The mathematical education of a pripary schoolchild is one of the directions at primary school. It gives an opportunity to a schoolchild to master successfully the program of secondary and high school. The question of education actions formation for junior schoolchildren through geometric training is considered in this article.

The article tells about an efficient using of modern software applicable for visualization of decision of theoretical mechanic’s tasks. It describes the whole process from a formulation of the problem to the final results with graphic and analytic representation as well. The student may choose the language of study, take some theoretical notes from syllabus and use the testing program.

The article describes the content and nature of changes in the value representations of young people in modern Kazakhstan society with its inherent difficulties and contradictions. Changes occurring in our society, and primarily in the economic, socio-political, spiritual spheres, affect the value orientations of young people.

he article presents the results of research on the idea of «conceptosphere» in modern science. The main emphasis is placed on the semantic spheres represented by the meanings of words in the language. The authors conclude how much is the culture of a nation, its folklore, literature, science, fine art, historical experience, and religion is rich, so the concept sphere of the people is richer. In addition, the concept sphere of a person is a field of knowledge made up of concepts as its units. There are reflected the sources of the conceptual unit of ideas from which the world view of the language speaker is formed. The article analyzes the main trends of concepts that form the concept sphere, which enter into correlating relationships, hierarchies with other concepts by their individual characteristics.The specific nature of the system relations of concepts requires research, but the General principle of systematicity undoubtedly applies to the national conceptual sphere, as thinking itself presupposes the categorization of thought objects, and categorization presupposes the ordering of its objects.The article summarizes the conceptual system, which should be considered in terms of mental representations, mental lexicon, and the language of thought that are part of it. The term «cognitive space» also defines an individual cognitive space – a structured set of knowledge and ideas that has any lingual person, every speaker. In their work, the authors highlight the collective cognitive space, represented by a structured set of knowledge and ideas that must be possessed by all individuals belonging to a particul ar society. Attention is paid to the distinction between the concept sphere and the semantic space of the language. According to the authors’opinions, the concept sphere presupposes the existence of a mental sphere. The mental sphere consists of concepts that exist in the form of concepts, diagrams, gestalts, mental pictures, frames, scenarios. The semantic space of a language is that part of the concept sphere that is expressed by means of language signs. The semantic space of language is the subject of co gnitive linguistics research due to the fact that most of the conceptosphere of the human ethnos is represented within the semantic space of language.

The study of the linguistic landscape of cities is currently one of the actively developing areas of modern linguistics. The linguistic landscape is considered in the article as an object of sociolinguistic research; the subject of these studies is the language of the city, its representation in the public communicative environment in the form of signs, inscriptions, advertising billboards and other visual forms of written language demonstration. The main methods of studying the language of the city are observation and analysis; the purpose of the study is to identify the means and ways of personal expression, and as a result, their recording in the linguistic space of the city. Self-expression of a person in the communicative environment of the city happens with the use of more and more non-trivial ways and linguistic and extralinguistic means in order to attract the attention of a certain target audience, a potential consumer of a product or service. The study of the linguistic landscapes of the city pursues the goal of understanding public multilingualism from the standpoint of the choice of a language, languages hierarchy, the phenomenon of language contacts, and the regulation of the written recording of languages. The linguistic landscape is, therefore, a kind of indicator of the language policy of society in relation to the languages of the peoples living in a given territory. The authors conclude that it is the linguistic landscape that is the most expressive and convincing indicator of linguistic diversity in a particular area. It is symbolic and can serve as a certain indicator of the mood of certain groups in society and regions. The degree and density of the presence of the particular language in the linguistic landscape is always an indicator of the significance, strength, and relevance of a language in society.

