Mathematics education. Continuing mathematical education and its components Center for Continuing Mathematical Training



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Moscow Center for Continuing Mathematical Education (MCNMO) is a non-state, non-profit educational institution that aims to preserve the traditions of mathematical education. Within the framework of the center, the Independent Moscow University operates, a publishing house operates, thematic portals math.ru and problems.ru are supported, mathematical Olympiads and clubs for schoolchildren are organized, including the organizer of the Moscow Mathematical Olympiad and the Summer Multidisciplinary School. Maintains a rating of Russian schools based on the results of unified state exams.

As part of its publishing activities, books are published for various levels of readers: from mathematical literature for schoolchildren to monographs on modern mathematics. The annual scientific journal “Mathematical Education” is published with applications for schoolchildren.

There is a “Mathematical Book” store in the center building. In the early 2010s, the center was involved in litigation with the former publisher of the magazine, the publishing house "Kvantum", regarding the rights to distribute the magazine "Kvant" and over the publication of the magazine "Kvant+".

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An excerpt characterizing the Moscow Center for Continuing Mathematical Education

Before we had time to be surprised by this, we immediately saw a very tall, gray-haired old man, proudly sitting on a strange, very beautiful chair, as if thereby emphasizing his importance to those who did not understand. He watched our approach completely calmly, not at all surprised and not yet expressing any emotions other than a warm, friendly smile.
The white, silver-shimmering, flowing clothes of the old man merged with the same, completely white, long hair, making him look like a good spirit. And only the eyes, as mysterious as those of our beautiful stranger, shocked us with boundless patience, wisdom and depth, making us shudder from the infinity visible in them...
- Hello, guests! – the old man greeted affectionately. – What brought you to us?
- Hello to you, grandpa! – Stella greeted joyfully.
And then, for the first time in the entire time of our already quite long acquaintance, I was surprised to hear that she had finally addressed someone as “you”...
Stella had a very funny way of addressing everyone as “you”, as if emphasizing that all the people she met, whether an adult or a completely toddler, were her good old friends, and that for each of them she had her heart wide open. the soul is open... Which, of course, instantly and completely endeared even the most withdrawn and loneliest people to it, and only very callous souls did not find a way to it.
– Why is it so “cold” here? – immediately, out of habit, questions started pouring in. – I mean, why do you have such an “icy” color everywhere?
The girl looked at Stella in surprise.
“I never thought about it...” she said thoughtfully. – Probably because we had enough warmth for the rest of our lives? We were burned on Earth, you see...
- How did they burn it?! – Stella stared at her, dumbfounded. - Really burned?.. - Well, yes. It’s just that I was a Witch there - I knew a lot... Like my whole family. Grandfather is a Sage, and mother, she was the strongest Sage at that time. This means that I saw what others could not see. She saw the future the same way we see the present. And the past too... And in general, she could and knew a lot - no one knew so much. But ordinary people apparently hated this - they didn’t like too many “knowledgeable” people... Although, when they needed help, it was us they turned to. And we helped... And then those whom we helped betrayed us...
The witch girl looked somewhere into the distance with darkened eyes, for a moment not seeing or hearing anything around, having gone into some distant world known to her alone. Then, shuddering, she shrugged her fragile shoulders, as if remembering something very terrible, and quietly continued:
“So many centuries have passed, and I still feel like the flames are devouring me... That’s probably why it’s “cold” here, as you say, dear,” the girl finished, turning to Stella.
“But you can’t possibly be a Witch!” Stella said confidently. – Witches can be old and scary and very bad. This is what it says in our fairy tales, what my grandmother read to me. And you are good! And so beautiful!..
“Well, fairy tales are different from fairy tales...” the witch girl smiled sadly. – After all, it’s people who create them... And the fact that they show us old and scary is probably more convenient for someone... It’s easier to explain the inexplicable, and it’s easier to cause hostility... You, too, will have more sympathy if they burn the young and beautiful rather than the old and scary, right?

They study almost twice as much as in a regular school. In addition to the required hours, there are scientific seminars, special courses, and homework for the entire evening. Mathematical analysis begins to be studied in the 8th grade. For 180 students there are fifty teachers, and everyone considers their subject to be the main one. Edutainme figured out how the St. Petersburg school where young scientists are trained works.

“An athlete has 3-4 hours of daily training, a musician – 5-6 hours. To become a real professional, you need to work hard in childhood. The main thing is that this work does not turn into a routine,” says school director Ilya Aleksandrovich Chistyakov. The Laboratory of Continuing Mathematical Education is a “school within a school”, small sites in public schools for teaching children from grades 8-11 who are ready to master two programs at once: general and additional education. Every teenager has a goal: to prepare a scientific research in the field of mathematics, programming or physics, to perform it at all-Russian competitions, and then to go to international scientific competitions. It is impossible to do without bright teachers: the Laboratory invites lecturers, graduates teach special courses, and winners of scientific shows and competitions come every day.

