Knowledge Economy Skills and their Relationship to Mathematical Culture among Secondary School Mathematics Teachers

The aim of the current research is to study the relationship between the skills of knowledge economy and mathematical culture for male and female mathematics teachers for the secondary stage. The knowledge economy consists of (34) items, and a measure of mathematical culture of (23) items. Appropriate statistical analyzes were conducted and the psychometric properties of the observation card and scale were verified, and by adopting the appropriate statistical tools to analyze the results, I came up with the following: 1. Mathematics teachers do not have knowledge economy skills. 2. Mathematics teachers have a mathematical culture. 3. There is a positive correlation between the skills of knowledge economy and mathematical culture among male and female mathematics teachers in the research sample.

Exploration of Comparative Concepts in the Ethnomathematics of The Buton Traditional House

The Buton community has practiced mathematical culture in the form of a Buton traditional house called banua tadha (right house). The purpose of this study was to explore the comparative concepts in the ethnomathematics of the Buton traditional house. This research is qualitative research with an ethnographic approach. The results of this study indicate that every Buton traditional house contains several comparative concepts in the ethnomathematical: (1) the width of the door and the width of the stairs, (2) the walls of the house and the tutumbu, (3) the width of the house and tutumbu, (4) wall and pillar heights, (5) the height of the bhate and the length of the limana bathe, (6) the height of the front wall to the height of the side walls, (7) the width of the stair post with the size of the rungs of the stairs, and (8) wall height and house pole height, and (9) the shape of a right triangle formed by a crutch (konta), a pole (ariy), and a buffer (tadha). These comparisons can be used in learning mathematics to pass on the ethnomathematical local wisdom of the Buton traditional house.

Exploring the Educational Value of Mathematical Beauty and Effective Ways of Discovering Mathematical Beauty

The precision of mathematical reasoning, the abstractness of mathematical language, the profundity of mathematical thought and method, as well as the excessive formalization of mathematics teaching have formed an impassable gap, hindering students in approaching mathematics. This has concealed the beauty of mathematics and the light of mathematical culture. However, if students are able to cross this gap, they would find that mathematics is a vast world full of vitality, imagination, wisdom, poetry, and beauty. The pursuit of mathematical beauty is one of the motivations for scientists to research this field. Experiencing mathematical beauty is of great significance to students’ learning and growth. In teaching, the value of mathematical beauty is explored, such as stimulating emotions, opening up to the truth, and cultivating goodness. Several effective ways are suggested in this article to guide students to discover the mathematical beauty in life while finding it in problem-solving methods and exploring it in knowledge systems.

Origami as a Means of Geometric Modeling: Environmental Approach to Self-Organization in Young Childhood

Origami is a means of geometric modeling and self-organization formation in young children. As a part of preschool education, it serves as propaedeutics of basic geometry. One of the tasks of modern education is to improve the social status of mathematics because of its ability to encourage self-development in children. The research was based on the synergetic paradigm which defines a young child as an open nonlinear system capable of self-development. The article gives a theoretical and conceptual justification of origami as a means of self-organization development through the nonlinear educational environment that introduces preschoolers to mathematical culture. Origami proved to be able to enrich preschool education as this activity concentrates the educational resources of the structure-forming environment.

Two Fish Moving in their Seas: How does the Body Language of Teachers Show itself who Teach Mathematical Equations?

