The sequential nested mixed methods study focused on comparative analysis of middle school mathematics teachers’ content knowledge in two countries. The study consisted of two stages: (1) quantitative study of teacher content knowledge; (2) qualitative study of teacher topic-specific content knowledge. The initial sample for the first stage included lower secondary mathematics teachers from the U.S. (grades 6–9, N=102) and Russia (grades 5–9, N=97). The Teacher Content Knowledge Survey (TCKS) was applied to assess teacher content knowledge based on the cognitive domains of Knowing, Applying, and Reasoning, as well as addressing the lower secondary mathematics topics of Number, Algebra, Geometry, Data and Chance. The second stage – an interpretive cross-case study – aimed at the examination of the U.S. and Russian teachers’ topic-specific knowledge on the division of fractions. For the second stage, N=16 teachers (8 – from the U.S., and 8 – from Russia) were selected for the study using non-probability purposive sampling technique based on teachers’ scores on the TCKS. Teachers were interviewed on the topic of fraction division using questions addressing their content and pedagogical content knowledge. The study revealed that there are explicit similarities and differences in teachers’ content knowledge as well as its cognitive types. The study results may inform the field on priorities placed on lower secondary mathematics teachers’ knowledge in the USA and Russia. It also suggests close comparison and learning about issues related to teacher knowledge in both countries with a potential focus on re-examining practices in teacher preparation and professional development.

The productive status of errors is discussed in Mexico and the US mathematics education reforms. However, teachers’ positionings toward mistakes may or may not converge with this productive status. For that reason, reflecting on teachers’ positioning during the teaching and learning process is crucial (Stooksberry et al., 2009). This study examines teachers’ positional framing during teacher and students’ moment-to-moment interaction in the context of errors occurring in the classroom. Findings reveled two opposite error frames that teachers used to address errors in their classrooms. One of these frames provided student support for using errors as tools for their learning. On the contrary, the other provided an idea of student incapacity to cope with errors.

The article is devoted to one of the urgent problems of modern mathematical education: the formation of educational and research skills of students in the process of solving problems in the subject area “Mathematics”. The levels of formation of educational and research skills of students are described, based on a set of criteria identified by N.A. Menshikova. It is shown that for the formation of educational and research skills of students it is advisable to use blocks of interrelated educational and research tasks that allow students with a low level of formation of educational institutions to participate in solving problems of a higher level of complexity.

The article is devoted to the problem of forming a culture of students’ thinking. It is noted that the formation of a culture of students’ thinking is interconnected with the process of formation and development of metadisciplinary actions, and the level of formation of cognitive skills characterizes the formation of a culture of students’ thinking. The solution is shown on the example of the organization of training of a functional content line integrated with tasks with parameters.

Heuristic techniques permeate the entire process of teaching mathematics and computer science, their application is relevant at any stage of the educational process, when solving any type of tasks. The teacher needs knowledge of heuristics in order to help students discover them in their own activities, understand the essence of methods and learn how to use them.

Along with the general subject, in the content of the logical-conceptual competence, the methodical and mathematical foundations of its formation are also singled out. In the object-mathematical plan, the methodical-mathematical adaptation of the psychological-didactic regularities of the formation of the system of subject-based subject knowledge is presented as a basic method. It is supplemented by specific methodical and mathematical patterns: the formation of abstract mathematical thinking and its components; structural formation of spatial and theoretical-spatial types of thinking; analysis of the system of mathematical knowledge in the content of the educational mathematical theory; integration of mathematical language, mathematical speech and mathematical thinking; conceptual-categorial integration of educational mathematical theories.

The article considers the role functions of a modern teacher in general secondary education institutions, determined by the polystructural nature of pedagogical activity: subject teacher, teacher-educator, teacher-methodologist + teacher-researcher. The tasks and contents of the methodological support of the discipline for the choice of students of a pedagogical university with a degree in “Mathematics and Computer Science”, focused on the formation of their research competencies, are given.

This article presents pedagogical recommendations based on experience of working with talented students.

The article describes the main difficulties that students face in the initial period of study at a higher educational institution as part of the study of mathematical disciplines. Possible ways of overcoming these difficulties for students in the field of training Pedagogical education – future teachers of mathematics – on the example of the discipline «Mathematical Analysis» are given.

