to identifying professional deficiencies among mathematics teachers, their structure and causes. Methodology (materials and methods). The research methodology consisted of a competence-based approach as the basis for structuring the professional competencies of a mathematics teacher; a systematic approach as a basis for diagnosing professional deficiencies of a mathematics teacher; Federal State Educational Standard of Higher Education in the direction of training “Pedagogical education”, professional standard “Teacher (pedagogical activities in the field of preschool, primary general, basic general, secondary general education)”; module “Discipline training. Mathematics”, the requirements of the Federal State Educational Standard for the mathematical training of secondary school students. Research results. The composition of professional deficits among mathematics teachers was revealed and substantiated: discipline-wise, methodological and general pedagogical competencies. The main causes for the emergence of professional deficits among mathematics teachers are formulated: shortcomings of professional training at the university; inconsistency of terms in the requirements for professional competence in the Federal State Educational Standards and the Professional Teacher Standard; overestimated requirements of the employer in terms of the workload; insufficient dissemination of experience obtained from individual advanced training of a mathematics teacher. Conclusion. The approach proposed in the article to structuring the professional deficits among mathematics teachers and describing the complex of causes for their occurrence can be extended to the study of professional teacher deficits in other subject areas.

TECHNOLOGY OF MIXED TRAINING OF FUTURE MECHANICAL ENGINEERS IN THE CONDITIONS OF UNPC «ALL-UKRAINIAN SCIENTIFIC AND EDUCATIONAL CONSORTIUM»

The article discusses the need to transform the traditional professional training of a future mechanical engineer, which is associated with a number of contradictions due to new requirements for a graduate of an agricultural university. The issues of improving the quality of the fundamental and practical component are actualized, which the professional activity of a specialist in modern high-tech production needs - the development, operation, maintenance and management of new equipment, technologies and technical systems. It is proved that a powerful means of eliminating these contradictions is the development of a strategy of agricultural educational institutions for the integration of science, education and production, focused on the current state of the agro-industrial complex. The scientific and educational industrial complex is considered as a concept of the mechanism for the transition of agro-industrial production to an innovative development model. Substantiated is the author's student-centered technology of blended learning of future mechanical engineers in the conditions of the Educational-scientific industrial complex USEC «Ukrainian scientific-educational consortium». It has been proven that in the process of training mechanical engineers in the conditions of scientific and educational industrial complexes, the technology of blended learning with elements of dual education, based on the integration of traditional classroom and distance forms, using the best capabilities of each, will be effective. The analysis of the existing practice of using distance and blended learning technologies in the process of training specialists is carried out, the psychological and pedagogical conditions for the design of student-centered education based on the blended learning technology are theoretically substantiated, a model for the design of blended learning technology is developed, the principles of selection of subject-specific information in the mathematical training of specialists are determined, student-centered technology of blended learning of future mechanical engineers (on the example of the course "Higher Mathematics"), prepared information resources and teaching materials are described.