Problems on the Brocard Circle
We present problems for students about the Brocard circle. The problems are discovered by the computer program “Discoverer”, created by the authors.
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We present problems for students about the Brocard circle. The problems are discovered by the computer program “Discoverer”, created by the authors.
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The research focuses on South-West University students’ response to the project “Student Practices” from 2013 until 2015. The author aims to evaluate the extend to which this additional practical training in a real professional environment gives students the opportunity to develop and improve their competencies and skills, according to the specifics of their academic major, professional training, and free time. The analysis of the results proves that the project is a successful attempt by the Ministry of Education to provide additional practical training for young specialists.
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In the recent decades, intensive studies have been performed on the interactions between polyelectrolytes and the possibilities for polyelectrolyte complex (PEC) formation. The main purpose of these studies is to investigate the properties of PECs and to extend their application in solving different technological and environmental problems. The interest in natural polyelectrolytes - polysaccharides, proteins, amino acids, DNA, etc., has been increased due to their role in living organisms, their bioavailability, biodegradability and uses in pharmacy and medicine. In the present study attractive, electrostatic interactions between oppositely charged polyelectrolytes have been used to prepare a novel complex between a polyampholyte casein and a natural polycation — chitosan. The complex casein/chitosan is formed during the mixing of acid chitosan solutions and basic casein solutions. The complex yield was investigated by viscometric, spectroscopic and gravimetric methods. The optimum stoichiometry of the complexes at different pH has been determined.
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The article is dedicated to tasks designed for the discipline Teaching English as a Foreign Language Practice for the binary specialty Biology and English, Faculty of Biology, Sofia University “St. Kliment Ohridski”. The focus is on optimization of the face-to-face classes by introducing blended learning tasks. An informed choice of relevant technology is proposed for each element of the task. The specifics of tasks for binary specialties is considered by identifying the similarities between the two different areas: teaching a foreign language and teaching science.
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The experimental environment Excel is used in the paper to check ideas, occurring and guesses in problem situations, which appear in solving trigonometric equations.
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The paper presents the experimental mathematics as a problem environment for students’ research activities. Such an area is available to students who have different level of mathematical competence. Theorganization of students’ research activities in experimental mathematicsenvironment is a basis for their preparation for work in the form “Science2.0”. Students will learn the following main characteristics of Science 2.0:working on a project, participation in crowd-sourcing, research network,computer supported research.
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The inclusion of children with special educational needs is a process of humanization of public relations and requires reconsidering traditional educational models. When it is well organized and tailored to individual and environmental factors, it is a way to improve the future and can, therefore, be our dominant paradigm. This report presents the experience of the team of Kindergarten No 37 in Sofia in the development of a model for the inclusion of children with special educational needs in the cultivation of habits for motor activity and culture of eating in early childhood – Parade of Health”.
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Formulas are derived and presented for the distances to the vertices and the midpoints of the sides and diagonals of a quadrilateral from three of its notable points. They are used to prove some inequalities in the quadrilateral, connecting the lengths of its sides and diagonals. An interesting property of the centroid of a quadrilateral inscribed in a circle has been found too.
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Older adults are part of vulnerable target groups due to their relative lack of social power and sociopolitical exclusion. The Active Aging Index place Slovenia at the 23rd place of the 28 EU member states. The prevalence of stereotypes about older adults (ageisms) and bad practices presents an obstacle for active aging, making the development of new socially inclusive practices essential. In this work, the authors present the importance of intergenerational educational programmes for social inclusion and development of active aging in connection with the concepts of sustainable development and community education. In contrast to economic development, sustainable development is not based on material development with exploitation of natural resources and instead focuses on care for all generations and the entire planet. The conceptual framework for this work is formed by the concepts of lifelong learning, social justice, and intergenerational dialog.
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This article explores the application of information and communication technologies in physics and astronomy. Shown is the achievement set goals in terms of expected results at certain cognitive levels. Special emphasis is placed on creating interest in physical and astronomical knowledge, preparing for self-training, forming elements of physical style of thinking and educating students’ environmental consciousness. Shown are results from implementing different methods to achieving the goals set.