Based on the psychological aspect of the concept of "qualification", the article analyzes the main directions of the formation of methodological qualifications of future teachers of mathematics and advanced training in pedagogical universities. It is possible to achieve high-quality teaching of geometric subjects in higher educational institutions by using methodological and meaningful methods in organizing the educational process. The creation of a certain structure of the educational process, the definition of teaching methods and means, the careful selection of subject content were determined by the specific principles of pedagogy. Basically, these principles are the real achievements of modern pedagogy and are constantly changing. The existing system of didactic principles can be gradually changed and expanded The purpose is to choose the main didactic principles and to offer a scientific-methodological basis for improving the methodological preparation of future mathematics teachers in the Pedagogical University for solving and teaching geometrical problems. In this regard, interviews, questionnaires, analysis of the curriculum and its content, as well as discussions with experienced teachers and methodologists in teaching geometry were conducted; pedagogical control and diagnostics of the educational process were carried out. In order to test the effectiveness of the methods proposed by us, pedagogical experiments were carried out. The entire system of training future teachers of mathematics faces new challenges related to the implementation of effective didactic principles for teaching geometry in pedagogical universities. First of all, it is the principle of mastering innovative teaching methods of the future teacher of mathematics and the principle of mastering new pedagogical and information technologies of education. The results of the study can be used as a methodological basis for further research on the professional orientation of teaching mathematics in universities.

Main problem: humane pedagogical thinking seeks to embrace the immensity, and this is the strength of educational systems and processes born in its bowels. To actualize the value of self-disclosure of students’ innovative abilities with the accompanying, providing role of a teacher, it is necessary to recognize a one’s intellectual reflective mechanism as the main subject of education. Developed reflexive abilities are a logical condition for a person to independently overcome all sorts of difficulties in life and activity. Purpose: understanding and formalization of the “golden principles” of socio-natural thinking and activity of a human as a biological organism. Methods: the method of ascending from the abstract to the concrete, the method of transforming specific images of objects based on their abstract essence, the speculative language of schematic representation of a thought. Results and their significance: considering a high dynamics of technological changes in the world of activity, we accept the reflective ability for self-education as the main means to independently discover certain professional abilities necessary in life. This means that, first of all, students must learn how to learn, i.e. learn to think independently, critically perceive and transform the received information into knowledge, pose their own questions, offer a range of answers, logically formulate and coordinate different points of view, build knowledge together with others. Innovative methods and models of pedagogical activity encourage students’ innovative abilities which cause innovative and technological development of a country.

In recent years, the Republic of Kazakhstan has maintained an ambiguous criminal situation, and there is an increase in certain types of crimes, against the background of the overall positive dynamics of decline. Special attention of criminologists has recently been attracted to the study of crimes in the family and household sphere, and crimes committed in the sphere of religious and spiritual relations, since both of these types are showing increasing prevalence. Therefore, considering such an important institution as a «voluntary refusal», it would be advisable to consider them from the perspective of the offenses we have named, especially since countering them is one of the main directions of state criminal policy. In general, the study of the institution of voluntary refusal to commit an offense is based not only on coercive measures, but also on incentive measures, which means the opportunity to correct the behavior of the offender until the end of the illegal act. The purpose of this scientific article is to study the features of voluntary refusal to commit a criminal offense in crimes committed in the sphere of religious, spiritual and family-household relations, taking into account practice and making recommendations for improving regulations of a criminal nature. The leading methodological tools of the scientific article are dialectical, phenomenological, synergetic and systematic approaches of scientific cognition. Before proceeding to the analysis of the concept of voluntary refusal, it should be noted that the norms about it are far from perfect. There is no unambiguous understanding of the signs of voluntary refusal among scientists, which complicates law enforcement practice. One of the most important tasks of any scientific research is the development of scientific concepts. The consolidation of such concepts in legislation is an effective way to establish a uniform understanding of the norms, a clear idea of their content and, as a result, an increase in the effectiveness of the impact of criminal law in the process of legal regulation. However, these concepts themselves do not reflect reality like contemplation or representation, they are closer to the essence of the phenomenon. The article concludes that the essential features of the concept itself somewhat narrow the objective reality. But, at the same time, the correct identification of the main features in the concept is an important task of scientific research.