School for Scientists: Principles and Practices

The teaching methods and programs, the educational concept, the model of the educational process - everything is different from the usual preparation for the Olympiads. Here are some of the school's principles:

No typical tasks, no algorithmic activities.
The development of thinking is associated with the formation of the ability to translate one sign system into another, most convenient for assimilation by a particular person.
A child of 14 years old is already capable of perceiving the most complex abstract concepts.
Develops oral speech, not problem solving itself.
Sports competition kills the creative process; an atmosphere of cooperation is necessary.

The embodiment of these principles triggers such powerful processes of intellectual development that it is not the student who owns the computer, but the student who owns the computer.

The office with ten green boards looks like a theater stage. High speed of presentation of material, writing in notebooks followed by rewriting draft notes and explaining the material, using incredible techniques that work to understand complex terms... Here they teach mathematics based on the physiology of a teenager: the speed of the teacher’s writing on the board corresponds to the speed of the thinking process, and speech works at different systems of perception. More than a third of the school’s graduates become graduate students, and about a quarter become candidates of physical and mathematical sciences.

“It is unknown how the child’s fate will turn out, so he should receive the widest possible education” - this is another principle of the Laboratory. Dreams of a multidisciplinary lyceum have so far been realized on two small sites - mathematical and biological. Moreover, no matter what specialization a student receives, he has 6 hours of English and 8 hours of literature. By the way, every year mathematics students pass the Unified State Exam in English better than students from specialized gymnasiums.

The school model is, at its core, network-based. The programs of general, higher and additional education, study and project activities, the rules of the public school and the freedom of the private lyceum are interconnected. How it works? Every year, about a hundred children decide to study according to the “network curriculum”: for this they need to pass three tests - a written exam in mathematics, an oral physics and mathematics competition and a humanitarian marathon (history and literature). The competition is very small - approximately 2 people per place. Schoolchildren in grades 8-11 simultaneously become students of a public school and a non-profit center for additional education. Subjects that are not sufficiently represented in the standard program are introduced into the curriculum of additional education. At the end of each semester, students take exams based on the integrated course they have taken and have the opportunity to work with a supervisor. He talks about possible problems of future research and poses a scientific problem for the student to solve independently.

What do they teach in the Laboratory?

About a third of the Laboratory’s teachers once studied there. Thus, biology teacher Ilya Smolensky graduated from a mathematics class in 2007, then studied at the Faculty of Biology and Soil Sciences of St. Petersburg State University, and is now mastering a new specialty - creating computer programs that allow building models of biomolecules. Schoolchildren can get acquainted with such models in a special course, where they are taught modern modeling technologies, and at the same time, organic chemistry.

Biology lessons also receive serious technological support. Galina Mikhailovna Kultiasova, a famous St. Petersburg biologist, conducts classes only on the basis of the material that schoolchildren independently find on the Internet. Any findings are discussed, researched, and at the end of the lesson they are posted on a separate website.

IT teachers are required to teach biologists courses on statistics, statistical research methods, and teach how to create databases for future scientific projects. This leads to serious research that has been awarded at international competitions: for example, monitoring the condition of rivers or analyzing the restoration of vegetation cover after fires.

In addition, schoolchildren independently develop programming languages and look for new approaches to information systems. For example, Gadzhi Osmanov proposed a more efficient way of working with memory: the project won the Intel-ISEF competition, and now a Minor Planet of the Solar System is named after the developer. Gleb Novikov and Alexander Goncharov came up with a distributed computing system SocialGrid, which allows people to use their computers with the consent - the development was noted as the best in the Yandex competition.

The main thing they teach in the Laboratory is not to give up and go towards your goal, no matter how large-scale it may seem. This year, seven students were included in the Russian team to participate in Intel-ISEF, the largest school scientific competition. It is interesting that the winners of the qualifying round were mainly team projects: the leaders of LNMO gather into one team children from different classes, united by an interest in a certain scientific field. For about six months or a year they work together at scientific seminars, and then receive tasks based on their interests and talents: someone does calculations, someone does analytics, someone translates the necessary articles, someone draws up abstracts.

Elena Abasheva, Sasha Milyakina

Moscow Center for Continuing Mathematical Education (MCCME)– a non-profit educational organization whose goal is to preserve and develop the traditions of mathematics education in Moscow, support various forms of extracurricular work with schoolchildren (clubs, olympiads, tournaments, etc.), methodological assistance to the heads of clubs and teachers of classes with in-depth study of mathematics , support for programs in the field of teaching mathematics in higher education and graduate school, scientific work.

