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| 1 | 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 | 1338 | ||||
| 2 | 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 | 1370 | ||||