Implementation of the concept of mathematical education in school presentation. Problems of modern mathematical education
"Mathematical Symmetry" - Symmetry in Chemistry. translational symmetry. Symmetry in the arts. Translational. Axial. central symmetry. Radial (radial) symmetry. So symmetry is perhaps the most important thing in the universe. rotational symmetry. Unlike physical symmetry, mathematical symmetry is found in many sciences.
"Mathematical induction" - In the XVIII century, L. Euler found that with n = 5. Composite number. Before us is a sequence of odd numbers of the natural series. 1,3,5,7,9,11,13… Proof algorithm by mathematical induction. The principle of mathematical induction. Every person in the world shook a certain number of hands. Prove that the number of people shaking an odd number of hands is even.
"Mathematical Sciences" - You just need to understand and see. Addition. One of the greatest mathematicians. Creator of classical mechanics. Math examples. Carl Gauss (1777-1855). Five diggers dig a 5 m ditch in 5 hours. I stand on four legs, but I can't walk at all. Established the principle of action of liquids and gases. Isaac Newton.
"Math games" - Basic functions. The game is one of the main types of human activity. Group games. Group. Regatta. Math games are a great way not only to identify, but also to train talented children. The game is research. individual games. Development of skills and abilities necessary for research activities.
"Mathematical Riddles" - Only the shavings turned white. Yes, there are four pieces in the oven, Grandchildren count pies. Answer. Do not put our mosquitoes in a row. How many sisters were there? Yes, another pie the Cat dragged under the bench. Komarich counted forty pairs, And Komaro himself continued counting. My brothers helped me. The grandmother planted in the oven Patties with cabbage oven.
"Mathematical Education" - The material itself makes it possible to teach the child to work intellectually. BP Geydman, "On School Mathematical Education". I will talk about teaching mathematics beyond the minimum later. We need unique specialists who combine pedagogical skills with good mathematical training. B.P. Geidman.
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The concept of the development of mathematical education in the Russian Federation. Structure (forms and content) of mathematical education: 1. Preschool 2 . School 3. Circle 4 . Olympiad 5. University
Preschool mathematics education. Objectives: To get acquainted with the basics of mathematical culture; Instilling interest in further knowledge of the world around. Forms of learning: Simple communication; Individual sessions.
Mathematical education at school. Primary school (grades 1-4): Education is compulsory for all; unified; There is no need for specialized classes for the gifted; Program variations are possible.
Basic school (grades 5-7) Introduction of the primary study of geometry from grade 5; Solving practical problems: on logic, on movement and work, tasks with integers; Creation of a base for further, in-depth study of more complex concepts.
Basic school (grades 8-9) Separation of classes (starting from 8) into mathematical and non-mathematical; The ability to change the type of class in the process of studying;
Senior school (grades 10-11) Additional division of mathematical classes into two streams: Mathematics is the main subject of study. Mathematics is a tool for mastering a future specialty.
Mathematical circles, olympiads, competitions. At schools, universities and educational centers; Remote (correspondence) forms of optional work.
Conclusions. In elementary school, reduce the ideological and abstract-conceptual load, increasing the time for solving textual and practical problems; In elementary and high school, keep tasks for solving equations and inequalities; Shift to a later time (better to remove) material related to probability theory, mathematical statistics, combinatorics, set theory and logic. Pay special attention to the study of geometry, a subject that is unique in its role in mathematical education.
education. Teachers of preschool institutions and scientists are currently faced with a common task - to improve all educational work and improve the preparation of children for schooling.
