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| 1 | At present the problem of changing quality of education is very urgent. It’s necessary to work out a new conceptual scheme of measuring the system of students’ intellectual abilities and of the qualities which constitute their competence. The project-research activity which is realized in a process of study, helps, on the one hand, to develop competence, methodic and research culture of students, giving the possibility to show one’s knowledge and to get appraisal of one’s achievements. On the other hand, this project-research activity becomes the means of finding out and monitoring interests and capabilities of each student at math lessons. | 1579 | ||||
| 2 | The potential of computer-based testing for teaching mathematics in high school is discussed. It is shown how a teacher can make tests to help students to understand new material. Practices on problems solving and self-assess of the results of student’s studies are also treated. On the basis of the software system «Iren» the various options for testing and quiz’s preparation are described. Keywords: teaching mathematics in higher school, quizzes, software system “Iren”, testing organization | 1623 | ||||
| 3 | The article is devoted to the project of education in the development of universal educational actions. On the example of studying the theme “Sequence” there are various types of educational texts, which are directed to development of the project activities of the students at the lessons of mathematics. Keywords: method of projects at mathematics lessons, educational texts, regulatory, cognitive and communicative universal educational actions | 1583 | ||||
| 4 | The article demonstrates the experience of work for the student training for the unified state exam on mathematics at the institutions of post-secondary education as one of the directions of realization of the continuous mathematical education in the system «school – pre-university education – university – postgraduate education, self-education». The basic recommendations for the student training for the unified state exam on mathematics in view of the features of the exam in the test form are proposed. Keywords: continuous mathematical education, training for the unified state exam, quality improvement of school education | 1379 | ||||
| 5 | From the standpoint of activity theory we discuss the methodological features of teaching students skills for solving mathematics problems of higher level of complexity. We propose a classification of this type of problems (problems with parameters, problems on divisibility, problems on the decimal representation of numbers, Diophantine equations, problems on finding the largest or smallest natural values satisfying given conditions, problems on the integer part of numbers, etc.) and a step-by-step method for solving them. For each type we provide a set of examples of non-standard problems with full solutions aimed at development of students’ positive motivation, independent thinking, and action skills necessary for their successful mastering of mathematical activity. The developed materials can be used as part of a school course in advanced study of mathematics, as well as to prepare students for the All-Russian Olympiads in mathematics. Keywords: mathematics problems of higher complexity, step-by-step method for solving non-standard problems, problem-centered approach to learning, mathematical activity | 1345 | ||||
| 6 | Formation of universal learning activities aimed at thoughtful reading and writing, critical comprehension of the available information and the creation of educational product among pupils in any subject area, including mathematics classes, is a major concern throughout modern general education. The article considers issues of perception, understanding, interpretation and generation of the learning text as a communicative sign system used in the training process. Authors have formulated theoretical foundations, based on which it is possible to analyze the cognitivesemantic content of educational texts, and the features of text designing in order to achieve understanding and improve the quality of education. Examples of mathematical educational texts are provided as an illustration of these foundations. The developed educational texts (research challenges, dialogues, methodical recommendations, applications, historical overviews, etc.) allow us to create context, suitable for each pupil. Also these texts help to individualize learning, to understand better varying levels of the reflection processes and the formation of personality during training, to carry out the educational process on designing new personal educational products and educational texts in the process of studying mathematics. Educational texts should prepare pupils for independent reading of educational, popular science-oriented and scientific literature; promote the creative acquisition of knowledge and gathering experience in critical, creative thinking and conducting design and research work. Keywords: semantics, educational text, dialogization, competence approach to teaching, understanding and designing of educational texts on mathematics | 1374 | ||||
| 7 | Introduction. The content of school subjects is the most important factor in the intellectual development of students. Accordingly, the question arises about the requirements for a modern textbook in the framework of the psychodidactic approach. The aim of the article is to develop a typology of developing educational texts aimed at enriching various forms of mental experience of students. Material and methods. The study was based on the analysis of the psychological characteristics of the intellectual education of students in the framework of the psychodidactic approach, based on the psychological and pedagogical substantiation of the polyfunctionality of modern educational mathematics materials. Results and discussion. The concept of developing educational text is introduced. The specificity of developing educational texts lies in the fact that they, being a projection of the structure of scientific mathematical knowledge, at the same time, firstly, ensure the formation of the main components of a student’s mental experience (including cognitive, conceptual, metacognitive and intentional experience) and, secondly, create conditions for the manifestation and formation of individual cognitive styles of students. Such an educational text should be built as some multidimensional semantic space (hypertext), its structure, along with its “core” (certain subject information), includes context and subtext. The typology of developing educational texts (the study of school mathematics) developed on the basis of the ontological theory of intelligence is presented. Examples of educational texts of different types in the course of mathematics of the basic school are given. Conclusion. The implementation of a complex of developing educational texts creates conditions for increasing the level of understanding of educational mathematical material and the growth of intellectual resources of students by enriching the main components of their mental (mental) experience – cognitive, conceptual, metacognitive, intentional (emotional-evaluative). Keywords: learning, school mathematics, psychodidactics, developing educational text, mental (cognitive, conceptual, metacognitive, intentional) experience, intellectual development | 1599 | ||||