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133) on the segment fc Kf Kf (strengthening
begins when reached f3) for the t ~ y simplest approximation is used:
T = TCH(y -yc),
where H ( x ) - Heaviside function
1, if x > 0,
(0.1)
H ( x ) =
0, if x < 0.
(0.2)
We introduce the yield strength Ts , which is determined from the ratio
f3
\(t-ts ) dy = 0,
requiring that the area of the approximating curve (Fig. 1) be zero in the interval fc < f . This condition is equivalent to the requirement of approximation of the dependence to give the same value of the surface energy density. The accepted simplifications lead to the linearization of all equations of problems and allow to obtain its approximate solution.
The described model of shear band formation resembles the model of dislocation motion, when the "quantum" of plastic shear is defined as the displacement of the dislocation by a distance equal to the length of the Burgers vector b0 . The model assumes that plastic deformation for polycrystalline material develops due to plastic displacements of individual grains (crystallites), and the "quantum" of plastic deformation is
defined as the slip within a pair of grains 8 .
Only tangential stresses will be considered within the localization band. Given the above simplifications, we can assume that at the edges of the localization band
in the region 0 < X < l are active only tangential
stresses Ts , and in areas l < |x| < b tangential
stresses can vary between them ts tc . This model of
the band bending load is similar to the Dugdale model, but with the significant difference that the stresses
within the band are not equal to zero (Ts > 0).
The proposed campaign allows us to describe the flow site and subsequent hardening, as well as the effect of the Bauschinger effect on the flow site and on the site of hardening under cyclic loading.
Conclusions. The paper describes a model of shear band formation, which resembles the model of dislocation motion, when the "quantum" of plastic shear is defined as the displacement of the dislocation by a distance equal to the length of the Burgers vector. The model assumes that the plastic deformation for pol-ycrystalline material develops due to plastic displacements of individual grains (crystallites), and the "quantum" of plastic deformation is defined as the slip within a pair of grains. at the site of fluidity and at the site of hardening under cyclic loading. This approach can be widely used on functional materials [4].
References
1. Ю. И. Кадашевич, В. В. Новожилов, Теория пластичности, учитывающая эффект Баушин-гера, Докл. АН СССР, 1957, том 117, номер 4, -с.586-588
2. В. В. Новожилов, Ю. И. Кадашевич, Ю. А. Черняков, "Теория пластичности, учитывающая микродеформации", Докл. АН СССР, 284:4 (1985), - с. 821-823
3. Новожилов В.В. Теория упру гости /. - Л: Судпромгиз, 1958. - 371 с.
4. Petrov A. Development of the method with enhanced accuracy for solving problems from the theory of thermo-psevdoelastic-plasticity / А. Petrov, Yu. Chernyakov, P. Steblyanko, K. Demichev, V. Hay-durov // Eastern-European Journal of Enterprise Technologies. 2018. Vol. 4/7 (94). P. 25-33.
SCIENTIFIC APPROACHES AND PRINCIPLES OF ENTREPRENEURIAL COMPETENCE
FORMATION IN PHYSICS LESSONS
Mukha A.
PhD student,
Sumy State A. S. Makarenko Pedagogical University,
teacher of physics,
Sumy comprehensive school №15 named after D. Turbin,
Sumy region, Ukraine ORCID ID: 0000-0002-2892-7495
У
с
Abstract
The article deals with the formation of entrepreneurial competence of students in physics lessons. It focuses on the structure of entrepreneurial competence. The main attention is focused on highlighting the potential of scientific approaches and principles to the formation of entrepreneurial competence. The expediency of applying axiological, problem-based, system-activity, competence-based, personality-oriented and acmeological approaches as an important methodological basis for the formation of entrepreneurial competence in physics lessons is substantiated.
Keywords: scientific approaches, scientific principles, entrepreneurial competence, problem approach, problem situations, axiological approach, integration approach, system-activity approach, personality-oriented approach, competence approach, acmeological approache.