Source: http://www.mccme.ru

Founders of ICSME

Prefecture of the Central Administrative District of Moscow
Moscow Department of Education
Department of Mathematics RAS
Steklov Mathematical Institute RAS
named after M.V. Lomonosov

Web projects of the Moscow Center for Continuing Mathematical Education

Magazine "Kvant".
Math.Ru - this site is for schoolchildren, students, teachers and for everyone who is interested in mathematics.
Problems.ru is a website with problems in mathematics.
Geometry problems

Structure of the Moscow Center for Continuing Mathematical Education

Math clubs
MCCM circles
Club "Olympiads and Mathematics"
Circles of the Small Faculty of Mechanics and Mathematics
About visiting schools

Math schools and classes

Olympiads for schoolchildren

Moscow Mathematical Olympiad
Correspondence mathematics competition
Tournament of Cities
Oral mathematics olympiads
Programming Olympiads
Mathematical holiday
Mathematical regattas
Lomonosov Tournament
Math fights
Olympiad in Geometry named after. I.F. Sharygina

Independent Moscow University

Schedule for the current semester
NMU Library
Course materials
Seminar "Globe"
Program "Math in Moscow"
Scientific competitions

Russian-French laboratory

Summer School “Modern Mathematics”

For schools and teachers: courses for teachers

Creative competition
About school ratings
Seminar for mathematics teachers

Mathematics education (in documents, articles, publications)

Contacts of the Moscow Center for Continuing Mathematical Education

Website: http://www.mccme.ru/

Address: Moscow, 119002, Bolshoy Vlasyevsky lane, building 11

Phones: +7–(499)–241–0500, 241–1237, 241–4086

FAX: +7–(499)–795–1015

Educational activities

At the ICSME there is a publishing house that organizes the publication of mathematical literature at a wide variety of levels: from school literature to those devoted to modern mathematics. In particular, the annual scientific journal “Mathematical Education” is published with applications for schoolchildren.

Mathematical Book Store

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Books

Diary of a mathematical circle: the first year of classes, Burago A.G.. The book contains all the necessary material for conducting a mathematical circle in grades 5-7 throughout the school year. Topics for discussion in class, sets are provided in detail... Buy for 379 UAH (Ukraine only)
Diary of a mathematical circle. First year of classes, Anna Burago. The book contains all the necessary material for conducting a mathematical circle in grades 5-7 throughout the school year. Topics for class discussion, sets of...

1.2. Subjects of goal setting in general mathematical education, features of coordination of their goals.

In different historical periods, scientists and government leaders held different views on the answer to the first question. This was determined by the nature of the political system.

Totalitarianism of the Soviet state manifested itself in the fact that the social order (the desire of society) was considered decisive(see Methods of teaching mathematics in secondary school: General methodology // Compiled by R.S. Cherkasov, A.A. Stolyar. - M.: Education, 1985 - 9-10).

Democratization of the Russian state during the period of perestroika led to the fact that concepts began to appear in TiMOM, expressing a position on the need to find compromise solution between the needs of society and the student himself (Dorofeev G.V. Mathematics for everyone - M.: Ajax, 1999 - P. 19-20).

In pedagogical science, different positions in answering this question have manifested themselves in the development of various pedagogical models of teaching, differing in the sources of goal setting and their hierarchy.

Sources of goal setting	Learning Models
Put the child in the initiative	“Free model” – children are encouraged to improvise in determining learning goals, choosing content and methods of teaching (R. Steiner, F. G. Coombe, V. S. Bibler, R. Barth, etc.)
1. Child’s initiative 2. Teacher’s desire 3. Social order	“Personal model” - the leading role in determining the goal belongs to the teacher and student as subjects of pedagogical communication, and social attitudes manifest themselves through their consciousness (V.V. Serikov and others)
Social order	“Formative model” - the formation in the learning process of a personality with predetermined socially significant qualities (V.P. Bespalko, S.I. Shapiro, etc.)

Many real-life contradictions between teaching practice and learning theory are related to this problem.

Exercise 1. Select from the proposed methods of resolving the contradiction between the goals of the student and the teacher in the best way, from your point of view, in the following professional situation:

“The teacher, considering it necessary to develop in students the need to turn to theory when solving algebraic problems, introduced additional requirements for the design of solutions to independent work tasks - to describe in detail each step in the solution with its justification and began to reduce the grade for failure to fulfill these requirements even if they were correct. solutions. These actions of the teacher lead to a conflict situation with the student, who correctly completed all the tasks of independent work, but received a grade lower than expected.”

To get out of a conflict situation, the teacher must:

A). Explain to the student the significance of your requirements and leave the grade unchanged.

B). Provide the student with the opportunity to modify the presented solution in accordance with the new requirements and revise the assessment taking into account the results of this modification.

IN). Temporarily remove your requirements, reconsider the assessment and conduct a series of training sessions aimed at creating the need for justification in a different way.

G). Your own option.

There is an official position, which is recorded in a number of state regulations on education:

1). "Law of the Russian Federation on Education"- a social order is presented and the rights of the student in determining the goals of their education and the responsibilities of educational institutions to the state and students in the implementation of these goals are recorded (see Article 14).

2) "GOS in Mathematics"- the goals of general mathematical education at different levels of education are described, taking into account the needs of the student (see Methodological letter on teaching mathematics // authors - compilers: V.M. Ishchenko, P.F. Sevryukov, T.I. Chernousenko table 1)