Subject competences of General mathematical education in the category of subject development

2019 ◽  
Author(s):  
Vasiliy Gorbachev
Keyword(s):  
General Education ◽  
Mathematical Thinking ◽  
Classification Criteria ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Mathematical Activity ◽  
Educational Activities ◽  
Teaching Activities ◽  
University Teachers ◽  
The Subject

The monograph investigates the methodology of formation in mathematical activity of the teaching of subject and General subject competences: principles of allocation, method of classification, criteria of formation. The subject realization of specific competencies is substantiated and detailed by adequate types of teaching activities, which significantly deepen the understanding of classical methods of teaching mathematics. In the content of General subject internal-procedural and theoretical-developing competencies, special attention is paid to the category of development of the subject of teaching. Within the framework of substantiation of internal procedural competence in the spectrum of educational mathematical theories, the problem of system formation of abstract mathematical thinking in the objective sequence of its levels is investigated. For University teachers, researchers in the areas of content of General education, competence approach in educational activities, methods of teaching mathematics, as well as teachers of mathematics and students of bachelor's and master's pedagogical education.

scholarly journals Impulsing the Development of Students' Competency Related to Mathematical Thinking and Reasoning through Teaching Straight-Line Equations

2021 ◽  
Vol 20 (6) ◽  
pp. 38-65
Author(s):  
Bui Phuong Uyen ◽  
Lu Kim Ngan ◽  
Nguyen Phuong Thao ◽  
Duong Huu Tong
Keyword(s):  
General Education ◽  
Mathematical Thinking ◽  
Visual Images ◽  
Control Group ◽  
Study Group ◽  
Positive Thinking ◽  
Teaching Activities ◽  
Straight Line ◽  
Experimental Group ◽  
Development Of Students

The research was carried out to develop students' ability to think and reason mathematically by teaching straight-line equations in a plane. Accordingly, teaching activities were designed according to five learning stages, which were integrated with mathematical thinking levels according to Van Hiele's model. Simultaneously, the learners' mathematical thinking and reasoning competencies were assessed according to the competency requirements specified in the Mathematics General Education Program and the levels of Van Hiele's model, the above three aspects of knowledge, skills and attitudes. The experiment involved 84 students in class 10, 44 of whom were in the experimental group, and 40 were in the control group. The research results showed that students in the experimental group achieved higher mathematical thinking and reasoning skills. Specifically, the two groups had equivalent results for the level of visualization and analysis. However, at the informal deduction and formal deduction and rigor levels, the ranking results of the two groups had a clear difference. The study group observations and students' opinion surveys also revealed that learning stages were designed according to Van Hiele's model and thought-provoking measures and visual images and language contributed to students' interest in learning and positive thinking.

scholarly journals A Hipótese dos Experimentos Mentais na Construção de Conceitos em Matemática

2018 ◽  
Vol 11 (2) ◽  
pp. 104
Author(s):  
Willian José Cruz
Keyword(s):  
Mathematical Thinking ◽  
Thought Experiments ◽  
Sao Paulo ◽  
Theoretical Research ◽  
Mathematical Education ◽  
São Paulo ◽  
Mathematical Proofs ◽  
Research Activities ◽  
The Subject ◽  
Phd Program

Este artigo tem a intenção de apresentar a hipótese dos experimentos mentais e suas caracterizações, com a pretensão de justificar ainda mais o interesse em atividades de investigação matemática, por meio dos experimentos mentais, e das bases semióticas da matemática. Parte desse trabalho foi resultado de uma pesquisa teórica desenvolvida no âmbito do programa de doutorado em Educação Matemática, pela Universidade Anhanguera de São Paulo, e teve como objetivo construir e analisar as características dos experimentos mentais na matemática e suas consequências no âmbito da Educação Matemática. Buscou-se também uma analogia entre os experimentos mentais e as provas matemáticas formais. Experimentos mentais são formas que o sujeito tem de colocar seus próprios pensamentos, dentro de um contexto previamente considerado, como objetos de considerações numa dada atividade e/ou problema, por meio de representações. Esses pensamentos são considerados abdutivos, ou seja, implicam generalizações na Matemática e exige uma teoria de experimentação e de análise. Buscar-se-á nesse texto esclarecer, com a construção de um cálculo de segmentos, quais aspectos se julgam importantes na dinâmica de considerar os experimentos mentais na construção do pensamento matemático, sem desconsiderar a importância de provas matemáticas formais.Palavras-chave: Experimentos Mentais. Semiótica. Intuição. Pensamento Abdutivo.AbstractThis text intends to present the theory of thought experiments and their characterizations, with the aim of further justifying the interest in mathematical research activities, by means of thought experiments, and the semiotic bases of mathematics. Part of this work was the result of a theoretical research developed within the PhD Program in Mathematical Education, by the Anhanguera University of São Paulo, and had the objective of constructing and analyzing the characteristics of thought experiments in mathematics and its consequences in Mathematical Education. An analogy was also sought between mental experiments and formal mathematical proofs. Thought experiments are forms that the subject has to put his own thinking, within a previously considered context, as objects of considerations in a given activity and / or problem, by means of representations. These thinking are considered abductive, that is, they imply generalizations in Mathematics and require a theory of experimentation and analysis. It will be sought in this text to clarify, with the construction of a segment calculus, which aspects are considered important in the dynamics of considering the thought experiments in the construction of mathematical thinking, without disregard the importance of formal mathematical proofs.Keywords: Thought Experiments. Semiotics. Intuition. Thinking Abductive.