Problem statement. The course of human life in a dynamic world is determined by globalization, the scientific and technological revolution and the informatization of society. One of the characteristic features of the realities of modern social progress is the requirements for training competitive, competent and educated specialists who are adaptive to the conditions of a rapidly changing environment, able to master new technologies for self - education and be innovative in terms of information use. The experience of the European community, in particular in determining the key competencies of students, is extremely valuable for Ukraine to effectively move towards change. To successfully live in an intelligent society, young people need skills that consist of characteristics such as critical thinking, the ability to solve complex interdisciplinary problems, entrepreneurial thinking, decision-making, creative thinking, communication, and collaboration.
The formation and comprehensive development of a person who has a desire for self - improvement and lifelong learning, is ready for conscious life choices, self-realization, responsibility - these are vital requirements of our time, which, according to the state standards of basic and complete general secondary education, is the basis of the physical component of education. It is no exaggeration to say that the possession of entrepreneurial competence is the main trend in the labor market. The role of education in promoting entrepreneurial attitudes and behaviors is generally accepted. The question " How to make education applicants more enterprising? How to create an environment that promotes the entrepreneurial development of each child? To what extent is the school able to form the entrepreneurial competence of students? These actual problems can be solved by applying axiological, integration, problem-based, competence-based, system-activity, and personality-oriented approaches to teaching physics at school.
Analysis of research and publications
In the law of Ukraine "On Education" it is stated: "competence is a dynamic combination of knowledge, skills, ways of thinking, views, values, and other personal qualities that determines the ability of a person to successfully socialize, conduct professional and/or further educational activities". Among the key competencies that Ukrainian citizens should master as a result of lifelong learning, we will highlight entrepreneurial competence. The relevance of the problem under study is evidenced by the works of Y. Belova, V. Morozova, T. Matveeva, N. Morse, N. Balyk, M. Strelnikov, O. Serebrennikova, O. Sulaeva , S. Belyaeva, D. Mesh-cheryakova, O. Khamanturova. Entrepreneurial competence is also studied by: R. Shiyan, E. Bobinskaya, A. Gelbak, A. German, G. Nazarenko, V. Morozova, V. Maikovskaya, G. Matukova, and others. The development of personal qualities of an entrepreneur, in particular, the formation of entrepreneurial competence, is considered in the works of N. Akaev, N. Pobirchenko , Y. Belov, G. Matukov, A. Protsenko and others.
According to the dictionary of the Ukrainian language, "enterprising" is the same as inventive, one who has practical ingenuity, the ability to actively act; proactive. A synonym for the word "enterprising" is persistent, that is, active, energetic, persistently overcoming difficulties, relentlessly achieving the goal. In the dictionary of the Ukrainian language, "enterprising" means energetic and agile, with practical ingenuity, inventiveness and energy. [15] In the concept of the "New Ukrainian School", initiative and entrepreneurship are the ability to generate new ideas and initiatives and implement them in order to increase both own social status and well - being, as well as the development of society and the state. Ability to behave rationally as a consumer, effectively use individual savings, make appropriate decisions in the field of employment, finance, and so on. [6]
Liskovich A.V. recorded in the research: "entrepreneurial competence of a student is a structured set of personality qualities that ensure effective solution of issues in various spheres of life related to their own social status and well-being, as well as the development of society and the state as a whole."
A. Protsenko notes that the formation of entrepreneurial competence is a complex, contradictory, multilevel process that involves the acquisition of entrepreneurial knowledge by a person, the formation of entrepreneurial behavior, provided that consciousness is formed accordingly. [13]
Consider another interpretation. "Entrepreneur-ship is business activity, initiative, the ability to start and implement a business that brings success. To do something means to take an initiative, proactive action, to be active before its conditions and consequences are clearly defined.» [12]
The purpose of the article: to investigate the potential of scientific approaches and principles that are the basis for the formation of entrepreneurial competence among students in basic school physics lessons
Presentation of the main material. Based on the theoretical understanding of the works, we note that an enterprising person, even in failure, is always looking for opportunities, new options for achieving the goal. The concept of entrepreneurship comes from the English word "entrepreneurship", which means the ability of an individual to find new opportunities, the ability to realize himself and create economic or social values. Researchers say the only way to make people more adventurous is to use a learning-based approach. Let's look at the list of traits of the most successful people. How do enterprising individuals think? What are their biggest priorities? In our opinion, the opinion of Mark Coopersmith, a teacher at the Berkeley Haas School of business, who identified the main features of successful people - entrepreneurs, is correct:
- propensity to act: each strategy and plan is just a set of hypotheses until they start working, and here entrepreneurs are masters of their craft.