Teaching preschoolers the basics of mathematics should be given an important place. This is due to a number of reasons: - the beginning of schooling from the age of six, the abundance of information received by the child, increased attention to computerization, the desire to make the learning process more intense, the desire of parents in this regard to teach the child to recognize numbers, count, solve problems as early as possible . The main goal is pursued: to raise children as people who can think, navigate well in everything that surrounds them, correctly assess the various situations that they encounter in life, and make independent decisions. Teaching children mathematics at preschool age contributes to the formation and improvement of intellectual abilities: the logic of thought, reasoning and action, the flexibility of the thought process, ingenuity and ingenuity, the development of creative thinking. The human brain requires constant training, exercises. As a result of exercises, the mind of a person becomes sharper, and he himself becomes more resourceful, quick-witted.
Cognitive development involves the development of children's interests, curiosity and cognitive motivation; the formation of cognitive actions, the formation of consciousness; development of imagination and creative activity; the formation of primary ideas about oneself, other people, objects of the surrounding world, about the properties and relations of objects of the surrounding world (shape, color, size, material, sound, rhythm, tempo, quantity, number, part and whole, space and time, movement and rest , causes and consequences, etc.), about the small homeland and Fatherland, ideas about the socio-cultural values of our people, about domestic traditions and holidays, about the planet Earth as a common home of people, about the features of its nature, the diversity of countries and peoples of the world.
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Mathematics in Russia has always been a priority in the development of science, technology and engineering.
On May 7, 2012, the President of the Russian Federation signed a decree, according to which, by December 2013, the Concepts for the development of mathematical education in the Russian Federation.
And on the basis of analytical data on the state of mathematical education at various levels of education, the Decree of the Government of the Russian Federation of December 24, 2013 approved the Concept for the Development of Mathematical Education in the Russian Federation.
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The concept puts forward many topical problems of mathematical education. Emphasis has been placed on what
- the needs of future specialists in mathematical knowledge are not sufficiently taken into account; the content of mathematical education is formal and divorced from life.
- graduates of educational institutions of higher education with a pedagogical focus have little experience in teaching and applying knowledge.
- low educational motivation of schoolchildren associated with public underestimation of the importance of mathematical education; - outdated content and the lack of curricula that correspond to the actual level of their training.
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Research shows that the main factors that have a negative impact on students' attitudes towards learning mathematics are:
- the need to solve a large number of problems with complex calculations (70%),
- unemotionality of the subject (65%),
- the need for constant reliance on past experience (60%)
- a large number of obscure terms that need to be remembered (65%)
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In this regard, the objectives of the development of mathematical education in the Russian Federation are:
modernization of the content of mathematics education curricula at all levels(with ensuring their continuity) based on the needs of students and the needs of society in general mathematical literacy, in specialists of various profiles and levels of mathematical training, in high achievements in science and practice;
ensuring that there are no gaps in basic knowledge for each student, the formation among the participants of educational relations of the attitude “there are no children incapable of mathematics”, ensuring confidence in an honest and adequate state final certification for the tasks of education, providing teachers with diagnostic tools (including automated ones) and overcoming individual difficulties;
ensuring the availability of publicly available information resources necessary for the implementation of curricula of mathematical education, including in electronic format, tools for the activities of students and teachers, the use of modern technologies in the educational process;
improving the quality of work of mathematics teachers(from pedagogical workers of general educational organizations to scientific and pedagogical workers of educational institutions of higher education), strengthening the mechanisms for their material and social support, providing them with the opportunity to refer to the best examples of Russian and world mathematical education, the achievements of pedagogical science and modern educational technologies, the creation and implementation by them own pedagogical approaches and author's programs;
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- support for leaders in mathematics education(organizations and individual educators and scientists, as well as structures formed around leaders), identifying new active leaders;
- providing students highly motivated and showing outstanding mathematical ability, all conditions for the development and application of these abilities;
- popularization of mathematical knowledge and mathematical education
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In the history of education, the content of the school mathematics course has changed many times. Innovation and tradition are the two elements of the world of education. Does the development of mathematics as a science and the changing requirements of society for the preparedness of graduates, both schools and universities, require an update in approaches? receiving? mathematical education.