Theory as a Platform for the Education of Museum Staff. Development of the Centre for the Study of Museology in the Years 1967–1982

2017 ◽  
Vol 55 (2) ◽  
pp. 3-15
Author(s):  
Otakar Kirsch ◽  
Lucie Jagošová
Keyword(s):  
Staff Development ◽  
Theoretical Concept ◽  
National Museum ◽  
Educational Activities ◽  
Teaching Activities ◽  
The Arts ◽  
Starting Point ◽  
The Subject ◽  
Museum Staff

AbstractThe aim of the presented study is to bring together almost fifteen years of the Centre for the Study of Museology of the Charles University’s Faculty of the Arts at the National Museum in Prague (herein - after referred to as the Centre), one of the most important contemporary methodological and educational centres in the field of museology. The subject of interest will gradually become an analysis of the factors and phenomena that led to its establishment in 1967, including the theoretical concept of the head of the Centre, Jiří Neustupný, which became the starting point for the final form of its curriculum. In addition to outlining the structure for the curriculum for the students of Charles University’s daily study and for the museum staff and introducing personalities who have participated in educational activities, the text also deals with its non-teaching activities (such as research and methodological activities, cooperation within both the domestic and the international museum organisations, while collecting and publishing museological literature). The work was created to commemorate the 50th anniversary of the museological centre which is recognised by international authorities and, as the first one, this work seeks to map its development.

scholarly journals CONCEPTUAL GUIDELINES OF TEACHING MATHEMATICS IN THE 1ST GRADE OF A GENERAL EDUCATION SCHOOL

2021 ◽  
pp. 172-185
Author(s):  
Александр Александрович Никитин ◽  
Ольга Александровна Никитина
Keyword(s):  
General Education ◽  
Federal State ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Multivariate Tests ◽  
Global Trends ◽  
Educational Standard ◽  
Education School ◽  
Teaching Of Mathematics ◽  
State Educational

Преподавание математики, начиная с начальной школы, должно отражать общемировые тенденции развития математической и педагогической научной мысли и представлять собой проекцию математической науки на школьное обучение. Авторы разрабатывают направления обучения математике в 1-м классе на основании Федерального государственного образовательного стандарта с учетом разбиений на элементы знаний. На основании этого описывается структура и формирование содержания разрабатываемого учебника по главам. Теоретическая часть должна позволять учащимся получать ответы на контрольные вопросы, помогать решать одновариантные и многовариантные тесты, задачи и упражнения. Определяемые авторами концептуальные направления обучения математике в 1-м классе обеспечивают формирование фундамента вертикали математического образования в 11-х классах общеобразовательной школы. The teaching of mathematics should reflect the global trends in the development of mathematical and pedagogical scientific thoughts. The authors develop guidelines of studying mathematics in the 1st grade on the basis of the Federal State Educational Standard, taking into account the partitions into knowledge elements. Thus, the structure and the formation of the being developed textbook content by chapters are described. The theoretical part should allow to students to get answers to control questions, univariate and multivariate tests, problems and exercises. Each chapter of the being developed textbook is divided into paragraphs, each paragraph is divided into items. One item of theoretical material contains either one new idea to study, or a set of interrelated concepts that define one new idea to study. According to this it is possible to form the mathematical knowledge trajectories. So, there are broad opportunities to transform knowledge elements into multimedia forms, including presentations, videos, test modules and other newly emerging means of representation and visualization, using the achievements of artificial intelligence. There can be defined such main directions as natural numbers counting, acquaintance with geometric shapes, comparison of objects in the value and quantity, acquaintance with a squared paper and measurement standards, the study of objects position, the sets consideration, introduction to the algorithm concept. The conceptual directions of teaching mathematics in the 1st grade determined by the authors provide the foundation for the vertical of mathematical education in the 1–11th grades of general education schools.