- experiment: the best way to test an assumption is to conduct a lot of experiments.
- adaptation to change: entrepreneurs strive for change, because change creates opportunities. Entrepreneurs who do not pay attention to changes very quickly disappear against the background of competitors who are chasing changes.
- optimism: entrepreneurs expect positive results, despite the fact that 80% of startups fail. Despite obstacles and doubts, they believe that the project will be successful.
- decision - making skills: quick and effective response is very important. Successful people understand that a solution today is better than a solution in two weeks.
- great curiosity and interest: as an addition to constant experiments, entrepreneurs absorb an extremely large amount of information and look for partners.
- understanding risk and being able to reduce it: one of the traits that is usually attributed to successful people is that they take risks. They find ways to reduce the risk at each stage of their actions. They experiment to determine what will work and what won't, and work out ways to overcome problem situations;
- resourcefulness: successful entrepreneurs are able to recognize opportunities in every failure. Successful entrepreneurs know that "today's failure is a lesson for tomorrow." They try, through failure, to get an idea of the problems.
- sociability: entrepreneurs communicate with their clients on a daily basis, know them deeply and are able to convince them. [3]
The characteristic requirements and features of an entrepreneur are considered in his work by Madzigon V., namely: readiness for risk, initiative, purposeful-ness, sociability, honesty, determination, high information content, observation, ability to persuade. [9]
As you can see, the development of entrepreneurial skills occurs through the development of qualities such as determination, courage, creativity, and so on. And even if students do not dream of becoming entrepreneurs in the future, they will need entrepreneurial competence in life. Having analyzed the publications of scientists I. Brizhan, I. Minyailenko, Y. Ushakova [2], we see that the structure of entrepreneurial competence includes: the ability to negotiate in order to solve certain problems; resistance to psychological and physical stress; the ability to establish connections; the ability to act in conditions of uncertainty; willingness to take risks, a high level of personal responsibility, and so on.
Supporting this, we believe that entrepreneurial competence is an integral psychological quality of the individual, which is manifested in his motivated ability to creatively search for and implement new economic ideas, aimed not only at creating his own well-being, but also at the development of society as a whole. All the entrepreneurial skills that are necessary for global competitiveness in the future can be achieved by teaching physics in primary school. Note that the formation of these skills is achieved within the framework of an entrepreneurial lesson, during which the knowledge and skills acquired in connection with life are implemented in practice.
The methodological basis for the formation of entrepreneurial competence is scientific approaches: axi-ological, system-activity, competence-based, problem-based, integration, personality-oriented.
Approach is a strategy used by official educational systems and individual educators to influence the learning process of students.
- axiological approach that allows us to make objective analysis of the leading trends in the development of modern society and determine value priorities in the light of this. (M. Boguslavsky, V. Vorontsova, I. Isaev, V. Slastenin, G. Chizhakova, I. Bekh, V. Bu-tenko, I. Zyazyun, S. Polyakov, G. Selevko, N. Tkacheva Yu. Artyukhovich, M. Kagan, I. Nadolny, I. Bychko, M. Gorlach, O. Vlasenko, V. Sharko). The central category of the axiological approach is values that are transformed into an integral personal asset and set the orientation of the applicant for education, motivation in relation to life aspirations. Value attitudes, norms and ideals of the individual, his intellectual and moral potential, expressed in the ability to freely navigate in difficult life situations, act as defining guidelines in designing the future, in planning and implementing entrepreneurial activities. Within the framework of the axiological approach, when teaching physics, the priority task is to convince students of the need for physical knowledge and its value for later life.
Physics is one of the sciences that is extremely necessary for the technological breakthrough of our nation. It is the heart of Science and the center of technological activity. Physics is the science that studies the most fundamental rules in the universe. It deals with matter, energy, their behavior and structure. The study of physics has been and will continue to be extremely important for humanity, since it is able to explain natural and everyday phenomena [11]. Indeed, physics plays a very important role in scientific and technological progress and in the development of enterprising people. Young people should be able to acquire knowledge of physics, as well as use knowledge about physical phenomena and processes for their own well-being in everyday life and their own life. This approach also forms internal motives that encourage the individual to be active, the moral and ethical attitude of the individual to entrepreneurial values, such as self-realization, prudence, enterprise, thrift, hard work, honesty, care, willingness to take risks. A stable system of values and value orientations of an entrepreneurial nature creates the foundation for motivated behavior and productive activities of an student for the development of society as a whole.
