ОТ СОСТАВИТЕЛЕЙ
Настоящий тематический выпуск журнала «Электронные библиотеки» включает выборочные статьи, подготовленные их авторами на основе материалов, представленных ими на 9-й Международной научно-практической конференции «Математическое образование в школе и вузе: опыт, проблемы, перспективы (MATHEDU’ 2019)». Эта конференция состоялась 23–27 октября 2019 г. в Институте математики и механики (ИММ) им. Н.И. Лобачевского Казанского федерального университета (КФУ) и была посвящена 215-летию основания КФУ. Организаторами конференции были Региональный научно-образовательный математический центр КФУ и ИММ им. Н.И. Лобачевского КФУ.
Конференция собрала около 300 участников из разных городов России, в т. ч. Москвы, Санкт-Петербурга, Абакана, Архангельска, Астрахани, Брянска, Великого Новгорода, Владивостока, Владикавказа, Волгограда, Вологды, Грозного, Екатеринбурга, Йошкар-Олы, Кирова, Коломны, Красногорска, Краснодара, Красноярска, Курска, Липецка, Майкопа, Мурманска, Набережных Челнов, Нижнего Новгорода, Нового Уренгоя, Новосибирска, Ногинска, Омска, Оренбурга, Орла, Орска, Пензы, Перми, Ростова-на-Дону, Рязани, Самары, Саратова, Симферополя, Стерлитамака, Сургута, Сыктывкара, Тамбова, Тольятти, Томска, Ульяновска, Уссурийска, Уфы, Ухты, Хабаровска, Чебоксар, Челябинска, Энгельса, Элисты, Ялты, Ярославля и, конечно же, Казани и городов Республики Татарстан. В ней приняли участие специалисты из США, Мексики, Колумбии, Азербайджана, Белоруси, Казахстана, Узбекистана, Таджикистана, Украины.
Тематический выпуск состоит из трех частей. Тематика первой части связана с современными технологиями обучения математике и информатике в школе, созданием цифровой образовательной среды, опытом организации непрерывного образования учителей математики и информатики. Одна из ведущих тем – проблема математического образования одаренных детей. В полной мере эта тема нашла отражение в материалах, представленных в данном выпуске.
Номер журнала подготовлен за счет средств субсидии, выделенной КФУ для выполнения государственного задания в сфере научной деятельности, проект № 1.13556.2019/13.1.
А.М. Елизаров, Л. Р. ШакироваPublished: 13.11.2019
Full Issue
Articles
Mixed methods study of middle school mathematics teachers’ content knowledge in usa and russia using sequential nested design
Abstract:
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.
Keywords:
cross-national comparison, teacher knowledge, topic-specific content knowledge, lower secondary school mathematics.
From mistakes, we learn: teachers` positional framing toward errors in mathematical classrooms
Abstract:
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.
Keywords:
disposition, positioning, errors.
Educational research problems as a means of forming educational research abilities studying in the process of teaching mathematics
Abstract:
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.
Keywords:
educational research skills, criteria for the formation of educational research skills, educational research task.
The formation of culture of students’ thinking during teaching mathematics
Abstract:
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.
Keywords:
culture of thinking, cognitive skills, formation, activity, mathematics, functional content line, task, parameter, teaching, students, methods, integration, program, advanced qualification.
Mechanisms for using mobile devices in distributed computing
Abstract:
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.
Keywords:
mathematics, computer science, giftedness.
Methodical and mathematical bases of logical-conceptual competence in the activities of modern teacherof mathematics and computer science
Abstract:
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.
Keywords:
subject competence of educational mathematical activity, content of logical-conceptual competence, methodical and mathematical foundations.
Formation of research competencies of the future teacher of mathematics and informatics in a pedagogical university
Abstract:
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.
Keywords:
methodological training, role functions of a teacher, teacher of mathematics and computer science, pedagogical practice, discipline for the choice of students, research competencies of the future teachers of mathematics and computer science.