8 slide or maybe it’s more literate to say the developers of the concept
The concept proposes to single out different levels of training of students in mathematical education:
- "General" level - level of training necessary for everyday life, which should include the most important elements mathematics course which are of particular value to intelligence development and formation worldview of students;
- The “applied” level is what future engineers, technologists, economists and specialists of other professions who will apply mathematics in their work.
- "Creative level" is the level of training of future scientists and researchers.
The Concept states that "it is necessary to provide each student, regardless of place and living conditions, with the opportunity to achieve any level of mathematical education in accordance with his individual needs and abilities."
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(Therefore, a level system for assessing the mathematical training of graduates has been introduced. The mark is tied to the level that the graduate is going to achieve in accordance with his needs and abilities.) The possibility of achieving the required level of mathematical education should be supported by the individualization of education. learning achievement should not interfere with the possibility of continuing education at a higher lesson.
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The implementation of the Concept of Mathematical Education, its further prospects and problems arising on the way were discussed in September 2015 at the round table of the International Multimedia Press Center "Russia Today". The Concept is entrusted with a responsible mission - to bring Russian mathematical education to a leading position in the world, to once again make mathematics an advanced field of knowledge and activity.
In this regard, substantive, personnel and motivational tasks will be solved over the next five years. Thus, the Ministry of Education and Science of the Russian Federation has prepared changes to the standard of basic general education regarding the requirements for the subject results of mastering mathematics and computer science.
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Aleksey Blaginin, Deputy Director of the Department of State Policy in the Sphere of General Education of the Ministry of Education and Science of the Russian Federation, noted that Russian schools are already working on exemplary basic educational programs, in which the share of practice-oriented tasks, as well as logical and arithmetic tasks related to real life, has been increased.
For the first time, the National Studies of Education in Mathematics and Computer Science were held in the elementary school. In addition, a system of all-Russian test papers is being built in the country: already this academic year, current fourth-graders wrote them in our region.
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According to Ivan Yashchenko, a member of the Council for Science and Education under the President of the Russian Federation, everything that is done within the framework of the concept is aimed not at creating difficulties for teachers, but at the result: to enable the teacher to teach children well, and the latter to study well. Both the new programs and the two-level USE make it possible to get away from imitating the teacher's activities. According to Yashchenko, the 2014 national study of the quality of education showed that half of the lessons, especially in high school, were formal passage of the program: “We tried to teach, and we are still trying in many ways to teach everyone everything - maybe someone This threw out a huge number of children from the educational process, instilling in them a hatred for mathematics, "the expert believes. He is confident that the USE and model programs will help create measures to eliminate the problems of each child at any level of education, without throwing him out of the educational process.
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A serious direction in the implementation of the concept will be to improve the quality of training of mathematics teachers. Every tenth Russian teacher will take refresher courses on updating the content structure. Particular attention will be paid to ensuring the availability of thematic and information resources, methodological support for raising the level of mass mathematical education, as well as the formation of the attitude “There are no children incapable of mathematics” in society.
The implementation of the concept also implies increased support for gifted children. According to the head of the Department of Science and Technology of the Ministry of Education and Science of the Russian Federation Sergey Salikhov, in accordance with the order of the Minister of Education and Science of the Russian Federation Dmitry Livanov, international mathematical centers for gifted children will be created, like the recently opened "Sirius" in Sochi.
The implementation of the Concept of Mathematical Education takes place in all regions of the country and affects all levels of education.
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By order of the Ministry of Education of the Saratov Region dated December 28, 2015 "On the implementation of the Concept for the Development of Mathematical Education in the Russian Federation on the Territory of the Saratov Region", the Saratov Regional Institute for the Development of Education was appointed the regional coordinator for the implementation of the Concept for the Development of Mathematics Education.
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According to the recommendations of the Organizational and Methodological Center of Educational Institutions of the Atkarsky Municipal District on the implementation of the Concept for the Development of Mathematical Education in the Atkarsky District, all educational institutions are developing a plan according to which the work of mathematics teachers is built.