- system-activity approach (V. Sadovsky, E. Yudin, A. Averyanov, JI. Vygotsky, P. Podkasisty, A. Leontiev, A. Asmolov, L. Novikova, M. Tovkalo, etc.), which implements the principle of consciousness and activity, which allows us to focus on the formation of entrepreneurial competence in the process of activity. Systematic approach is an effective means of scientific knowledge, an interdisciplinary study of any problem, which is an integration of the purpose, content of training and upbringing. Of great importance for the development of entrepreneurial competence is an approach
that has a common point of reference - an action orientation. The activity aspect is aimed at the activity of the subject in cognition, work. The activity-based approach can be implemented through forms of work that allow students to be more active, proactive, responsible, inventive, and so on. One of the characteristics of action-oriented learning is the high activity of participants. This approach is the best form for stimulating independent work of schoolchildren, promotes an active life position of children, encourages children to think and act. Consider the full-action sequence of W. Beck, which has such a complete storyline:
- Define goals and understand tasks
- Analyze the initial situation
- Plan your actions
- Evaluate plans and make decisions
- Make a plan of action
- Check the results
- Rate the action
The full action consists of informing, analyzing, planning, making decisions, executing, monitoring, and evaluating. If the evaluation of an action reveals that the task could not be solved satisfactorily, it is necessary to analyze, the process starts again, then the actions are performed, but at a different level. [10]
Owing to interactive forms of work, project method, case method, methods of "mixed" learning, based on mutual exchange of experience, students in physics lessons take responsibility for the readiness of all group members, analyze risks, predict results of activities, are able to present their own projects and creatively solve various problems, which will help in the future to use their own budget efficiently; make informed economic decisions. You can implement a system-activity approach in physics lessons even outside the classroom, because excursions and outdoor research increase the horizons of young people. Undoubtedly, we agree that entrepreneurial competence is formed if training is based on the experience of students.
- competence approach is the approach that allows shifting the focus from students' accumulation of physical knowledge, skills and abilities to the formation of creative personalities and considers the formation of entrepreneurial competence as a component of preparing students for the labor market in the future. The main aspects of formation are described in the works of P. Atamanchuk, O. Lyashenko, M. Martynyuk, M. shut, N. Bibik, O. Ovcharuk, O. Pometun, A. Khutorsky, V. Adolf, V. Bolotov, I. Isaev, I. Zimnya, L. Vashchenko, T. Dobudko, O. Zablotskaya, B. Gershunsky. The essence of the approach is not so much to transfer a certain amount of knowledge in physics to students, but to teach them to use this knowledge to solve real problems in life. Thus, young people after graduation enter independent life prepared, able to solve problems independently and take responsibility for their own decisions. In modern social-economic conditions, when there is a reorientation of educational programs and pedagogical technologies to a competence-based approach, the teacher is given a responsible role of the organizer of the process.
The competence-based approach provides modern schools with broad potential opportunities to improve the quality of training of students, contributes to the modernization of education, develops the ability of young people to find information, use research methods of work, put forward hypotheses, listen to the opinions of other participants in the educational process, convince in discussions, perform various social roles, overcome conflicts.
- problem approach (V. Pavlenko, S. Arkhan-gelsky, A. Brushlinsky, M. Danilov, V. Zabotin, T. Ilina, V. Kraevsky, M. Kruglyak, V. Krutetsky, T. Kudryavtsev, Ch. Kupisevich, I. Lerner, O. Matyush-kin, M. Makhmutov, V. Okon, M. Skatkin) is a situa-tional learning approach. The term "problem" is of Greek origin, meaning "task, complication". In everyday use, this concept is understood as a complex theoretical or practical question that needs to be solved, studied, or researched.