Experience of improving the quality of teaching mathematics through stem education elements
Abstract:
This article presents pedagogical recommendations based on experience of working with talented students.
Keywords:
professional goals, giftedness.
Some ways to overcome difficulties in studying mathematical disciplines by future teachers
Abstract:
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.
Keywords:
study of mathematical disciplines, difficulties in mastering the mathematical content, training teachers of mathematics.
Mathematical modeling as a means of development of general professional competences of students in the study of mathematics
Abstract:
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.
Keywords:
General professional competence, a method of constructing a mathematical model.
Methodological aspects of training a mathematics teacher to ensure the sustainability of the educational processvladimir grigorievich ermakov – d.sc. in pedagogic sciences ph.d. of physical and mathematical sciences, associate professor, francisk skorina gomel state university, gomel.
Abstract:
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.
Keywords:
pedagogical education, mathematics training, pedagogical correction, sustainability.
Sorting problem on graths in programming contests
Abstract:
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).
Keywords:
mathematical olympiads, programming contests, informatics olympiads, multilevel tasks in mathematics, multilevel tasks in informatics contests, sorting problem on graphs.
On the problem of relevance of application tasks in the information society
Abstract:
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.
Keywords:
application task, information society, competence, probability theory, mathematical statistics.
Elementary mathematics as the central discipline of subject-methodical preparation of future teachers of mathematics
Abstract:
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.
Keywords:
elementary mathematics, subject-methodical preparation, bachelor of teacher education, future teachers of mathematics.
Problems of teaching mathematics at the preparatory department for foreign citizens in perm national research polytechnic university
Abstract:
The problems of teaching elementary mathematics for foreign citizens at Perm National Research Polytechnic University are considered.
Keywords:
elementary mathematics, additional education, foreign citizens.
Scientific research activity of future mathematical teachers in the context of implementation federal state educational standards of higher education 3++
Abstract:
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.
Keywords:
future teacher of mathematics, research activities, pedagogical expertise.
Implementation of the humanitarian potential of the discipline “differential equations”
Abstract:
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.
Keywords:
higher education, humanization, differential equations, emotional component.
About implementation of the national project «Education» at teaching of specialists in the field of mathematics at the university
Abstract:
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.
Keywords:
modernization of the education system, teaching mathematics and informatics, information technologies, interdisciplinary approach.
Formation of the value attitude of students to mathematical nowledge in the learning process
Abstract:
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.
Keywords:
formation of a value relation, mathematical knowledge, value-goals, value-content, value-means, technology values.
Characteristics of the universality of statistical criteria
Abstract:
This article discusses the main characteristics of the universality of statistical criteria.
Keywords:
universality of statistical criteria, Mann-Whitney test, Link-Wallace test.
Management of quality of mathematical training in secondary and higher education
Abstract:
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).
Keywords:
quality, mathematical training, management, general, higher, education.
Ontological approach in teaching geometry
Abstract:
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.
Keywords:
ontological approach, learning math, Plane geometry.
Particular sides with working with talented students in professional training of a teacher
Abstract:
This presentation presents pedagogical recommendations based on experience of working with talented students.
Keywords:
professional goals, giftedness.
Forming of the professionalism of the future mathematic teacher during the practice
Abstract:
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.
Keywords:
professional training of the future teacher of mathematics, teaching practice, professionalism of the teacher of mathematics.
Score-rating system for assessing the results of educational activities of bachelors in the study of the discipline “Algebra”
Abstract:
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.
Keywords:
score-rating system, algebra, mathematical disciplines, evaluation of results.
We are looking for the creative students… where do children grow, learnt for the main competative – possible to think
Abstract:
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.
Keywords:
the competitive specialist preparation, student must have creative, logic and critical thinking.
The mathematical component of the cluster olympiads of the Chuvash Republic
Abstract:
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.
Keywords:
interdisciplinary Olympiad, electrical engineering, mechanical engineering.