The implementation of this plan has something in common with the federal state educational standard of general education: “the organization of educational activities of students in the classroom and the creation of an appropriate space for the implementation of the acquired knowledge, skills and abilities in practical socially and personally significant activities outside of school hours should ensure the achievement of a complex of personal, meta-subject and subject results .
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I implement work on the programs of the "Entertaining Geometry" circle, the elective course "Secrets of Combinatorics", "Training of Olympiad Winners", I develop a special course program for the 8th grade.
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Participation of children in distance learning on the basis of the Novosibirsk Center for Productive Learning "SCHOOL PLUS", the subject week in mathematics, scientific conferences of various levels, disputes, quizzes (Source of knowledge on the portal proshkolu.ru).
Creation of learning conditions in accordance with SanPiN standards.
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Timely completion of advanced training courses, participation in the work of scientific and methodological conferences, seminars, webinars, videoconferences correspond to the implementation of the concept of mathematical education.
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In extracurricular work, incomparably more than in the classroom, conditions are created for the development of individual inclinations, interests, and inclinations of students. Children are happy to take part in distance competitions of different levels of complexity and status.
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More than 7 thousand students and schoolchildren, among them students of our school, took an active part in the All-Russian action "I love mathematics", which was launched by the Ministry of Education and Science of Russia on November 30, 2015.
From the perspective of the past tense, I can draw positive conclusions about the effectiveness of the implementation of the concept of mathematical education. Gradually, a set of measures to implement the concept will increase the prestige and level of Russian mathematical education.
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The concept of development of mathematical education in the Russian Federation Breitigam E.K. , doctor ped. sciences, professor AltGPA, sept. 2014
Decree of the President of the Russian Federation of May 7, 2012 National pride, an element of the national idea National brand The basis of past and future achievements Government - December 2013 Concept, system of events Roadmap Federal, regional projects
Three projects presented by MSU staff (on the MSU website); project submitted by the team Alexei Lvovich Semenov based on the work of the Working Group (Site http://math.ru/conc/); the project presented by Stanislav Konstantinovich Smirnov, Russian mathematician, winner of the Fields Prize (2010), is a member of the Public Council under the Ministry of Education and Science.
General characteristics They are consistent with the State Program of the Russian Federation "Development of Education" for 2013-2020, adopted in October 2012 and the law of the Russian Federation "On Education", adopted in December 2012. 2. All concepts do not imply a radical breakdown of the system, and are aimed at maintaining continuity with the current system, its improvement in terms of modernization, access to advanced international positions; development of continuous mathematical education and the development of objective criteria for assessing the quality of mathematical training of schoolchildren, students and teachers of mathematics.
The main developers The concept of the working group led by Alexei Lvovich Semyonov (born October 13, 1950, Moscow - Russian mathematician, methodologist and teacher of mathematics. Academician of the Russian Academy of Sciences (2011), full member of the Russian Academy of Education, Doctor of Physical and Mathematical Sciences; since 1993 - Rector of the Moscow Institute open education, since 2013 - rector of the Moscow State Pedagogical University) - coordinator of the working group. The group was created under the Ministry of Education and Science of the Russian Federation, 16 people, participates and supervises A.A. Fursenko.
From the report of A.L. Semyonov November 28, 2013. Why math? Mathematical activities are the most important in the 21st century: Fundamental mathematics IT (programming,…) Applications of mathematics Key role in most industries Importance of mathematical literacy and logic of reasoning for everyone Effective investment in infrastructure National tradition and existing level
The main sections of the Concept I. The value of mathematics in the modern world and in Russia II. Problems of the development of mathematical education - motivation - content (selection of content is outdated) - frames III. Goals and objectives of the Concept IV . The main directions for the implementation of the Concept of A.L. Semenov said that the unifying concept of the Concept is "mathematical activity".