The main condition for the problem approach is the teacher's use of problem situations during the physics lesson with an entrepreneurial background. The teacher formulates a problem that is based on real practical situations, but also adapted to the requirements of students. The teacher creates a problem situation, and students want to find the answer to the problem, solve the problem, but they do not have enough specific knowledge, and therefore they begin to search for such information on their own, put forward hypotheses, arguing their own position. Through solving a problem situation, students defend their own views, discuss, make sure of the importance of the acquired knowledge, and make optimal decisions. Problematic situations stimulate increased interest among students and involve awareness not only of traditional knowledge in physics, but also of the connection of science with the surrounding world. Real-world examples are useful for students to understand the content of the physics course and contribute to the formation of entrepreneurial competence. All students' statements are then tested experimentally or theoretically.
It is worth noting that motivational questions in the physics lesson arouse students' interest in the topic, increase activity during the lesson and stimulate independence in finding additional information. The self-esteem of students increases, and confidence in their abilities appears.
- integration approach (I. Kozlovskaya, V. Buzko, O. Voitovich, S. Rybak, N. Sychevskaya, M. Pak, V. Zagvyazinsky, V. Ledneva, S. Velichko, S. Goncharenko, V. Ilchenko, Y. Dik, V. Zavyalov, Y. Lukyanov, V. Razumovsky, O. Sergeev, N. Stukhin-skaya, O. Lyashenko, Galatyuk, M. Tovkalo). The approach leads to the integration of the content of education, that is, with the help of which it is possible to create a complete picture of the world among students. Integration (from Lat. integratio - restoration, replenishment, from integer - whole) is a concept that means the state of connectivity of individual differentiated parts and functions of a system, an organism into a whole, as well as the process leading to such a state.
The integration approach to the content of training involves integration both external and internal, both semantic and procedural [7]
The integration approach provides an organic combination of subjects, reveals general patterns, ideas that have found themselves in different sciences, and connects information from several sciences into one whole, because the laws of physics, mathematics, biology, chemistry, etc apply simultaneously in the world. The use of intersubject connections stimulates the cognitive interest of students, activates the educational process, helps to expand the worldview, stimulate creative potential, provide motivation, identify personal resources of students to achieve success in future professional activities. The emphasis is on setting an intersub-ject learning problem. The search for its solution contributes to the development of entrepreneurial thinking of students and forms the ability to apply theoretical knowledge of physics in practice, in real life, that is, it contributes to a comprehensive vision of life problems. This approach to teaching physics allows students to understand global relationships in the world, synthesize knowledge outside of disciplines, raise the level of creative thinking, form new knowledge better, solve problems and quickly navigate when mastering physics.
When solving new problems that arise at the intersection of several disciplines, young people have a deeper understanding of the problems of our time. The result of an integration approach can be the integrity of knowledge at different levels - the integrity of knowledge about reality; about nature; from a particular educational field; subject, course, section, topic. [4] Thus, intersubject integration contributes to: increasing motivation to study physics, facilitates the understanding of educational phenomena and processes studied by applicants. Integrated lessons contribute to the formation of analytical skills, the development of a culture of thinking, increasing creative activity; the formation of a holistic scientific picture of the world; improving the assimilation of knowledge in physics and other disciplines; reducing students' fatigue from overload; expanding the scope of information acquisition. Students are able to compare facts from different branches of knowledge, classify and summarize information, and this makes the learning process truly rich and interesting. [8]
We believe that the integration of content is a necessary condition for a holistic perception of the world, understanding the phenomena of the surrounding reality by students, and an important factor in creating entrepreneurial competence in the course of physics lessons.
- personality-oriented approach: (I. Bekh, V. Belousova, E. Bondarevskaya, O. Vishnevsky, Ya. Galperin, G. Dorofeev, O. Dubasenyuk, O. Kobernik, O. Savchenko, G. Shchedrovitsky, K. Ushinsky, L. Vygotsky). This approach is important from the following positions: it is the general orientation of pedagogical work on the student, and partner-tutor support of the teacher, and adaptation to new conditions of the structure and methodology of the lesson, and maximum attention to the individual psychological characteristics of schoolchildren, empathy, experience, perception,
etc. All these elements are simultaneously necessary for the methodology of forming entrepreneurial competence in physics lessons. This can be organized using differentiated tasks that correspond to the individual traits of students, providing opportunities to solve problems in different ways, using different individual forms of work, and helping students.
