Puzzles as a didactic tool for development of mathematical abilities of junior schoolchildren in basic and additional mathematical education

Pedagogical science has always faced the issue of finding effective means for achieving educational results. This problem is especially urgent today, when in the rapidly changing world the tools, which yesterday could be used to support the interest of schoolchildren in study of mathematics and could provide an opportunity for the development of their mathematical abilities, quickly become obsolete. Today it is very important to search for new means that foster the development of students with the help of mathematics and mechanisms for including mathematics in the educational process. Thus, the aim of the article is to analyze puzzles as a didactic tool and study the possibilities of using puzzles in the process of teaching junior schoolchildren mathematics, both in the classroom and extra-curricular activities. The leading method here is the modeling of the methodical training system in general and additional mathematical education of schoolchildren, with the inclusion of a new didactic tool that fosters the students' interest to the subject, develops individual mathematical abilities: logical thinking, abstraction, combining, operating spatial images, critical thinking, mathematical memory, etc. As a result of the research, the authors have determined the place, features and methodological aspects of the inclusion of puzzles in the process of teaching mathematics in general and additional school education. They can be used in the system of classical and creative math lessons and in extra-curricular activities of students: a mathematical club, a system of mathematical competitions, a mathematical camp, etc. The practical use of this model makes it possible to reduce the lack of tools in teaching for the development of students' mathematical abilities, which in its turn, makes it possible to speak of purposefully high results in students' mathematical activities, which is confirmed by the conducted experimental research. © 2018 by the authors

Conception of intuition: From the western philosophy, science, and religion to traditional Vietnamese philosophical thought

© 2020, Slovenska Vzdelavacia Obstaravacia. All rights reserved. Intuition is one of the unique human powers to quickly and directly realize the truth of things without any rational analysis or logical thinking process. However, intuition has not really been properly stressed in Western rationalist philosophy. In this article, based on analyzing some conceptions on intuition in the history of Western philosophy, science and religion, we give some comparative interpretations on intuition from traditional Vietnamese philosophical thoughts, especially Confucianism, Daoism, Buddhism, Zen Buddhism… to show that (1) intuition is a universal term that is valid not only in Western philosophy but also in Eastern philosophy, particularly in Vietnamese philosophical thought; (2) intuition is understood in traditional Vietnamese philosophical thoughts mainly as irrational, mystical intuition, and (3) this view has certain similarities to some irrational conceptions in Western philosophy in the twentieth century and today. Since this topic has been scarcely discussed in the academic literature, especially in terms of East-West comparison, the aim of our study is to offer a comparative analysis of existing views and their historical roots

Key Problems of Complex Topics in Mathematics as the Basis of Teaching Methods in the Conditions of Self-Education

Ensuring a high quality of teaching mathematics to students is inextricably linked with teaching how to solve creative mathematical problems. These problems traditionally include tasks of high educational, developmental and diagnostic value. Teaching how to solve such problems allows training graduates with the highest level of the subject knowledge. The problem under study is relevant due to the need to form students’ ability to solve problems with parameters in order to achieve high results in mathematics, intellectual and personal growth. The problem has a new meaning during temporary distance learning, emphasizing the need to create educational and methodological materials that allow students to organize self-education on complex topics in mathematics. The purpose of this research is to develop and describe a teaching methodology for solving problems with parameters based on the allocation of basic (key) problems. The authors have developed a methodology for constructing a system of tasks based on systematizing the theoretical and task material, highlighting students’ basic knowledge and skills, describing the intra-and inter-subject connections of the topic “Equation of a circle in tasks with parameters”. This methodology includes a typology of problems with parameters containing the equation of a circle, a substantiated description of the system of basic (key) problems, the role and content of the propaedeutic stage of teaching. The materials have passed multi-stage approbation and shown their consistency in achieving high results in mathematics. They can help teachers to prepare lessons and extracurricular activities, authors to provide teaching aids for students and teachers, and serve as the basis for a special course for students of pedagogical universities

Development of a Career Enhancement Training is Inherent Part of an Educational Project

Career enhancement training is common for teachers, yet participating in the project requires special training. Project training courses expose project objectives and allow getting necessary skills, materials and tools to determine the results. Training course have to include a content for which teachers will need to make a report. R. A. Valeeva, Ph.D., Professor, was the manager of a project “Development and testing of new modules and rules for the implementing of the basic bachelor educational program in an "Education and Pedagogy" aggregated group (psycho-pedagogical training direction), which implies academic mobility of students studying education science (non-educational training directions) in the context of networking”. To implement the project, it was decided to establish close partnerships with five higher educational institutions in the country. We have developed training courses to prepare teaching and resource staff of our university, as well as our partners to strong partnership in the project execution