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Pupils, thanks to the internet, have unlimited access to practically all humans knowledge. One of the most important tasks of today’s education is to help young people develop skills for orientation in the information flow. The methodical renewal of teaching is one of the greatest challenges towards modern educational system. To keep pace with the dynamics of today's life, learning should go beyond the current models that rely on the emancipation of individual learning disciplines and should highlight their synergistic interaction. The article discusses a lesson model based on cross-curricular links when combining two courses - Bulgarian language and mathematics. It is often assumed that these two objects are mutually exclusive and do not have any interference. We believe that there are no dividing lines in the field of knowledge. We see links in places that other see borders. If one looks in this manner at different sciences, it becomes clear that they complement each other. If used in learning, this can turn the lesson to be interesting and amusing.
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In this paper we consider a really very useful inequality, the so called rearrangement inequality, which has may applications and could be used in proving other inequalities. The paper contains a proof of the rearrangement inequality and several examples of its application
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In the system of medical education physiology is a discipline of key importance based on very dynamic field of scientific knowledge. Permanent emergence and accumulation of new facts and concepts make teaching of physiology challenging task where success and effectiveness are highly dependent on abilities of teaching staff and authors of textbooks constantly to evaluate, re-evaluate and improve teaching approaches, learning objectives and sometimes even to revise whole paradigms in organizing and prioritizing essential parts of the curriculum. Resting membrane potential (RMP) is a concept of critical importance in physiology and particularly in physiology of excitable structures. Equations quantitatively characterizing RMP are widely used in teaching practice as a tool bridging the gap between fundamental biophysical phenomena and complex physiological processes. Use of different equations in introduction of the concept of RMP in modern teaching literature is studied and critically evaluated. Alternative approaches are discussed in search for improvement and optimization of traditional methods of teaching resting membrane potential in courses and textbooks of human physiology. Study is based on the review and content analysis of different editions of more than 25 modern textbooks of human physiology.
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The current article is about the implementation of cloud technologies in secondary education in Bulgaria. An overview of the development and nature of cloud technologies is made. Practical experience is gained from the deployment of cloud technologies in a particular Bulgarian school. The use of cloud technologies facilitating the work of the school administration and increasing pupils’ interest in the learning process, as well as their activity in the school, is shown.
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The introduction of digital technologies into education changes the medium and tools used to achieve the learning objectives. Traditional textbooks have to be adapted to suit to the needs and characteristics of the digital generation learners. Textbooks, combined with innovative technologies, are becoming a modern way for knowledge transfer. They engage learners and bring them new sensations and opportunities to interact with the content. The current paper presents the essence and benefits of augmented textbooks in education. An augmented textbook is presented as an example of effective use of modern technologies, combined with traditional training tools.
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A geometric relation is derived concerning the roots of a special type polynomials of n -th degree and the roots of their derivatives.
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The characteristics and tendencies of education in the future, of the postmodern paradigm in the field of education, should constitute the fundamental characteristics of current educational systems and be manifested in dimensions such as: centring on the learning process, on learning competencies and skills; learning through problem solving and critical thinking; monitoring through high performance and success; planning and management within a partnership between school and community; education centred on students/adults; varied rhythms and styles of learning; personalized, individualized instructive-educational activities; adapting school to the characteristics of the student; the prevalence of interactive experiences that generate in-depth learning: cooperative teaching-learning with lessons based on life experiences. Regarding the relationship between traditional didactics and modern/postmodern didactics within educational practice, aside from adjusting the weight of the elements of the different paradigms according to each individual educational situation, a balance could be found by appropriately combining three major tendencies: the tendency to retain and capitalize on the valuable aspects of traditional didactics; the tendency to enrich traditional didactics with scientific results that would create a foundation for the modernization of education and a qualitatively superior training of teaching staff; the tendency to create a balance between the two aspects of the instructive-educational process: informative and formative.
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The problem concerning unity of scientific knowledge and hence its transformation into educational knowledge is not new to research. In recent years, the idea of implementing this unity has been present in the normative documentation for the management of pre-school and school education. The question remains how the concept of integration is materialized in the aforementioned documentation, and especially how it is technologically enshrined in the practice of training. The article presents a comprehensive model for integration, which is in the intersection of formal and non-formal education and its professional pedagogical decoding in three interconnected sections - normative, contentive and technological. In these three sections, integral constructs are brought out as a new kind of entity aimed at forming students’ cognitive, affective, reflective and social skills through content-based emphasis in environmental education.
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