We give preference to methods that ensure self-development, self-actualization of the student and allow them to form positive self-esteem, tolerance and empathy, recognize and appreciate the skills of others, thereby receiving confirmation of self-esteem. Priority is given to developing cooperation skills, not competition. [5] In the conditions of a person-oriented approach to teaching, the main task of education is set and performed, which is the creation of conditions for the development of a harmonious, morally perfect, socially active personality: through the activation of internal reserves, an enterprising and capable of self-development personality is fostered. [16]
So, the individual, his motives, his needs for self-realization, self-development, self-determination, and interests are at the center of learning.
- Acmeological approach: A. Derkach, A. Boda-lev, S. Pozharsky, B. Akimova, N. Vishnyakova, G. Danilova, O. Dubasenyuk, Y. Gagin, V. Zazikin, V. Maksimova, N. Kuzmina, M. Potashnik devoted their scientific research to the study of the problems of ac-meology and the acmeological approach. "Acme" means "peak or highest degree of prosperity" in Greek. We are talking about the personal and professional development of students, the development of abilities and talents, strengthening motivational attitudes, orientation of young people to constant self-improvement, self-realization of their creative potential, the desire of the individual to achieve higher levels of his development, the formation of interests to achieve success in professional activities, taking into account various aspects of training and improving his educational level. [1]
An important task for the formation of entrepreneurial competence is to create a situation of success and positive attitude of students. In this aspect, one of the first places is taken by personal qualities that allow the student to be successful, namely activity, creativity, responsibility, ambition, independence, self-confidence, the ability to solve problems independently, that is, those factors that are the basis of entrepreneurial competence. In the context of the formation of entrepreneurial competence, the acmeological approach ensures the creative and independent nature of educational activities, the integration of important entrepreneurial qualities and abilities into the system of professional characteristics of every student.
The approaches described above - axiological, system-activity, competence-based, problem-based, integration, personality-oriented, acmeological in our opinion, are fundamental for the development of methods for the formation of entrepreneurial competence in primary school students in physics lessons.
Let's look at the main regulatory provisions that should be followed in order for training to be effective,
that is, the principles of training. Among the general didactic principles, we distinguish the principle of scientific character; systematicity and consistency; strength of knowledge; activity, accessibility; consciousness; visibility; problem-based, individualization of learning, the principle of practice orientation. As specific principles, we note the orientation of the process of training students to the formation of their components of entrepreneurial competence, the unity and interrelation of theoretical, practical and entrepreneurial training. [14] Complementarity of certain approaches and pedagogical principles should provide a solid theoretical and methodological basis for the successful implementation of the process of forming entrepreneurial competence among students, which integrates the following components: motivational; cognitive, activity; creative.
Conclusions: The use of an axiological, system-activity, competence-based, problem-based, integration approach in the formation of entrepreneurial competence among students in the classroom is appropriate and makes it possible to integrate and use all the described approaches at a qualitatively new level. The application of approaches makes it possible to most effectively use the entire set of organizational forms of development of entrepreneurial competence.
References
1. Antonova O. (2011). Akmeolohichnyi pidkhid do vyznachennia sutnosti pedahohichnoi obdarovanosti. [Acmeological approach to determining the essence of pedagogical talent]. Akmeolohiia -nauka XXI stolittia: materialy III Mizhnarodnoi nau-kovo-praktychnoi konferentsii. [Acmeology - the science of the XXI century: materials of the III International scientific-practical conference]. Retrieved from http ://eprints.zu. edu.ua/id/file/186177. [Ukraine]
2. Bryzhan I., Miniailenko I., Ushakova. Yu. (2018). Suchasni pidkhody do otsiniuvannia modeli formuvannia pidpryiemnytskoi kompetentnosti personalu za metodom «360 hradusiv». Efektyvna ekonomika. [Modern approaches to the evaluation of the model of formation of entrepreneurial competence of staff by the method of "360 degrees". Efficient economy]. Retrieved from http://surl.li/miko
3. Coopersmith Mark. (2019). The Entrepreneurial Mindset. Strive Magazine. Retrieved from https ://markcoopersmith. com/top-10-traits/.