Tasks for the development of mathematical education in the Russian Federation Modernization of the content of curricula for mathematical education at all levels (with ensuring their continuity) based on the needs of students and the needs of society in general mathematical literacy, in specialists of various profiles and levels of mathematical training, in high achievements of science and practice; ensuring that there are no gaps in basic knowledge for each student, forming among the participants of educational relations the attitude “there are no children incapable of mathematics”, ensuring confidence in an honest and adequate state final certification for the tasks of education, providing teachers with diagnostic tools (including automated ones) and overcoming individual difficulties ;
Tasks for the development of mathematical education in the Russian Federation (continued) ensuring the availability of publicly available information resources necessary for the implementation of curricula for mathematical education, including in electronic format, tools for the activities of students and teachers, the use of modern technologies in the educational process; improving the quality of work of mathematics teachers (from pedagogical workers of general educational institutions to scientific and pedagogical workers of educational institutions of higher education), strengthening the mechanisms for their material and social support, providing them with the opportunity to refer to the best examples of Russian and world mathematical education, the achievements of pedagogical science and modern educational technologies , creation and implementation of their own pedagogical approaches and copyright programs;
Tasks for the development of mathematics education in the Russian Federation (continued) support for leaders in mathematics education (organizations and individual teachers and scientists, as well as structures formed around leaders), identifying new active leaders; providing students with high motivation and showing outstanding mathematical abilities with all the conditions for the development and application of these abilities; popularization of mathematical knowledge and mathematical education.
Levels of education – Pre-school and primary general education Pre-school Creation of environments and situations Not “ready for school”, but recording the level achieved, diagnosing difficulties No children incapable of mathematics
Levels of education - Preschool and primary general education Primary education Expansion: Logic Algorithms of the Game Basic objects Visualization Design (projects are managed by tutors, not teachers - Sedova E.A.) GEF
Levels of education - Preschool and primary general education Primary education: From the requirements for subject results in mathematics, mastering the basics of logical and algorithmic thinking, spatial imagination and mathematical speech, measurement, recalculation, estimation and evaluation, visual representation of data and processes, recording and execution of algorithms Individualization Automated diagnostics (Example - Matreshka)
Levels of Education - Basic General and Secondary General Education "In basic general and secondary general education, it is necessary to provide for the preparation of students in accordance with their requests for the level of training in the field of mathematical education." Basic general Work with the lagging behind (tutors) Identification and support of highly motivated Continuation of the content of the elementary school Final certification
Levels of education - Basic general and secondary general education Secondary general education Three levels Literacy (in grades 10-11 they complete the basic school program)
Levels of education - Vocational education (from the report) Pedagogical Mathematics Technical, economic, etc. Pedagogical education The best teachers go to school The activity basis of the educational process Solving problems of elementary mathematics Work at school (+ junior students) as the starting point of psychological and pedagogical training What about the rest? Pedagogical education is universal and not all graduates of pedagogical universities have to go to school!
Continuation of education (from the report) Creation of scientific and educational centers; Internships for teachers A positive requirement is that working teachers are admitted to the Master's and PhD Programs in Mathematics Education first of all. Such a requirement existed in the 70-80s of the last century. The system of additional professional education for working teachers requires retraining of their own teachers, primarily in the field of ICT, distance learning technologies. It is necessary to ensure that the teacher can choose additional professional education programs among a wide range, including territorial ones, with the removal of budget barriers. Especially the problem of postgraduate professional training becomes relevant in connection with the transition to a two-level system of higher education, in which graduates of a pedagogical bachelor's degree in the direction, for example, "Mathematics and Informatics", will come to work at the school.