Background: “Culture hides much more than it reveals and, strangely enough, what it hides, it hides more effectively from its own participants” (Hall, 1959, p. 39). This quote corresponds well to a Persian proverb, also a well-known aphorism that has been widely cited in many ethnographic articles: “a fish will be the last to discover water.” Being immersed in water, surrounded by it, makes it invisible and almost impossible to perceive. In other words, we often do not know our interactional behaviour as mathematics teachers when we perform it in our usual and localised professional practice. Objective: To discuss mathematics teacher’s body language when teaching equations and thus perceive this language in terms of possible fruitful educational action when teaching equations in the classroom. Design: Qualitative methodology. Data collection and analysis: Based on theoretical references that deal with body language, corporeality, and perception, we analysed individually and comparatively the classes of two mathematics teachers who taught equations in Birmingham (United Kingdom) and Rolante (Brazil). Thus, particularly attentive to mathematical culture in the classroom and analysing the localised gestures in the teachers’ teaching of equations and the non-verbal behaviour, we can understand mathematics teaching through body movement, which often goes unnoticed. Results: We understand from the results of this research that perceiving the body language of mathematics teachers, which is produced with speech, gives us indications of the materialisation of the meanings attributed to the equation and how this will possibly affect the very constitution of the student’s mathematical knowledge, in terms of possible meanings attributed to each gesture. Conclusions: We consider that knowing the body language can favour the teacher’s teaching, i.e., metaphorically, knowing the sea can favour the fish to swim.

DEVELOPMENT OF THE MATHEMATICAL CULTURE OF FUTURE TEACHERS OF MATHEMATICS IN THE PROCESS OF PROFESSIONAL TRAINING AT THE UNIVERSITY

Подготовка будущего учителя математики представляет собой сложный процесс, поскольку в данной профессии выделяются две важные составляющие: технологическая и методологическая. В настоящей статье будет сделан акцент на таком проявлении методологического компонента профессии, как математическая культура. Сквозь призму современных педагогических концепций и технологий рассмотрен процесс методологической фундаментализации профессиональной подготовки будущего учителя математики и проведен анализ данного процесса. Основные положения аналитического обозрения основывались на состоянии современной образовательной системы, развитии цифровизации в культуре и науке, общей структуре математической культуры и математического развития личности человека. В связи с этим в заключительных положениях были сформулированы выводы относительно перечня компетенций, необходимых современному учителю математики в целях обеспечения его профессиональной эффективности. Обобщенный теоретический опыт может быть положен в основу актуальных обучающих программ и курсов для российских педагогических вузов, ведущих подготовку по специальности «учитель математики». The training of a future Mathematics teacher is a difficult process, since there are two important components in this profession: technological and methodological. This article will focus on such a manifestation of the methodological component of the profession as mathematical culture. Through the prism of modern pedagogical concepts and technologies, the analysis of the process of methodological fundamentalization of the professional training of the future mathematics teacher is carried out. The main provisions of the analytical review were based on the state of the modern educational system, the development of digitalization in culture and science, the general structure of mathematical culture and the mathematical development of a person’s personality. In this connection, in the final provisions, conclusions were formulated regarding the list of competences necessary for a modern Mathematics teacher in order to ensure his professional effectiveness. Generalized theoretical experience can be used as the basis for current training programs and courses for Russian pedagogical universities providing the major of Mathematics Teacher.

The role of mathematics in transdisciplinarity content of modern education

Introduction. In the context of modernisation in modern education, a deeper (by contrast to interdisciplinary) transdisciplinary level of cognition is becoming prevalent. Transdisciplinary level generates a universal methodology capable of addressing the complex multi-factorial interdisciplinary problems of nature and society. The result is transdisciplinary branches of science such as cybernetics, disaster theory, synergetics, artificial intelligence, big data, etc. All these concepts have been developed on the basis of the achievements of mathematics over the past 70-80 years, the era of mathematical sciences. As a consequence, mathematics has become the basis of the language of information technologies and processes, and, thereby, this science has given rise to a global digital transformation of society based on the use of the unique computer capabilities.The aim of the present research was to explore the role of mathematics in the transdisciplinary trend in updating the content of education with a view to bringing education to a higher (by contrast to interdisciplinary) level, based on the inclusion of modern mathematical theories and methods in the content of education and their applications depending on the direction and profile of the student training.Methodology and research methods. In the course of research, the systemic, cultural, and meta-subject approaches were employed to analyse the role of mathematics in education and to solve the transdisciplinary problems of education content modernisation (based on the most striking manifestations of modern mathematical culture). As a result of the synthesis of these approaches, a holistic scientific worldview emerges, which not only goes beyond the traditional disciplines and methods, but also appears above them.Results and scientific novelty. The analysis of transdisciplinary trend in postindustrial education was carried out. Mathematical and pedagogical aspects of the implementation of systemic, cultural and meta-subject approaches were investigated in order to achieve a higher level of educational process. At the same time, the authors justified the use of mathematical modelling, discrete mathematics, computational processes and artificial intelligence in the training, i.e. formation of a new superdisciplinary way of thinking in students, acquisition of a general cultural cognitive strategy to perform professional and transprofessional tasks.Practical importance. The findings of the current publication contribute to the realisation of the transdisciplinary trend in the content of student training, and will be of interest to both educational theorists and teachers, who train students in many fields. Moreover, this work will be useful for all those interested in the future advancement of the system of education.