4. Intehrovani uroky: vid teorii do praktyky. (2018). [Integrated lessons: from theory to practice]. Retrieved from https://osvitanova.com.ua/posts/1776-intehrovani-uroky-vid-teorii-do-praktyky. [Ukraine]
5. Ivanii V. Mukha A. (2016). Formuvannia kliuchovykh kompetentnostei uchniv osnovnoi shkoly na urokakh fizyky z pidpryiemnytskym tlom. [Formation of key competencies of primary school students in physics lessons with an entrepreneurial background]. Pedahohichni nauky: teoriia, istoriia, innovatsiini tekhnolohii. [Pedagogical sciences: theory, history, innovative technologies]. Retrieved from http://nbuv.gov.ua/UJRN/pednauk_2016_8_6. [Ukraine]
6. Kontseptsiia «Novoi ukrainskoi shkoly». (2016). Retrieved from http://surl.li/mikm
7. Korchevskyi D. Filosofski aspekty intehratsii zmistu pidhotovky maibutnikh fakhivtsiv kompiuter-noho profiliu. [Philosophical aspects of integration of the content of training of future computer specialists]. Naukovyi chasopys Natsionalnyi pedahohichnyi uni-versytet imeni M. P. Drahomanova. Seriia 17. Teoriia i praktyka navchannia ta vykhovannia. [Scientific journal National Pedagogical University named after Dra-homanov. Series 17. Theory and practice of teaching and education]. Vyp. 24, zbirnyk naukovykh prats. [Ukraine]
8. Kozlovska I. (2001). Intehratsiia ta nastupnist u rozvytku navchalnoho znannia: metodolohichnyi aspekt [Integration and continuity in the development of educational knowledge: methodological aspect]. Ne-perervna profesiina osvita: teoriia i praktyka [Continuing professional education: theory and practice], zbirnyk naukovykh prats, 2 ch. [Ukraine]
9. Madzihon V. (2010). Pidpryiemets yak vyznachalna osobystist u biznesi v rynkovii ekonomitsi [Entrepreneur as a defining figure in business in a market economy]. Pedahohika i psykholohiia profesiinoi osvity. [Pedagogy and psychology of vocational education]. № 3. Retrieved from http://nbuv.gov.ua/UJRN/Nzped_2014_116_25. [Ukraine]
10. Oberländer Anja. (2017). Entwicklung unternehmerischer Persönlichkeiten bei Existenzgründungen aus der Arbeitslosigkeit. Entrepreneurship Education. Band VI. Retrieved from http://surl.li/mikf Okeke. N. (2011). Enhancing teaching and learning of mathematics in primary schools through pupils involvement. Journal of Issues and Mathematics,Vol. 14.
11. Pozniakov V. Predpryymchyvost. (2012).[Entrepreneurship] Retrieved from https://cyberleninka.ru/article/n/predpriimchivost-1/viewer. [Russian]
12. Protsenko O. (2013). Pidpryiemnyts'ki uminnia yak skladnyk zhyttievoi kompetentnosti uchniv profesiino-tekhnichnykh navchal'nykh zakladiv. [Entrepreneurial Skills as a Component of Vital Competence of Vocational Schools Students]. Pedahohika formuvannia tvorchoi osobystosti u vyshchii i zahalnoosvitnii shkolakh [Pedagogy of Formation of Creative Personality at Higher and Secondary Schools]. Vyp. 30 (83).
13. Pryshchepa S. (2019). Do problemy formuvannia pidpryiemnytskoi kompetentnosti uchniv: suchasni pidkhody. [To the problem of formation of pupils' entrepreneurial competence: modern approaches]. Young Scientist, № 1 (65). Retrieved from http://surl.li/miki
14. Slovnyk ukrainskoi movy: u 20 tomakh. (2010). Retrieved from http://surl.li/mikk
15. Verchenko N. (2011) Osobystisno-diialnisnyi pidkhid yak holovna peredumova suchasnoi osvity. [Personality-activity approach as the main prerequisite of modern education]. Visnyk pisliadyplomnoi osvity. [Bulletin of postgraduate education]. Vyp. 4. Retrieved from http://nbuv.gov.ua/UJRN/Vpo_2011_4_5.