The concept of Moscow State University Proposed: “Revise the Federal State Educational Standards of higher education for mathematical areas and specialties: establish the necessary minimum knowledge, skills and abilities separately for each mathematical discipline; establish the required minimum of classroom lessons in the disciplines of the professional cycle with full-time education in the amount of at least 50 percent of the total number of hours. This point is included in the main version. Consider it necessary: “To develop and approve federal state requirements for additional professional education for the programs “Teacher of Mathematics”, “Teacher of Mathematics”
The concept of Moscow State University To revise the standards of the teaching load of teachers and teachers of mathematics in the direction of reduction, to include hours for checking homework in the workload. Revise the standards for the number of positions for teachers in mathematics departments in relation to the number of students. The number of stakes should not depend on the number of "remaining" students. -This proposal is also important in terms of improving the quality of training of future teachers of mathematics and will somehow solve the problem of assessing universities by the Ministry to preserve the contingent of students. Now, due to the fact that in the natural science areas of training students it is not possible to avoid dropouts of students, universities are on the path of reducing the number of students in the mathematical, physical and information direction. As a result, in the regions there is an acute problem of a shortage of mathematics teachers in schools, and a teacher training university is reducing enrollment in the Faculty of Physics and Mathematics Education.
Moscow State University project To create free and accessible to all centers of distance mathematical education at large universities for secondary school programs, programs of various natural sciences and engineering and technical areas of education, provide for federal funding for these centers. Semester training for university teachers To create conditions for the broad inclusion of universities in school education: organization of joint projects; participation in the assessment of schoolchildren's knowledge (exams, USE); involvement in teaching in specialized classes and schools.
From the project of Smirnov S.K. 1. Significant factors in effective mathematical education are the quality training of teachers and teachers of mathematics for all levels, as well as the prestige and social security of the teaching profession. 2. International integration 3 · Creation of state certification of levels of school mathematical training. Achievement of the basic level is controlled mainly at the end of the basic school. Achievement of advanced and high levels - upon completion of complete secondary school. 4. Increasing the prestige of the profession of a teacher of mathematics 5. Mathematical education of the population and indicators of the effectiveness of mathematics. education and educational achievements of different groups of students and the population
Elena Alexandrovna Sedova - Head. Department of Natural Science and Mathematics Education of the Federal State Scientific Institution ISMO RAO The formation of the fundamental core of mathematical education has not been completed and the desire for the fundamentalization of mathematical education; Return to the humanistic paradigm: individual educational trajectory and activity orientation (activity in the zone of proximal development); The problem of the formation of a new methodological system of teaching mathematics as one of the components of the new methodological system of education.
The Government of the Russian Federation approved the Concept for the Development of Mathematical Education in the Russian Federation by a special order dated December 24, 2013 No. 2506-r
The action plan consists of sections General system activities General education Vocational education, including additional education, training of scientific and pedagogical workers of educational institutions of higher education and scientific workers of scientific organizations, mathematical science Mathematical education and popularization of mathematics, additional education Monitoring and control of the implementation of the Concept
System-wide activities Development of methodological recommendations for the preparation of curricula and programs, new teaching materials, holding olympiads and competitive events for scientists, teachers and teachers of mathematics, support for talented mathematicians through grants, support for non-standard organizations that have received results; support for professional associations, holding all-Russian events.
General education Improvement of the state certification system, KIMs, open bank of video lectures, development of ICT, creation of a nationwide Internet school (at least three) for students in grades 5-11 in mathematics Development of guidelines for working with lagging behind Supporting the participation of schoolchildren and students in international assessment systems quality of education
Professional education, including additional education, training of scientific and pedagogical workers of educational institutions of higher education and scientists of scientific organizations, mathematical science Development of the DL system Support for programs for the development of mathematical faculties of universities Attraction of foreign teachers and researchers. Development of academic mobility of teachers and students Creation of at least 6 world-class scientific and educational centers in the field of mathematics Access to international information and educational resources Development of models of additional mathematical education, advanced training
Mathematical education and popularization of mathematics, additional education Support for interactive museums of Russian mathematicians Support for mathematical Internet portals, television programs aimed at popularizing mathematics Organization of the development of mathematical educational games and stimulating games on a competitive basis Organization of the development of a calendar of significant dates in the field of mathematics