scholarly journals THE CONCEPT OF TEACHING MATHEMATICS IN THE 1ST GRADE OF A GENERAL EDUCATION SCHOOL

2021 ◽  
pp. 88-100
Author(s):  
Aleksandr Aleksandrovich Nikitin ◽  
Olga Aleksandrovna Nikitina
Keyword(s):  
General Education ◽  
Federal State ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Multivariate Tests ◽  
Global Trends ◽  
Educational Standard ◽  
Screening Questions ◽  
Teaching Of Mathematics ◽  
State Educational

The teaching of mathematics should reflect the global trends in the development of mathematical and pedagogical scientific thought. The authors develop guidelines for studying mathematics in the 1st grade based on the Federal State Educational Standard. Thus, the structure and the form of the textbook content are described by chapter. The theoretical part should allow students to complete screening questions, univariate and multivariate tests, problems, and exercises. Each chapter of the developed textbook is divided into paragraphs, and each paragraph is divided into items. One item of theoretical material contains either a new idea to study or a set of interrelated concepts that define a new idea. According to this, it is possible to form mathematical knowledge trajectories. So, there are broad opportunities to transform knowledge elements into multimedia forms, including presentations, videos, test modules, and other newly emerging means of representation and visualization, using the achievements of artificial intelligence. It is possible to define main themes such as natural numbers counting, acquaintance with geometric shapes, comparison of objects in the value and quantity, acquaintance with a squared paper and measurement standards, the study of objects position, the sets consideration, introduction to the algorithm concept can. The authors’ conceptual directions of teaching mathematics in the 1st grade provide the foundation for mathematical education in general education schools for all the years of study.

scholarly journals FORMATION OF VALUE ORIENTATIONS IN THE PROCESS OF TEACHING MATHEMATICS

2020 ◽  
pp. 213-218
Author(s):  
Hamlet MIKAELIAN ◽  
Keyword(s):  
General Education ◽  
Real Life ◽  
Value Orientation ◽  
Value Orientations ◽  
Point Of View ◽  
Formal Structure ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Value System

The general education school is the most important link in the formation of value orientations and the value system of students, which is due to the general content of the educational goals of the school and the student's relationship with teachers, friends and other participants in school life. The school is of decisive importance from the point of view of the community of value orientations and the system of values of students, the inclusion of national and universal values in them, the solution of global problems of moral and aesthetic education, the formation of a single system of cognitive values. And how does mathematics or mathematical education affect a person's value orientation, the direction of his life? Can a person, in certain situations, give preference to similar values over other values? And what is the role of mathematics education in the value system of the student and the person as a whole? The answer depends on what we mean by mathematical education or what goals it pursues. If the process of teaching mathematics is reduced to teaching mathematics, then mathematics with its formal structure of lan- guage and abstract figures is far from life and school interests (with rare exceptions in each class for individual students). Mathematical knowledge also does not lead to wisdom and philosophy of life, it even reduces the stu- dent's vital activity. However, if the process of teaching mathematics is aimed at implementing education through mathematics, then the role of mathematics increases as a means of forming cognitive, aesthetic, moral, mental and other values. This view of mathematics gives the student the opportunity to appreciate the objects studied with the help of mathematics, to look at the world in a different way. He feels more confident in different real life situations. The article deals with the problem of the formation of value orientations of students in the process of teaching mathematics. The dependence of the problem on various types of internal and external factors in the formation of value orientations in this process is considered. The problem of the formation of different levels of value orientations in the process of teaching mathematics is also considered. These are the perception, response, or recognition of value, the acquisition of value orientations, the organization of value orientations and the spread of a value orientation or a set of orientations towards activity.

scholarly journals Inter-subject links within the content-methodical lines of Math school course

2019 ◽  
Vol 8 (3) ◽  
pp. 290-295
Author(s):  
Natalya Vasilievna Kononenko ◽  
Julia Sergeevna Tokareva ◽  
Pavel Aleksandrovich Chukhriy
Keyword(s):  
General Education ◽  
Linear Equations ◽  
Subject Area ◽  
Practical Significance ◽  
Federal State ◽  
Teaching Mathematics ◽  
Practical Application ◽  
The Subject ◽  
Teaching Of Mathematics ◽  
State Educational