The quality of professional training of students is analyzed. The solutions of two typical professional problems with the help of a mathematical model are given.

The relevance of preparing a teacher to ensure the sustainability of the educational process is justified, the content of a special course designed to solve this problem is described and the concept of an innovative center of active methods of pedagogical correction is proposed.

The problem of sorting data is analyzed, the order relation between which is described as the adjacency relation of vertices on an arbitrary graph. Subtasks and issues related to the ‘neighborhood‘ of the problem are highlighted; their solution is the level of ‘immersion‘ in the solution of the general problem. Algorithms for solving individual subtasks for graphs of a special kind are discussed, as well as various approaches to solving the sorting problem in the general case. A sorting task of this type was proposed at the ISI-Junior School Programming Cup in July 2019 (Innopolis).

Information society is characterized by constant updating of ideas, theories, techniques and technologies. Under these conditions, achieving the actual level of application tasks is a problem. The article suggests ways of forming set of application tasks.

The article the role and place of the course «Elementary mathematics» in the subject-methodical preparation of the future teacher of mathematics at the present stage of higher pedagogical education.

The problems of teaching elementary mathematics for foreign citizens at Perm National Research Polytechnic University are considered.

The article briefly describes the changes in the main types of professional activity of future mathematics teachers, describes the experience of organizing research activities of future mathematics teachers at the undergraduate and graduate levels.

Humanitarianization is one of the main attributes of technologies of personality-oriented education. Some ways of implementing of the humanitarian potential of discipline “Differential Equations” are described in the article. The role of the emotional part of the historical component of humanitarian potential of the discipline is substantiated. The way how to make the acquaintance with historical-mathematical facts of emotionally rich and significant for students are considered in detail.

The article analyzes the relationship of the national project «Education» of the state program of the Russian Federation «Development of education» with the training of teachers of mathematics and computer science at the university. The paper identifies the main directions of the national project, which should be the basis for the modernization of educational programs aimed at training specialists in the field of mathematics and computer science, teachers of the subject areas.

The article presents the results of an analysis of the formation in schoolchildren of a valuable attitude to mathematical knowledge, emphasizes that goal values are the dominant component of the mathematical activity of high school students and are determined by the specific motives and interests of schoolchildren, the acceptance of the content of mathematical knowledge as a value is determined by their structuring, re-arrangement, the role of mathematical problems is noted. in mastering schoolchildren by mathematical knowledge.

This article discusses the main characteristics of the universality of statistical criteria.

The article discusses the relevance of quality management of mathematical training of students mastering the program of General and higher education. The characteristic of this process, problems are given, management actions at the level of the organization are designated. The article presents the results of pedagogical research of educational institutions of General and higher education of the Eastern zone of the Orenburg region, obtained in the framework of the research “quality Management in General and vocational education” (state registration number НИОКТР № 01201151519).

The translation of the school system of knowledge into a formal language to create an ontology of school educational mathematics showed that there are gaps indicating significant shortcomings in the design of the contents of the geometry course. A study among students of N.I. Lobachevsky Institute of mathematics and mechanics of KFU to determine the quality of understanding of generic concepts, graphic representations of geometric figures, the results of which showed the relationship between the problems in the presentation of the content of the school course of Plane geometry and the quality of students' knowledge.

This presentation presents pedagogical recommendations based on experience of working with talented students.

The article describes the experience of organizing joint activities of undergraduate and graduate students in analyzing the forming of professional activities during the period of teaching practice.

The article presents a version of the rating system of evaluation of educational achievements of students in the study of “Algebra”. The stages of formation of the final assessment and its correction during the semester are described.

The global problem of the pedagogical science is consists of education continuous in the period of extremely development of the innovative economic branches, where a pupil must become the creative specialist who can develop the social progress. A human who possible to modeling, analyzing and critically drops inside the new area of knowledge always becomes the demanded specialist. This is the main target of the advanced training school.

The article is devoted to the interdisciplinary Olympiads held in Chuvashia, supported by industrial enterprises of electrotechnical and machine-building clusters. Examples of mathematical problems of these Olympiads are given.