THE CONCEPT OF "ROOT N-TH DEGREE" IN SOLVING CUBIC EQUATIONS. THE FORMULA OF CARDANO

The main task of teaching mathematics in secondary schools is to ensure that students have a solid and conscious mastery of the system of mathematical knowledge and skills necessary in everyday life and work for each member of modern society, sufficient to study related disciplines and continue their education. Along with solving the main problem, advanced study of mathematics provides for the formation of students ' sustained interest in the subject, the identification and development of their mathematical abilities. In-depth study of the subject should provide preparation for entering the UNIVERSITY and continuing education, as well as for professional activities that require a sufficiently high mathematical culture. The topic "Root of the nth degree" is necessary for the study of many sections of algebra, namely, to find the derivative and primitive. The article deals with the solution of cubic equations using the Cardano formula. The algorithm for applying this feature is described.

THE PECULIARITIES OF VLADIMIR LEVYTSKY’S PEDAGOGICAL AND PROFESSORAL ACTIVITY

The content of V. Levitstky’s pedagogical activity is analyzed in the article, his place and role as a sincere youth advisor and teacher of Lviv educational institutions, professor in the development of Ukrainian pedagogical thought are determined. The process of the formation of the scientist’s pedagogical ideology is also characterized. It was found out that in 1890, as a student of Lviv University, he began his scientific work. The author of the article pointed out that Volodymyr Levitsky, being in love with his favorite activity, was not satisfied only with his personal interest in mathematics, but tried to spread this curiosity among his students. In addition, it is noted that the aspects of higher mathematics, in particular differential equations and the theory of functions of a complex variable were the range of his scientific and mathematical interests. The content of Volodymyr Levitsky’s scientific works and pedagogical ideas in the conditions of problematic use of the Ukrainian language of the first half of the XX century in Ukraine during the Polish rule in Galicia and the domination of the USSR, the provisions of which are used not only by domestic but also foreign scientists. It is generalized that the scientist was the author of the first scientific article on mathematics in Ukrainian, the editor of the first scientific journal of the natural sciences in Ukrainian, the first author of materials on Ukrainian terminology in mathematics, physics and chemistry, author of Ukrainian textbooks of mathematics, physics and physics. taught in the name of Peter Mohyla, the founder, pedagogue and teacher of mathematics in Lviv educational institutions, but also an outstanding scientist-mathematician of Ukraine, in particular the West. The author of the article noted that Volodymyr Levytsky lived a life full of pedagogical activity, during which he worked tirelessly and sincerely in the field of the Ukrainian science and education, as well as the fact that the scientist was the first to raise mathematical culture on Ukrainian soil during his work in Galicia.Key words: inspector of secondary schools, mathematical culture, Scientific Society named after Taras Shevchenko, pedagogical activity, teacher, natural section, terminology commission, professional instructor.

The Core Literacy of Mathematics-The Cultivation of Mathematical Operation Ability

The core literacy of mathematics can be divided into the following aspects: mathematical abstraction, mathematical thinking, mathematical application, mathematical operation, logical reasoning, data analysis, mathematical modeling, intuitive imagination, number-shape connection, rigorous verification, mathematical emotion, reasonable guessing, Mathematical culture, careful thinking, use of mathematical tools, mathematical language or symbolic language. Mathematical ability is the most basic and main ability, and it is the foundation of other mathematical literacy. Cultivation of Mathematical Ability