This paper considers some ways of inter-subject links realization within the content-methodical lines of Math school course. The course of Math at school is permeated with inter-subject links, which are the foundation of the subject and through which a succession is implemented in teaching of Mathematics. The implementation of inter-subject links in teaching Mathematics requires a special organization of educational material and the process of its study and, therefore, acts as a didactic principle. In this paper, inter-subject links are revealed at two levels: the level of content and the level of methods for solving problems. The inter-subject links at the substantial level are learning numerical sequences and linear equations and inequalities, while at the level of methods - examples of transcendental equations. The implementation of inter-subject links at the content level takes place in conjunction with their implementation at the level of methods and has a wide practical application at Mathematics lessons. The conducted researches have shown that inter-subject links naturally extend on the subject area Mathematics and Computer Science according to the Federal state educational standards of the basic and secondary general education. The practical significance of the study is that its results can be used for teaching Mathematics at school.

Distance Learning in Russian Universities During the Period of Restrictive Measures Related to Preventing the Spread of the New Coronavirus Infection Covid-2019: the View of Lecturers

2021 ◽  
pp. 39-42
Author(s):  
N. Bulaeva ◽  
A. Ganeev
Keyword(s):  
Distance Learning ◽  
General Education ◽  
Educational Programs ◽  
Learning Technologies ◽  
Educational Activities ◽  
University Teachers ◽  
Distance Learning Technologies ◽  
Restrictive Measures ◽  
Independent Assessment

The article presents the results of a survey of university teachers in 2020, commissioned by the Ministry of Science and Higher Education of the Russian Federation, regarding the specifics of work with the use of distance learning technologies as part of a study on an independent assessment of the quality of conditions for the implementation of educational activities by organizations carrying out educational activities in basic general educational programs. educational programs of secondary vocational education, basic vocational training programs, additional general education programs.

scholarly journals An integrated assessment of the quality of teaching Mathematics in school

2021 ◽  
Vol 101 ◽  
pp. 03039
Author(s):  
Liana Sagatelova ◽  
Irina Tarasova ◽  
Nataliya Asanova
Keyword(s):  
General Education ◽  
Education Quality ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Complex Objects ◽  
Quality Of Teaching ◽  
Volgograd Region ◽  
Integral Assessment ◽  
High Level

This article presents a diagnostic criteria-based methodology for a systematic and complex assessment of the quality of teaching Mathematics in school. This methodology may help assess the prospects of applied approaches to teaching Mathematics as well as monitor it and describe in terms of ensuring the high quality of general education in Mathematics. We used Kolmogorov’s “convolution of qualities” as a basis for developing this methodology for the systematic and complex diagnostics of mathematical education in school. This methodology is used to assess the quality and optimization of complex objects in mechanics, chemical industry, economics, and higher education. The suggested integral assessment (systematic and complex diagnostics) was successfully applied to evaluate the quality of teaching Mathematics in schools of the Volgograd region. We defined three levels of mathematical education quality: discrete (minimal and restricted level), fragmentary (average functional level), and integrated and comprehensive (a rather high level).

scholarly journals TECHNOLOGY OF DESIGNING OF MATHEMATICAL EDUCATION ON AN INNOVATIVE BASIS IN A GENERAL EDUCATIONAL ORGANIZATION

PRIMO ASPECTU ◽  
2020 ◽  
pp. 83-92
Author(s):  
Liana SAGATELOVA
Keyword(s):  
General Education ◽  
Educational System ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Design Algorithm ◽  
Design Procedures ◽  
Pedagogical Design ◽  
Education Organization ◽  
The Individual

The actual need of the design of mathematical education in a general education organization that takes into account socio-economic and pedagogical realities, is substantiates in this article. The concepts “design of mathematical education in a general education organization”, “innovative educational system for teaching mathematics”, “design technology” are defined. The design of mathematical education as an innovative educational system for teaching mathematics in a general education organization has a landmark nature. It is reflected in specific design procedures, which determines the manufacturability of pedagogical design. The technology includes instructions for step-by-step actions and methods for their implementation, forms and methods of activity. The technology of designing mathematical education on an innovative basis is presented in the form of an algorithm (consisting of three interrelated steps and 9 procedures) describing a sequence of actions and methods for their implementation. The design algorithm developed in the framework of the research is an organizational form of development and further effective implementation of the design model of mathematical education on an innovative basis. Designing of mathematics education in a general education organization allows you to balance the individual desires and capabilities of all subjects of education, taking into account the socio-economic context, which improves the quality of mathematical education.

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